\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\r\n\r\n \t- Manipulate basic functions<\/li>\r\n \t
- Interpret equations and graphs of the basic classes of functions<\/li>\r\n \t
- Identify trigonometric functions and their features<\/li>\r\n \t
- Analyze inverse functions<\/li>\r\n \t
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\r\n<\/ul>\r\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\r\n\r\n \t- Relate the tangent and area problems to differential and integral calculus<\/li>\r\n \t
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\r\n \t
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\r\n \t
- Discuss continuity at a point and continuity over an interval<\/li>\r\n \t
- Interpret the epsilon-delta definition of a limit<\/li>\r\n<\/ul>\r\n
Module 3: Find the derivatives of various function types<\/h2>\r\n\r\n \t- Interpret the derivative of a function at a point<\/li>\r\n \t
- Express the derivative of a function as an equation or a graph<\/li>\r\n \t
- Apply the differentiation rules to determine a derivative<\/li>\r\n \t
- Explain rate of change and its applications<\/li>\r\n \t
- Find the derivatives of trigonometric functions<\/li>\r\n \t
- Apply the chain rule in a variety of situations<\/li>\r\n \t
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\r\n \t
- Use implicit differentiation to find derivatives<\/li>\r\n \t
- Determine the derivative of an exponential or logarithmic function<\/li>\r\n<\/ul>\r\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\r\n\r\n \t- Explain related rates<\/li>\r\n \t
- Use linear approximation and differentials<\/li>\r\n \t
- Identify extrema and critical points of a function<\/li>\r\n \t
- Interpret the mean value theorem<\/li>\r\n \t
- Evaluate the graph of a function using the first and second derivative test<\/li>\r\n \t
- Identify functions with limits and asymptotes<\/li>\r\n \t
- Solve optimization problems<\/li>\r\n \t
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\r\n \t
- Explain Newton's Method as an iterative process to approximate<\/li>\r\n \t
- Identify the antiderivative<\/li>\r\n<\/ul>\r\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>","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 I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n\n- Manipulate basic functions<\/li>\n
- Interpret equations and graphs of the basic classes of functions<\/li>\n
- Identify trigonometric functions and their features<\/li>\n
- Analyze inverse functions<\/li>\n
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\n<\/ul>\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n\n- Relate the tangent and area problems to differential and integral calculus<\/li>\n
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\n
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\n
- Discuss continuity at a point and continuity over an interval<\/li>\n
- Interpret the epsilon-delta definition of a limit<\/li>\n<\/ul>\n
Module 3: Find the derivatives of various function types<\/h2>\n\n- Interpret the derivative of a function at a point<\/li>\n
- Express the derivative of a function as an equation or a graph<\/li>\n
- Apply the differentiation rules to determine a derivative<\/li>\n
- Explain rate of change and its applications<\/li>\n
- Find the derivatives of trigonometric functions<\/li>\n
- Apply the chain rule in a variety of situations<\/li>\n
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\n
- Use implicit differentiation to find derivatives<\/li>\n
- Determine the derivative of an exponential or logarithmic function<\/li>\n<\/ul>\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n\n- Explain related rates<\/li>\n
- Use linear approximation and differentials<\/li>\n
- Identify extrema and critical points of a function<\/li>\n
- Interpret the mean value theorem<\/li>\n
- Evaluate the graph of a function using the first and second derivative test<\/li>\n
- Identify functions with limits and asymptotes<\/li>\n
- Solve optimization problems<\/li>\n
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\n
- Explain Newton’s Method as an iterative process to approximate<\/li>\n
- Identify the antiderivative<\/li>\n<\/ul>\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>\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>
- Skill Level Outcomes from Calculus Volume 1. Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. Provided by<\/strong>: OpenStax. Located at<\/strong>: https:\/\/openstax.org\/details\/books\/calculus-volume-1<\/a>. License<\/strong>: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction<\/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\":\"\"},{\"type\":\"cc\",\"description\":\"Skill Level Outcomes from Calculus Volume 1\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/details\/books\/calculus-volume-1\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3759","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions"}],"predecessor-version":[{"id":4233,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions\/4233"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3759"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3759"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\r\n\r\n \t- Relate the tangent and area problems to differential and integral calculus<\/li>\r\n \t
