MAC2313 - Calculus 3 with Analytic Geometry

Topical Outline with Specific Course Objectives

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

Department Policies

  • Graphing Calculator not allowed on proctored tests or final exam
  • Comprehensive Final
Top