MAT 341: Calculus III
Undergraduate course, Southern Virginia University, 2026
Calculus in more than one dimension: parametric equations and polar coordinates, vectors and the geometry of space, vector-valued functions, functions of several variables, multiple integration, and vector analysis.
About the course
Calculus III takes the ideas of the first two semesters, the derivative and the integral, and extends them to curves, surfaces, and vector fields in space. The course ends with the higher-dimensional versions of the Fundamental Theorem of Calculus: Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
Students read before class with the help of a reading guide and take a short reading quiz, so that class time can be spent on the hard parts. “Toughloves” make sure the foundational definitions and facts are known cold. Three midterm “Celebrations of Knowledge” and a final complete the course.
Textbook: Calculus Volume 3 by Edwin Herman and Gilbert Strang, from OpenStax, free online.
Prerequisite: MAT 242: Calculus II.
Syllabus (Spring 2026)
Helpful resources
- CalcPlot3D. A free 3D grapher made for this course: surfaces, space curves, vector fields, level curves, and regions of integration.
- GeoGebra 3D Calculator and Desmos. Quick graphing in three and two dimensions.
- Major Theorems Cheat Sheet. A one-page handout I wrote on the higher-dimensional versions of the Fundamental Theorem of Calculus. My vector calculus worksheets from the University of Arizona are also good extra practice.
- Paul’s Online Math Notes. The Calculus III notes have many worked examples.
- MIT OpenCourseWare 18.02SC: Multivariable Calculus. Full lecture videos and problem sets with solutions.
- Khan Academy: Multivariable Calculus. Short videos with very good visualizations.