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\r\n \t
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\r\n \t
- Discuss continuity at a point and continuity over an interval<\/li>\r\n \t
- Interpret the epsilon-delta definition of a limit<\/li>\r\n<\/ul>\r\n
Module 3: Find the derivatives of various function types<\/h2>\r\n\r\n \t- Interpret the derivative of a function at a point<\/li>\r\n \t
- Express the derivative of a function as an equation or a graph<\/li>\r\n \t
- Apply the differentiation rules to determine a derivative<\/li>\r\n \t
- Explain rate of change and its applications<\/li>\r\n \t
- Find the derivatives of trigonometric functions<\/li>\r\n \t
- Apply the chain rule in a variety of situations<\/li>\r\n \t
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\r\n \t
- Use implicit differentiation to find derivatives<\/li>\r\n \t
- Determine the derivative of an exponential or logarithmic function<\/li>\r\n<\/ul>\r\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\r\n\r\n \t- Explain related rates<\/li>\r\n \t
- Use linear approximation and differentials<\/li>\r\n \t
- Identify extrema and critical points of a function<\/li>\r\n \t
- Interpret the mean value theorem<\/li>\r\n \t
- Evaluate the graph of a function using the first and second derivative test<\/li>\r\n \t
- Identify functions with limits and asymptotes<\/li>\r\n \t
- Solve optimization problems<\/li>\r\n \t
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\r\n \t
- Explain Newton's Method as an iterative process to approximate<\/li>\r\n \t
- Identify the antiderivative<\/li>\r\n<\/ul>\r\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>","rendered":"<\/p>\n
The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n\n- Manipulate basic functions<\/li>\n
- Interpret equations and graphs of the basic classes of functions<\/li>\n
- Identify trigonometric functions and their features<\/li>\n
- Analyze inverse functions<\/li>\n
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\n<\/ul>\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n\n- Relate the tangent and area problems to differential and integral calculus<\/li>\n
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\n
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\n
- Discuss continuity at a point and continuity over an interval<\/li>\n
- Interpret the epsilon-delta definition of a limit<\/li>\n<\/ul>\n
Module 3: Find the derivatives of various function types<\/h2>\n\n- Interpret the derivative of a function at a point<\/li>\n
- Express the derivative of a function as an equation or a graph<\/li>\n
- Apply the differentiation rules to determine a derivative<\/li>\n
- Explain rate of change and its applications<\/li>\n
- Find the derivatives of trigonometric functions<\/li>\n
- Apply the chain rule in a variety of situations<\/li>\n
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\n
- Use implicit differentiation to find derivatives<\/li>\n
- Determine the derivative of an exponential or logarithmic function<\/li>\n<\/ul>\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n\n- Explain related rates<\/li>\n
- Use linear approximation and differentials<\/li>\n
- Identify extrema and critical points of a function<\/li>\n
- Interpret the mean value theorem<\/li>\n
- Evaluate the graph of a function using the first and second derivative test<\/li>\n
- Identify functions with limits and asymptotes<\/li>\n
- Solve optimization problems<\/li>\n
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\n
- Explain Newton’s Method as an iterative process to approximate<\/li>\n
- Identify the antiderivative<\/li>\n<\/ul>\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>\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>
- Skill Level Outcomes from Calculus Volume 1. Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. Provided by<\/strong>: OpenStax. Located at<\/strong>: https:\/\/openstax.org\/details\/books\/calculus-volume-1<\/a>. License<\/strong>: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction<\/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\":\"\"},{\"type\":\"cc\",\"description\":\"Skill Level Outcomes from Calculus Volume 1\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/details\/books\/calculus-volume-1\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3759","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions"}],"predecessor-version":[{"id":4233,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions\/4233"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3759"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3759"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 3: Find the derivatives of various function types<\/h2>\r\n\r\n \t- Interpret the derivative of a function at a point<\/li>\r\n \t
