Multivariable Calculus

Ben Woodruff, Mathematics Faculty at Brigham Young University-Idaho (, Jason Grout, Mathematics Faculty at Drake University (

With references to Calculus, Early Transcendental Functions, 5th edition, by Larson and Edwards.

This is an initial conversion of this pdf set of notes. Chapters 7 and 10-12 need more polish, so see the pdf file for a more finished set of problems over motion and double and triple integrals.

  1. Review
  2. Vectors, Lines, and Planes
  3. Curves
  4. Functions
  5. Transformations
  6. Derivatives
  7. Motion (rough conversion; see pdf)
  8. Line Integrals
  9. Optimization
  10. Double Integrals (rough conversion; see pdf)
  11. Surface Integrals (rough conversion; see pdf)
  12. Triple Integrals (rough conversion; see pdf)


This course may be like no other course in mathematics you have ever taken. We'll discuss in class some of the key differences, and eventually this section will contain a complete description of how this course works. For now, it's just a skeleton.

I received the following email about 6 months after a student took the course:

Hey Brother Woodruff,

I was reading Knowledge of Spiritual Things by Elder Scott. I thought the following quote would be awesome to share with your students, especially those in Math 215 :)

Profound [spiritual] truth cannot simply be poured from one mind and heart to another. It takes faith and diligent effort. Precious truth comes a small piece at a time through faith, with great exertion, and at times wrenching struggles.

Elder Scott's words perfectly describe how we acquire mathematical truth, as well as spiritual truth.


© 2013 Ben Woodruff and Jason Grout. Some Rights Reserved.

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The source code to this project can be obtained at