Topical Outline with Specific Course Objectives
- Functions and the Geometry of Space
- Identify, describe, and visualize equations in 3-space.
- Use contour maps for functions of two or three variables to analyze the functions.
- Use the algebra of vectors to study geometry in 3-space.
- Calculus of Vector-Valued Functions
- Use the calculus of vector-valued functions to analyze motions in 3-space.
- Find and interpret the unit tangent and unit normal vectors and curvature.
- Calculus of Functions of Several Variables - Differentiation
- Prove a limit does or does not exist.
- Find partial derivatives numerically and symbolically and use them to analyze and interpret the way a function varies.
- Find and interpret the gradient and directional derivatives for a function at a given point.
- Find the total differential of a function of several variables and use it to approximate incremental change in the function.
- Analyze and solve optimization problems using the Second Derivative Test and Lagrange multipliers.
- Calculus of Functions of Several Variables - Integration
- Explain the relationship between multiple and iterated integrals.
- Evaluate multiple integrals either by using iterated integrals or approximation methods.
- Evaluate multiple integrals using polar coordinates.
- Relate rectangular coordinates in 3-space to spherical and cylindrical coordinates, and use spherical and cylindrical coordinates as an aid in evaluating multiple integrals.
- Model applied problems using multiple integrals.
- Evaluate multiple integrals using a change of variables and the Jacobian.
- Vector Analysis
- Define a line integral, and use it to find the total change in a function given its gradient field.
- Understand and apply Fundamental Theorem for line integrals.
- Understand and apply Green’s Theorem.
- Calculate and interpret curl and divergence for a vector field.
- Define a surface integral, and use it to find the flux of a vector field over a surface.
- Understand and apply Stoke’s Theorem.
Department Policies
- Graphing Calculator not allowed on proctored tests or final exam
- Comprehensive Final