- Express the derivative of a function as an equation or a graph<\/li>\r\n \t
- Apply the differentiation rules to determine a derivative<\/li>\r\n \t
- Explain rate of change and its applications<\/li>\r\n \t
- Find the derivatives of trigonometric functions<\/li>\r\n \t
- Apply the chain rule in a variety of situations<\/li>\r\n \t
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\r\n \t
- Use implicit differentiation to find derivatives<\/li>\r\n \t
- Determine the derivative of an exponential or logarithmic function<\/li>\r\n<\/ul>\r\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\r\n\r\n \t- Explain related rates<\/li>\r\n \t
- Use linear approximation and differentials<\/li>\r\n \t
- Identify extrema and critical points of a function<\/li>\r\n \t
- Interpret the mean value theorem<\/li>\r\n \t
- Evaluate the graph of a function using the first and second derivative test<\/li>\r\n \t
- Identify functions with limits and asymptotes<\/li>\r\n \t
- Solve optimization problems<\/li>\r\n \t
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\r\n \t
- Explain Newton's Method as an iterative process to approximate<\/li>\r\n \t
- Identify the antiderivative<\/li>\r\n<\/ul>\r\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>","rendered":"<\/p>\n
The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n\n- Manipulate basic functions<\/li>\n
- Interpret equations and graphs of the basic classes of functions<\/li>\n
- Identify trigonometric functions and their features<\/li>\n
- Analyze inverse functions<\/li>\n
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\n<\/ul>\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n\n- Relate the tangent and area problems to differential and integral calculus<\/li>\n
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\n
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\n
- Discuss continuity at a point and continuity over an interval<\/li>\n
- Interpret the epsilon-delta definition of a limit<\/li>\n<\/ul>\n
Module 3: Find the derivatives of various function types<\/h2>\n\n- Interpret the derivative of a function at a point<\/li>\n
- Express the derivative of a function as an equation or a graph<\/li>\n
- Apply the differentiation rules to determine a derivative<\/li>\n
- Explain rate of change and its applications<\/li>\n
- Find the derivatives of trigonometric functions<\/li>\n
- Apply the chain rule in a variety of situations<\/li>\n
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\n
- Use implicit differentiation to find derivatives<\/li>\n
- Determine the derivative of an exponential or logarithmic function<\/li>\n<\/ul>\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n\n- Explain related rates<\/li>\n
- Use linear approximation and differentials<\/li>\n
- Identify extrema and critical points of a function<\/li>\n
- Interpret the mean value theorem<\/li>\n
- Evaluate the graph of a function using the first and second derivative test<\/li>\n
- Identify functions with limits and asymptotes<\/li>\n
- Solve optimization problems<\/li>\n
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\n
- Explain Newton’s Method as an iterative process to approximate<\/li>\n
- Identify the antiderivative<\/li>\n<\/ul>\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>\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>
- Skill Level Outcomes from Calculus Volume 1. Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. Provided by<\/strong>: OpenStax. Located at<\/strong>: https:\/\/openstax.org\/details\/books\/calculus-volume-1<\/a>. License<\/strong>: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction<\/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\":\"\"},{\"type\":\"cc\",\"description\":\"Skill Level Outcomes from Calculus Volume 1\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/details\/books\/calculus-volume-1\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3759","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions"}],"predecessor-version":[{"id":4233,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions\/4233"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3759"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3759"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\r\n\r\n \t- Explain related rates<\/li>\r\n \t
- Use linear approximation and differentials<\/li>\r\n \t
- Identify extrema and critical points of a function<\/li>\r\n \t
- Interpret the mean value theorem<\/li>\r\n \t
- Evaluate the graph of a function using the first and second derivative test<\/li>\r\n \t
- Identify functions with limits and asymptotes<\/li>\r\n \t
- Solve optimization problems<\/li>\r\n \t
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\r\n \t
- Explain Newton's Method as an iterative process to approximate<\/li>\r\n \t
- Identify the antiderivative<\/li>\r\n<\/ul>\r\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>","rendered":"<\/p>\n
The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n\n- Manipulate basic functions<\/li>\n
- Interpret equations and graphs of the basic classes of functions<\/li>\n
- Identify trigonometric functions and their features<\/li>\n
- Analyze inverse functions<\/li>\n
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\n<\/ul>\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n\n- Relate the tangent and area problems to differential and integral calculus<\/li>\n
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\n
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\n
- Discuss continuity at a point and continuity over an interval<\/li>\n
- Interpret the epsilon-delta definition of a limit<\/li>\n<\/ul>\n
Module 3: Find the derivatives of various function types<\/h2>\n\n- Interpret the derivative of a function at a point<\/li>\n
- Express the derivative of a function as an equation or a graph<\/li>\n
- Apply the differentiation rules to determine a derivative<\/li>\n
- Explain rate of change and its applications<\/li>\n
- Find the derivatives of trigonometric functions<\/li>\n
- Apply the chain rule in a variety of situations<\/li>\n
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\n
- Use implicit differentiation to find derivatives<\/li>\n
- Determine the derivative of an exponential or logarithmic function<\/li>\n<\/ul>\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n\n- Explain related rates<\/li>\n
- Use linear approximation and differentials<\/li>\n
- Identify extrema and critical points of a function<\/li>\n
- Interpret the mean value theorem<\/li>\n
- Evaluate the graph of a function using the first and second derivative test<\/li>\n
- Identify functions with limits and asymptotes<\/li>\n
- Solve optimization problems<\/li>\n
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\n
- Explain Newton’s Method as an iterative process to approximate<\/li>\n
- Identify the antiderivative<\/li>\n<\/ul>\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>\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>
- Skill Level Outcomes from Calculus Volume 1. Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. Provided by<\/strong>: OpenStax. Located at<\/strong>: https:\/\/openstax.org\/details\/books\/calculus-volume-1<\/a>. License<\/strong>: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction<\/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\":\"\"},{\"type\":\"cc\",\"description\":\"Skill Level Outcomes from Calculus Volume 1\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/details\/books\/calculus-volume-1\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3759","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions"}],"predecessor-version":[{"id":4233,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions\/4233"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3759"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3759"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>","rendered":"<\/p>\n
The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n\n- Manipulate basic functions<\/li>\n
- Interpret equations and graphs of the basic classes of functions<\/li>\n
- Identify trigonometric functions and their features<\/li>\n
- Analyze inverse functions<\/li>\n
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\n<\/ul>\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n\n- Relate the tangent and area problems to differential and integral calculus<\/li>\n
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\n
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\n
- Discuss continuity at a point and continuity over an interval<\/li>\n
- Interpret the epsilon-delta definition of a limit<\/li>\n<\/ul>\n
Module 3: Find the derivatives of various function types<\/h2>\n\n- Interpret the derivative of a function at a point<\/li>\n
- Express the derivative of a function as an equation or a graph<\/li>\n
- Apply the differentiation rules to determine a derivative<\/li>\n
- Explain rate of change and its applications<\/li>\n
- Find the derivatives of trigonometric functions<\/li>\n
- Apply the chain rule in a variety of situations<\/li>\n
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\n
- Use implicit differentiation to find derivatives<\/li>\n
- Determine the derivative of an exponential or logarithmic function<\/li>\n<\/ul>\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n\n- Explain related rates<\/li>\n
- Use linear approximation and differentials<\/li>\n
- Identify extrema and critical points of a function<\/li>\n
- Interpret the mean value theorem<\/li>\n
- Evaluate the graph of a function using the first and second derivative test<\/li>\n
- Identify functions with limits and asymptotes<\/li>\n
- Solve optimization problems<\/li>\n
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\n
- Explain Newton’s Method as an iterative process to approximate<\/li>\n
- Identify the antiderivative<\/li>\n<\/ul>\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>\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>
