McMullen C. Calculus with Multiple Variables. Essential Skills Workbook...2024

Textbook in PDF format

For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers:
Partial derivatives.
Extreme values with multiple variables (including saddle points).
Vectors, vector analysis (such as the dot and cross products), and vector calculus.
The gradient, divergence, and curl.
The main coordinate systems: Cartesian, 2D polar, spherical, and cylindrical.
Path integrals, surface integrals, and volume integrals.
Flux integrals, center of mass, and moment of inertia.
Tangent and normal vectors.
and more.
The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors