The content, assignments, and assessments for Calculus III are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus III Learning Outcomes.

Module 1: Describing curves through parametric equations and polar coordinates

• Identify parametric equations
• Apply calculus to parametric equations
• Understand polar coordinates and their application
• Determine area and arc length in polar coordinates
• Distinguish properties of parabolas, ellipses, and hyperbolas

Module 2: Interpret functions of two or three independent variables in multidimensional space

• Understand vectors and their operations
• Apply vectors to three-dimensional space
• Use the dot product
• Use the cross product
• Interpret equations of lines and planes in space
• Distinguish properties of cylinders, ellipsoids, paraboloids, and hyperboloids
• Convert coordinates between rectangular and nonrectangular coordinates

Module 3: Interpret vector-valued functions to determine the velocity, acceleration, arc length, and curvature of an object’s trajectory

• Apply vector-valued functions to curves in the plane and in three-dimensional space
• Apply calculus to vector-valued functions
• Determine arc length and curvature in space
• Describe motion in space

Module 4: Develop methods to solve differential equations of functions with several variables

• Interpret functions of several variables
• Determine limits and continuity of functions of several variables
• Calculate the derivatives of functions of several variables
• Apply tangent planes to three-dimensional surfaces
• Apply the chain rule to functions of several variables
• Calculate directional derivatives
• Identify extrema and critical points for a function of two variables
• Apply Lagrange multipliers to solve optimization problems

Module 5: Apply integration techniques to functions containing more than one variable and other coordinate systems

• Calculate double integrals over rectangular regions
• Apply double integrals to general regions
• Use double integrals on polar rectangular regions
• Calculate triple integrals over three-dimensional space
• Evaluate triple integrals using cylinderical and spherical coordinates
• Use triple integrals to locate centers of mass and moments of inertia
• Calculate mutliple integrals using a change of variables

Module 6: Generalize vector fields and its application to Green’s, Stokes’ and the divergence theorems

• Identify vector fields
• Calculate line integrals along curves
• Explain conservative vector fields
• Apply Green’s theorem
• Determine divergence and curl for a vector field
• Interpret surface integrals
• Use Stokes’ theorem
• Apply the Divergence theorem

Module 7: Develop methods to solve second-order differential equations

• Interpret second-order linear equations
• Solve nonhomogeneous linear equations
• Apply second-order differential equations to real-world concepts
• Use power series to solve differential equations