- Skill Level Outcomes from Calculus Volume 1. Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. Provided by<\/strong>: OpenStax. Located at<\/strong>: https:\/\/openstax.org\/details\/books\/calculus-volume-1<\/a>. License<\/strong>: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction<\/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\":\"\"},{\"type\":\"cc\",\"description\":\"Skill Level Outcomes from Calculus Volume 1\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/details\/books\/calculus-volume-1\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3759","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions"}],"predecessor-version":[{"id":4233,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions\/4233"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3759"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3759"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 6:\u00a0Apply 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
<\/section>","rendered":"<\/p>\n
The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n\n- Manipulate basic functions<\/li>\n
- Interpret equations and graphs of the basic classes of functions<\/li>\n
- Identify trigonometric functions and their features<\/li>\n
- Analyze inverse functions<\/li>\n
- Examine exponential, logarithmic, and hyperbolic functions<\/li>\n<\/ul>\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n\n- Relate the tangent and area problems to differential and integral calculus<\/li>\n
- Explain the difference between one-sided, two-sided, and infinite limits<\/li>\n
- Evaluate limits by using limit laws and other evaluation techniques<\/li>\n
- Discuss continuity at a point and continuity over an interval<\/li>\n
- Interpret the epsilon-delta definition of a limit<\/li>\n<\/ul>\n
Module 3: Find the derivatives of various function types<\/h2>\n\n- Interpret the derivative of a function at a point<\/li>\n
- Express the derivative of a function as an equation or a graph<\/li>\n
- Apply the differentiation rules to determine a derivative<\/li>\n
- Explain rate of change and its applications<\/li>\n
- Find the derivatives of trigonometric functions<\/li>\n
- Apply the chain rule in a variety of situations<\/li>\n
- Calculate the derivatives of an inverse function and inverse trigonometric functions<\/li>\n
- Use implicit differentiation to find derivatives<\/li>\n
- Determine the derivative of an exponential or logarithmic function<\/li>\n<\/ul>\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n\n- Explain related rates<\/li>\n
- Use linear approximation and differentials<\/li>\n
- Identify extrema and critical points of a function<\/li>\n
- Interpret the mean value theorem<\/li>\n
- Evaluate the graph of a function using the first and second derivative test<\/li>\n
- Identify functions with limits and asymptotes<\/li>\n
- Solve optimization problems<\/li>\n
- Describe how L\u2019H\u00f4pital\u2019s Rule is used to evaluate limits<\/li>\n
- Explain Newton’s Method as an iterative process to approximate<\/li>\n
- Identify the antiderivative<\/li>\n<\/ul>\n
Module 5: Use 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
Module 6:\u00a0Apply 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
<\/section>\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>
- Skill Level Outcomes from Calculus Volume 1. Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. Provided by<\/strong>: OpenStax. Located at<\/strong>: https:\/\/openstax.org\/details\/books\/calculus-volume-1<\/a>. License<\/strong>: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction<\/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\":\"\"},{\"type\":\"cc\",\"description\":\"Skill Level Outcomes from Calculus Volume 1\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/details\/books\/calculus-volume-1\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-1\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3759","chapter","type-chapter","status-publish","hentry"],"part":3756,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions"}],"predecessor-version":[{"id":4233,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/revisions\/4233"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/3756"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3759\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3759"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3759"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
<\/p>\n
The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes<\/a>.<\/p>\n\u00a0Module 1:\u00a0Evaluate the behaviors and graphs of functions<\/h2>\n
\n
Module 2:\u00a0Identify and analyze the limits of a function<\/h2>\n
\n
Module 3: Find the derivatives of various function types<\/h2>\n
\n
Module 4:\u00a0Examine the application of derivative calculation techniques<\/h2>\n
\n
Module 5: Use basic integration techniques to calculate area<\/h2>\n
\n
Module 6:\u00a0Apply integrals to geometric application, physical application, and modeling problems<\/h2>\n
\n
Candela Citations<\/h3>\n\t\t\t\t\t