Module 1: 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>\r\n
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\r\n\r\n \t- Understand vectors and their operations<\/li>\r\n \t
- Apply vectors to three-dimensional space<\/li>\r\n \t
- Use the dot product<\/li>\r\n \t
- Use the cross product<\/li>\r\n \t
- Interpret equations of lines and planes in space<\/li>\r\n \t
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\r\n \t
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\r\n<\/ul>\r\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\r\n\r\n \t- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\r\n \t
- Apply calculus to vector-valued functions<\/li>\r\n \t
- Determine arc length and curvature in space<\/li>\r\n \t
- Describe motion in space<\/li>\r\n<\/ul>\r\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\r\n\r\n \t- Interpret functions of several variables<\/li>\r\n \t
- Determine limits and continuity of functions of several variables<\/li>\r\n \t
- Calculate the derivatives of functions of several variables<\/li>\r\n \t
- Apply tangent planes to three-dimensional surfaces<\/li>\r\n \t
- Apply the chain rule to functions of several variables<\/li>\r\n \t
- Calculate directional derivatives<\/li>\r\n \t
- Identify extrema and critical points for a function of two variables<\/li>\r\n \t
- Apply Lagrange multipliers to solve optimization problems<\/li>\r\n<\/ul>\r\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\r\n\r\n \t- Calculate double integrals over rectangular regions<\/li>\r\n \t
- Apply double integrals to general regions<\/li>\r\n \t
- Use double integrals on polar rectangular regions<\/li>\r\n \t
- Calculate triple integrals over three-dimensional space<\/li>\r\n \t
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\r\n \t
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\r\n \t
- Calculate mutliple integrals using a change of variables<\/li>\r\n<\/ul>\r\n
Module 6: Generalize vector fields and its application to Green's, Stokes' and the divergence theorems<\/h2>\r\n\r\n \t- Identify vector fields<\/li>\r\n \t
- Calculate line integrals along curves<\/li>\r\n \t
- Explain conservative vector fields<\/li>\r\n \t
- Apply Green's theorem<\/li>\r\n \t
- Determine divergence and curl for a vector field<\/li>\r\n \t
- Interpret surface integrals<\/li>\r\n \t
- Use Stokes' theorem<\/li>\r\n \t
- Apply the Divergence theorem<\/li>\r\n<\/ul>\r\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/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 III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\r\n\r\n \t- Understand vectors and their operations<\/li>\r\n \t
- Apply vectors to three-dimensional space<\/li>\r\n \t
- Use the dot product<\/li>\r\n \t
- Use the cross product<\/li>\r\n \t
- Interpret equations of lines and planes in space<\/li>\r\n \t
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\r\n \t
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\r\n<\/ul>\r\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\r\n\r\n \t- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\r\n \t
- Apply calculus to vector-valued functions<\/li>\r\n \t
- Determine arc length and curvature in space<\/li>\r\n \t
- Describe motion in space<\/li>\r\n<\/ul>\r\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\r\n\r\n \t- Interpret functions of several variables<\/li>\r\n \t
- Determine limits and continuity of functions of several variables<\/li>\r\n \t
- Calculate the derivatives of functions of several variables<\/li>\r\n \t
- Apply tangent planes to three-dimensional surfaces<\/li>\r\n \t
- Apply the chain rule to functions of several variables<\/li>\r\n \t
- Calculate directional derivatives<\/li>\r\n \t
- Identify extrema and critical points for a function of two variables<\/li>\r\n \t
- Apply Lagrange multipliers to solve optimization problems<\/li>\r\n<\/ul>\r\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\r\n\r\n \t- Calculate double integrals over rectangular regions<\/li>\r\n \t
- Apply double integrals to general regions<\/li>\r\n \t
- Use double integrals on polar rectangular regions<\/li>\r\n \t
- Calculate triple integrals over three-dimensional space<\/li>\r\n \t
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\r\n \t
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\r\n \t
- Calculate mutliple integrals using a change of variables<\/li>\r\n<\/ul>\r\n
Module 6: Generalize vector fields and its application to Green's, Stokes' and the divergence theorems<\/h2>\r\n\r\n \t- Identify vector fields<\/li>\r\n \t
- Calculate line integrals along curves<\/li>\r\n \t
- Explain conservative vector fields<\/li>\r\n \t
- Apply Green's theorem<\/li>\r\n \t
- Determine divergence and curl for a vector field<\/li>\r\n \t
- Interpret surface integrals<\/li>\r\n \t
- Use Stokes' theorem<\/li>\r\n \t
