\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\r\n\r\n \t- Apply summation rules<\/li>\r\n \t
- Interpret definite integrals<\/li>\r\n \t
- Explain the Fundamental Theorem of Calculus<\/li>\r\n \t
- Use the net change theorem<\/li>\r\n \t
- Apply substitution to indefinite and definite integrals<\/li>\r\n \t
- Integrate functions involving exponential and logarithmic functions<\/li>\r\n \t
- Integrate functions resulting in inverse trigonometric functions<\/li>\r\n \t
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\r\n<\/ul>\r\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\r\n\r\n \t- Calculate the areas of curved regions by using integration methods<\/li>\r\n \t
- Find the volume of a solid of revolution using various methods<\/li>\r\n \t
- Compare different integration methods for determining volume<\/li>\r\n \t
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\r\n \t
- Quantify mass, density, work, force, and pressure using integration<\/li>\r\n \t
- Determine the center of mass in various dimensions<\/li>\r\n \t
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\r\n \t
- Apply the exponential growth model to explain real world concepts<\/li>\r\n \t
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\r\n<\/ul>\r\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\r\n\r\n \t- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\r\n \t
- Solve integration problems involving trigonometric functions<\/li>\r\n \t
- Solve integration problems involving trigonometric substitution<\/li>\r\n \t
- Identify linear and quadratic factors in rational functions<\/li>\r\n \t
- Solve integration problems using alternative strategies<\/li>\r\n \t
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\r\n \t
- Evaluate improper integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\r\n\r\n \t- Analyze differential equations and their solutions<\/li>\r\n \t
- Evaluate direction fields of first-order differential equations<\/li>\r\n \t
- Apply separation of variables to differential equations<\/li>\r\n \t
- Interpret the results and solution curves of logistic equations<\/li>\r\n \t
- Solve first-order linear equations<\/li>\r\n<\/ul>\r\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\r\n\r\n \t- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\r\n \t
- Interpret infinite, geometric, and telescoping series<\/li>\r\n \t
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\r\n \t
- Use the comparison test to determine the convergence of a series<\/li>\r\n \t
- Assess alternating series by testing for convergence and estimating the sum<\/li>\r\n \t
- Apply the ratio and root tests to a series<\/li>\r\n<\/ul>\r\n
\u00a0Module 6: Represent functions using power series<\/h2>\r\n\r\n \t- Use power series to represent functions and determine convergence<\/li>\r\n \t
- Apply the properties of a power series<\/li>\r\n \t
- Examine Taylor and Maclaurin series<\/li>\r\n \t
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
![\"icon](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/01225024\/outcomes.jpg\")
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\r\n\r\n \t- Calculate the areas of curved regions by using integration methods<\/li>\r\n \t
- Find the volume of a solid of revolution using various methods<\/li>\r\n \t
- Compare different integration methods for determining volume<\/li>\r\n \t
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\r\n \t
- Quantify mass, density, work, force, and pressure using integration<\/li>\r\n \t
- Determine the center of mass in various dimensions<\/li>\r\n \t
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\r\n \t
- Apply the exponential growth model to explain real world concepts<\/li>\r\n \t
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\r\n<\/ul>\r\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\r\n\r\n \t- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\r\n \t
- Solve integration problems involving trigonometric functions<\/li>\r\n \t
- Solve integration problems involving trigonometric substitution<\/li>\r\n \t
- Identify linear and quadratic factors in rational functions<\/li>\r\n \t
- Solve integration problems using alternative strategies<\/li>\r\n \t
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\r\n \t
- Evaluate improper integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\r\n\r\n \t- Analyze differential equations and their solutions<\/li>\r\n \t
- Evaluate direction fields of first-order differential equations<\/li>\r\n \t
- Apply separation of variables to differential equations<\/li>\r\n \t
- Interpret the results and solution curves of logistic equations<\/li>\r\n \t
- Solve first-order linear equations<\/li>\r\n<\/ul>\r\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\r\n\r\n \t- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\r\n \t
