Department of Mathematics

Course Objectives

Students entering MTH 234 should have a firm grasp on Calc I/II including all differentiation and integration techniques. By the end of Calculus III, students should have significant fundamental knowledge and skills so they can apply calculus to future STEM academic training and professional practice. Fundamental calculus knowledge and skills will be learned and evaluated based on specific objectives related to:

Functions and the Geometry of Space

  • Identify, describe, and visualize equations in 3-space.
  • 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 vectors and arc length.

Calculus of Functions of Several Variables - Differentiation

  • Use contour maps for functions of two or three variables to analyze the functions.
  • 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 multivariable optimization problems.

Calculus of Functions of Several Variables - Integration

  • Evaluate multiple integrals either by using iterated integrals or approximation methods.
  • Relate rectangular coordinates in 3-space to spherical and cylindrical coordinates, and use spherical and cylindrical coordinates as an aid in evaluating multiple integrals.

Vector Analysis

  • Interpret and evaluate line integrals.
  • Apply the Fundamental Theorem of Line integrals, Green's theorem, and Stokes' Theorem to line integrals appropriately.
  • Calculate and interpret the flow and divergence for a vector field.
  • Interpret and evaluate surface integrals
  • Apply Stokes' and Divergence theorems to surface integrals appropriately.