- Apply the Divergence theorem<\/li>\r\n<\/ul>\r\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\r\n\r\n \t- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\r\n \t
- Apply calculus to vector-valued functions<\/li>\r\n \t
- Determine arc length and curvature in space<\/li>\r\n \t
- Describe motion in space<\/li>\r\n<\/ul>\r\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\r\n\r\n \t- Interpret functions of several variables<\/li>\r\n \t
- Determine limits and continuity of functions of several variables<\/li>\r\n \t
- Calculate the derivatives of functions of several variables<\/li>\r\n \t
- Apply tangent planes to three-dimensional surfaces<\/li>\r\n \t
- Apply the chain rule to functions of several variables<\/li>\r\n \t
- Calculate directional derivatives<\/li>\r\n \t
- Identify extrema and critical points for a function of two variables<\/li>\r\n \t
- Apply Lagrange multipliers to solve optimization problems<\/li>\r\n<\/ul>\r\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\r\n\r\n \t- Calculate double integrals over rectangular regions<\/li>\r\n \t
- Apply double integrals to general regions<\/li>\r\n \t
- Use double integrals on polar rectangular regions<\/li>\r\n \t
- Calculate triple integrals over three-dimensional space<\/li>\r\n \t
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\r\n \t
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\r\n \t
- Calculate mutliple integrals using a change of variables<\/li>\r\n<\/ul>\r\n
Module 6: Generalize vector fields and its application to Green's, Stokes' and the divergence theorems<\/h2>\r\n\r\n \t- Identify vector fields<\/li>\r\n \t
- Calculate line integrals along curves<\/li>\r\n \t
- Explain conservative vector fields<\/li>\r\n \t
- Apply Green's theorem<\/li>\r\n \t
- Determine divergence and curl for a vector field<\/li>\r\n \t
- Interpret surface integrals<\/li>\r\n \t
- Use Stokes' theorem<\/li>\r\n \t
- Apply the Divergence theorem<\/li>\r\n<\/ul>\r\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\r\n\r\n \t- Interpret functions of several variables<\/li>\r\n \t
- Determine limits and continuity of functions of several variables<\/li>\r\n \t
- Calculate the derivatives of functions of several variables<\/li>\r\n \t
- Apply tangent planes to three-dimensional surfaces<\/li>\r\n \t
- Apply the chain rule to functions of several variables<\/li>\r\n \t
- Calculate directional derivatives<\/li>\r\n \t
- Identify extrema and critical points for a function of two variables<\/li>\r\n \t
- Apply Lagrange multipliers to solve optimization problems<\/li>\r\n<\/ul>\r\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\r\n\r\n \t- Calculate double integrals over rectangular regions<\/li>\r\n \t
- Apply double integrals to general regions<\/li>\r\n \t
- Use double integrals on polar rectangular regions<\/li>\r\n \t
- Calculate triple integrals over three-dimensional space<\/li>\r\n \t
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\r\n \t
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\r\n \t
- Calculate mutliple integrals using a change of variables<\/li>\r\n<\/ul>\r\n
Module 6: Generalize vector fields and its application to Green's, Stokes' and the divergence theorems<\/h2>\r\n\r\n \t- Identify vector fields<\/li>\r\n \t
- Calculate line integrals along curves<\/li>\r\n \t
- Explain conservative vector fields<\/li>\r\n \t
- Apply Green's theorem<\/li>\r\n \t
- Determine divergence and curl for a vector field<\/li>\r\n \t
- Interpret surface integrals<\/li>\r\n \t
- Use Stokes' theorem<\/li>\r\n \t
- Apply the Divergence theorem<\/li>\r\n<\/ul>\r\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\r\n\r\n \t- Calculate double integrals over rectangular regions<\/li>\r\n \t
- Apply double integrals to general regions<\/li>\r\n \t
- Use double integrals on polar rectangular regions<\/li>\r\n \t
- Calculate triple integrals over three-dimensional space<\/li>\r\n \t
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\r\n \t
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\r\n \t
- Calculate mutliple integrals using a change of variables<\/li>\r\n<\/ul>\r\n
Module 6: Generalize vector fields and its application to Green's, Stokes' and the divergence theorems<\/h2>\r\n\r\n \t- Identify vector fields<\/li>\r\n \t
- Calculate line integrals along curves<\/li>\r\n \t
- Explain conservative vector fields<\/li>\r\n \t
- Apply Green's theorem<\/li>\r\n \t
- Determine divergence and curl for a vector field<\/li>\r\n \t
- Interpret surface integrals<\/li>\r\n \t
- Use Stokes' theorem<\/li>\r\n \t
- Apply the Divergence theorem<\/li>\r\n<\/ul>\r\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 6: Generalize vector fields and its application to Green's, Stokes' and the divergence theorems<\/h2>\r\n\r\n \t- Identify vector fields<\/li>\r\n \t
