Woolsey K. Multivariable Calculus. An Introduction 2015

Textbook in PDF format

Many introductory textbooks on multivariable calculus try to include too many topics and applications or focus too much on small details and rigor. As a result, they end up becoming either a 1000 page confusing mess, or a little text incomprehensible to those not familiar with formal mathematics. In this book, I have attempted to explain the essential concepts of multivariable calculus in a clear and concise way. I choose clarity over rigor, including as many proofs as possible but leaving out those which only confuse the reader, and not focusing on minute details which only become relevant in obscure situations. Because this book is still intended as a supplement to a larger textbook or a class, I have not included many side topics and applications or exercises. The exercises present, however, all have solutions in the book, with step by step walkthroughs for some of the harder problems.
Vectors and Three Dimensional Space
Functions
Differential Calculus
Integral Calculus
Vector Calculus