- Interpret infinite, geometric, and telescoping series<\/li>\r\n \t
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\r\n \t
- Use the comparison test to determine the convergence of a series<\/li>\r\n \t
- Assess alternating series by testing for convergence and estimating the sum<\/li>\r\n \t
- Apply the ratio and root tests to a series<\/li>\r\n<\/ul>\r\n
\u00a0Module 6: Represent functions using power series<\/h2>\r\n\r\n \t- Use power series to represent functions and determine convergence<\/li>\r\n \t
- Apply the properties of a power series<\/li>\r\n \t
- Examine Taylor and Maclaurin series<\/li>\r\n \t
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\r\n\r\n \t- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\r\n \t
- Solve integration problems involving trigonometric functions<\/li>\r\n \t
- Solve integration problems involving trigonometric substitution<\/li>\r\n \t
- Identify linear and quadratic factors in rational functions<\/li>\r\n \t
- Solve integration problems using alternative strategies<\/li>\r\n \t
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\r\n \t
- Evaluate improper integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\r\n\r\n \t- Analyze differential equations and their solutions<\/li>\r\n \t
- Evaluate direction fields of first-order differential equations<\/li>\r\n \t
- Apply separation of variables to differential equations<\/li>\r\n \t
- Interpret the results and solution curves of logistic equations<\/li>\r\n \t
- Solve first-order linear equations<\/li>\r\n<\/ul>\r\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\r\n\r\n \t- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\r\n \t
- Interpret infinite, geometric, and telescoping series<\/li>\r\n \t
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\r\n \t
- Use the comparison test to determine the convergence of a series<\/li>\r\n \t
- Assess alternating series by testing for convergence and estimating the sum<\/li>\r\n \t
- Apply the ratio and root tests to a series<\/li>\r\n<\/ul>\r\n
\u00a0Module 6: Represent functions using power series<\/h2>\r\n\r\n \t- Use power series to represent functions and determine convergence<\/li>\r\n \t
- Apply the properties of a power series<\/li>\r\n \t
- Examine Taylor and Maclaurin series<\/li>\r\n \t
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\r\n\r\n \t- Analyze differential equations and their solutions<\/li>\r\n \t
- Evaluate direction fields of first-order differential equations<\/li>\r\n \t
- Apply separation of variables to differential equations<\/li>\r\n \t
- Interpret the results and solution curves of logistic equations<\/li>\r\n \t
- Solve first-order linear equations<\/li>\r\n<\/ul>\r\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\r\n\r\n \t- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\r\n \t
- Interpret infinite, geometric, and telescoping series<\/li>\r\n \t
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\r\n \t
- Use the comparison test to determine the convergence of a series<\/li>\r\n \t
- Assess alternating series by testing for convergence and estimating the sum<\/li>\r\n \t
- Apply the ratio and root tests to a series<\/li>\r\n<\/ul>\r\n
\u00a0Module 6: Represent functions using power series<\/h2>\r\n\r\n \t- Use power series to represent functions and determine convergence<\/li>\r\n \t
- Apply the properties of a power series<\/li>\r\n \t
- Examine Taylor and Maclaurin series<\/li>\r\n \t
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\r\n\r\n \t- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\r\n \t
- Interpret infinite, geometric, and telescoping series<\/li>\r\n \t
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\r\n \t
- Use the comparison test to determine the convergence of a series<\/li>\r\n \t
- Assess alternating series by testing for convergence and estimating the sum<\/li>\r\n \t
- Apply the ratio and root tests to a series<\/li>\r\n<\/ul>\r\n
\u00a0Module 6: Represent functions using power series<\/h2>\r\n\r\n \t- Use power series to represent functions and determine convergence<\/li>\r\n \t
- Apply the properties of a power series<\/li>\r\n \t
- Examine Taylor and Maclaurin series<\/li>\r\n \t
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0Module 6: Represent functions using power series<\/h2>\r\n\r\n \t- Use power series to represent functions and determine convergence<\/li>\r\n \t
- Apply the properties of a power series<\/li>\r\n \t
- Examine Taylor and Maclaurin series<\/li>\r\n \t
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\r\n<\/ul>\r\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\r\n\r\n \t- Identify parametric equations<\/li>\r\n \t
- Apply calculus to parametric equations<\/li>\r\n \t
- Understand polar coordinates and their application<\/li>\r\n \t
- Determine area and arc length in polar coordinates<\/li>\r\n \t
