Cloud M. Fundamentals of Multivariable Calculus 2025

Textbook in PDF format

This textbook is carefully designed as an early undergraduate introduction to the calculus of several real variables. The balanced coverage is devoted to limits, continuity, partial derivatives, extrema, the nabla operator, multiple integrals, line integrals, surface integrals, and the fundamental theorems of vector calculus.
Engaging and accessible with detailed diagrams and copious worked examples, the presentation is well suited to students pursuing applied fields such as engineering. Multiple integration is motivated intuitively through the calculation of mass. The chapter-end problems provide both drill and challenge.
Overall, the book should equip students with the knowledge and confidence needed for subsequent courses.
An appendix on hints renders the book suitable for self-study. Prerequisites are limited to single-variable calculus, linear algebra, and analytic geometry