MATH& 254: Calculus IV

Class Program
Weekly Contact Hours
Course ID
Meets Degree Requirements For
Natural Science,
Quantitative Skills

Focuses on multivariable and vector calculus, including: vector fields, gradients, curl, divergence, optimization, double and triple integrals in rectangular, polar, cylindrical, and spherical coordinate systems, line and surface integrals, Green's Theorem, Divergence Theorem, Stokes' Theorem.

Grading Basis

MATH&153 with a grade of C (2.0) or better or appropriate assessment score

Course Learning Outcomes

Core Topics


  1. Differentiation, limits, and integration with multivariable functions
  2. Calculating the directional derivative and gradient vector
  3. Determining local and absolute optimal points for functions of several variables.
  4. The method of Lagrange multipliers for optimization of a constrained system.
  5. Evaluation double integrals over rectangles and regions using rectangular and polar coordinates.
  6. The use of integration in rectangular and polar coordinate systems to determine surface area.
  7. Evaluation of triple integrals in rectangular, cylindrical, and spherical coordinates
  8. Working application problems using double and triple integrals.
  9. Level curves and associated gradient fields.
  10. Calculating, sketching, and interpreting vector fields.
  11. Determining curl and divergence of a vector field
  12. Evaluation of line and surface integrals
  13. Conservative vector fields and the Fundamental Theorem of Line Integrals.
  14. Green's, Stokes', and Divergence Theorems