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n\n- Apply summation rules<\/li>\n
- Interpret definite integrals<\/li>\n
- Explain the Fundamental Theorem of Calculus<\/li>\n
- Use the net change theorem<\/li>\n
- Apply substitution to indefinite and definite integrals<\/li>\n
- Integrate functions involving exponential and logarithmic functions<\/li>\n
- Integrate functions resulting in inverse trigonometric functions<\/li>\n
- Approximate integrals when the antiderivative is impossible to calculate<\/li>\n<\/ul>\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n\n- Calculate the areas of curved regions by using integration methods<\/li>\n
- Find the volume of a solid of revolution using various methods<\/li>\n
- Compare different integration methods for determining volume<\/li>\n
- Calculate the arc length of a curve and the surface area of a solid of revolution<\/li>\n
- Quantify mass, density, work, force, and pressure using integration<\/li>\n
- Determine the center of mass in various dimensions<\/li>\n
- Apply integration and derivatives to exponential and natural logarithmic functions<\/li>\n
- Apply the exponential growth model to explain real world concepts<\/li>\n
- Use integrals and derivatives to evaluate hyperbolic functions<\/li>\n<\/ul>\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n\n- Apply the integration-by-parts formula to solve indefinite and definite integrals<\/li>\n
- Solve integration problems involving trigonometric functions<\/li>\n
- Solve integration problems involving trigonometric substitution<\/li>\n
- Identify linear and quadratic factors in rational functions<\/li>\n
- Solve integration problems using alternative strategies<\/li>\n
- Use numerical integration techniques to determine the accuracy of integrals<\/li>\n
- Evaluate improper integrals<\/li>\n<\/ul>\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n\n- Analyze differential equations and their solutions<\/li>\n
- Evaluate direction fields of first-order differential equations<\/li>\n
- Apply separation of variables to differential equations<\/li>\n
- Interpret the results and solution curves of logistic equations<\/li>\n
- Solve first-order linear equations<\/li>\n<\/ul>\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n\n- Evaluate sequences by determining the formula, the limit, and the divergence<\/li>\n
- Interpret infinite, geometric, and telescoping series<\/li>\n
- Use the divergence and integral tests to determine the convergence or divergence of a series<\/li>\n
- Use the comparison test to determine the convergence of a series<\/li>\n
- Assess alternating series by testing for convergence and estimating the sum<\/li>\n
- Apply the ratio and root tests to a series<\/li>\n<\/ul>\n
\u00a0Module 6: Represent functions using power series<\/h2>\n\n- Use power series to represent functions and determine convergence<\/li>\n
- Apply the properties of a power series<\/li>\n
- Examine Taylor and Maclaurin series<\/li>\n
- Apply Taylor series to solve differential equations and nonelementary integrals<\/li>\n<\/ul>\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n\n- Identify parametric equations<\/li>\n
- Apply calculus to parametric equations<\/li>\n
- Understand polar coordinates and their application<\/li>\n
- Determine area and arc length in polar coordinates<\/li>\n
- Distinguish properties of parabolas, ellipses, and hyperbolas<\/li>\n<\/ul>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp. Provided by<\/strong>: Noun Project. Located at<\/strong>: https:\/\/thenounproject.com\/term\/magnify\/1276779\/<\/a>. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Magnify\",\"author\":\"Eucalyp\",\"organization\":\"Noun Project\",\"url\":\"https:\/\/thenounproject.com\/term\/magnify\/1276779\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":779,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":2447,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/2447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/779"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
<\/p>\n
The content, assignments, and assessments for Calculus II\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus II Learning Outcomes<\/a>.<\/span><\/p>\n\u00a0Module 1:\u00a0Use basic integration techniques to calculate area<\/h2>\n
\n
\u00a0Module 2: Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n
\n
\u00a0Module 3: Perform additional integration calculations and approximations<\/h2>\n
\n
\u00a0Module 4: Develop methods to solve differential equations<\/h2>\n
\n
\u00a0Module 5: Understand infinite series and how to use them to evaluate functions<\/h2>\n
\n
\u00a0Module 6: Represent functions using power series<\/h2>\n
\n
\u00a0Module 7: Describing curves through parametric equations and polar coordinates<\/h2>\n
\n
Candela Citations<\/h3>\n\t\t\t\t\t