Multivariable Calculus
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Multivariable Calculus

An Introduction

About the Book

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.

A paper copy of this book can be found on Amazon.

About the Author

Kevin Woolsey
Kevin Woolsey

I am just a senior in high school that likes to learn math and help others learn math.

Table of Contents

  • Vectors and Three Dimensional Space
    • Euclidean Space
    • Vectors
    • The Dot Product
    • The Cross Product
    • Equations of Lines and Planes
    • Quadric Surfaces
    • Cylindrical and Spherical Coordinates
  • Functions
    • Multivariable Functions
    • Visual Representations of Functions
    • Limits and Continuity
    • Linear Transformations
  • Differential Calculus
    • Parametric Curves
    • Directional Derivatives
    • Differentials
    • Gradients
    • The Chain Rule
    • The Implicit Function Theorem
    • Critical Points
    • Lagrange Multipliers
    • Optimization
  • Integral Calculus
    • Multiple Integrals
    • Iterated Integrals
    • Setting Up Integrals
    • Change of Variables
    • Integrals in Different Coordinate Systems
  • Vector Calculus
    • Line Integrals
    • Surface Integrals
    • Vector Fields
    • Integrals Over Vector Fields
    • The Gradient Theorem
    • The Theorems of Vector Calculus

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