- Calculate line integrals along curves<\/li>\r\n \t
- Explain conservative vector fields<\/li>\r\n \t
- Apply Green's theorem<\/li>\r\n \t
- Determine divergence and curl for a vector field<\/li>\r\n \t
- Interpret surface integrals<\/li>\r\n \t
- Use Stokes' theorem<\/li>\r\n \t
- Apply the Divergence theorem<\/li>\r\n<\/ul>\r\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Module 7: Develop methods to solve second-order differential equations<\/h2>\r\n\r\n \t- Interpret second-order linear equations<\/li>\r\n \t
- Solve nonhomogeneous linear equations<\/li>\r\n \t
- Apply second-order differential equations to real-world concepts<\/li>\r\n \t
- Use power series to solve differential equations<\/li>\r\n<\/ul>","rendered":"
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: 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
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n\n- Understand vectors and their operations<\/li>\n
- Apply vectors to three-dimensional space<\/li>\n
- Use the dot product<\/li>\n
- Use the cross product<\/li>\n
- Interpret equations of lines and planes in space<\/li>\n
- Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids<\/li>\n
- Convert coordinates between rectangular and nonrectangular coordinates<\/li>\n<\/ul>\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n\n- Apply vector-valued functions to curves in the plane and in three-dimensional space<\/li>\n
- Apply calculus to vector-valued functions<\/li>\n
- Determine arc length and curvature in space<\/li>\n
- Describe motion in space<\/li>\n<\/ul>\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n\n- Interpret functions of several variables<\/li>\n
- Determine limits and continuity of functions of several variables<\/li>\n
- Calculate the derivatives of functions of several variables<\/li>\n
- Apply tangent planes to three-dimensional surfaces<\/li>\n
- Apply the chain rule to functions of several variables<\/li>\n
- Calculate directional derivatives<\/li>\n
- Identify extrema and critical points for a function of two variables<\/li>\n
- Apply Lagrange multipliers to solve optimization problems<\/li>\n<\/ul>\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n\n- Calculate double integrals over rectangular regions<\/li>\n
- Apply double integrals to general regions<\/li>\n
- Use double integrals on polar rectangular regions<\/li>\n
- Calculate triple integrals over three-dimensional space<\/li>\n
- Evaluate triple integrals using cylinderical and spherical coordinates<\/li>\n
- Use triple integrals to locate centers of mass and moments of inertia<\/li>\n
- Calculate mutliple integrals using a change of variables<\/li>\n<\/ul>\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n\n- Identify vector fields<\/li>\n
- Calculate line integrals along curves<\/li>\n
- Explain conservative vector fields<\/li>\n
- Apply Green’s theorem<\/li>\n
- Determine divergence and curl for a vector field<\/li>\n
- Interpret surface integrals<\/li>\n
- Use Stokes’ theorem<\/li>\n
- Apply the Divergence theorem<\/li>\n<\/ul>\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n\n- Interpret second-order linear equations<\/li>\n
- Solve nonhomogeneous linear equations<\/li>\n
- Apply second-order differential equations to real-world concepts<\/li>\n
- Use power series to solve differential equations<\/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":349141,"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-4161","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/349141"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions"}],"predecessor-version":[{"id":6498,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/revisions\/6498"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/4161\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=4161"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=4161"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=4161"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=4161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
<\/p>\n
The content, assignments, and assessments for Calculus III\u00a0<\/strong>are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes<\/a>.<\/span><\/p>\nModule 1: Describing curves through parametric equations and polar coordinates<\/h2>\n
\n
Module 2: Interpret functions of two or three independent variables in multidimensional space<\/h2>\n
\n
Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object\u2019s trajectory<\/h2>\n
\n
Module 4: Develop methods to solve differential equations of functions with several variables<\/h2>\n
\n
Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems<\/h2>\n
\n
Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems<\/h2>\n
\n
Module 7: Develop methods to solve second-order differential equations<\/h2>\n
\n
Candela Citations<\/h3>\n\t\t\t\t\t