# Study Materials

## Study Guides

The Study Guides include pre-tests, photographs of every chalkboard used in the videotapes, reading assignments in the supplementary notes and textbook, and exercises with solutions.

LEC # TOPICS PHOTOS, READINGS, and EXERCISES SOLUTIONS
Part I: Vector Arithmetic
1 The "Game" of Mathematics
2 Three-Dimensional Vectors (PDF)
3 Three-Dimensional Vectors (PDF)
4 The Dot Product (PDF)
5 The Cross Product (PDF)
6 Equations of Lines & Planes (PDF)
Part II: Vector Calculus
1 Vector Functions of a Scalar Variable (PDF)
2 Tangential & Normal Vectors (PDF)
3 Polar Coordinates (PDF)
4 Vectors in Polar Coordinates (PDF)
Part III: Partial Derivatives
1 n-Dimensional Vector Spaces
2 Calculus of Several Variables (PDF)
3 Directional Derivatives (PDF)
4 The Chain Rule (PDF)
5 Integrals Involving Parameters (PDF)
6 Exact Differentials (PDF)
Part IV: Matrix Algebra
1 Linearity Revisited (PDF)
2 The "Game" of Matrices (PDF)
3 Inverting a Matrix (PDF)
4 Inverting More General Systems of Equations (PDF)
5 Maxima and Minima in Several Variables (PDF)
Part V: Multiple Integration
1 Double Multiple Sums
2 The Fundamental Theorem (PDF) (PDF 2.3MB)
3 Multiple Integration and the Jacobian (PDF)
4 Introduction to Line Integrals (PDF)
5 Green's Theorem (PDF)

## Supplementary Notes for Multivariable Calculus, Parts I through V

The Supplementary Notes include prerequisite materials, detailed proofs, and deeper treatments of selected topics.

• Chapter 1: An Introduction to Mathematical Structure
• Chapter 2: An Introduction to Vector Arithmetic
• Chapter 3: An Introduction to Vector Calculus
• Chapter 4: An Introduction to Functions of Several Real Variables
• Chapter 5: Derivatives in n-Dimensional Spaces
• Chapter 6: Matrix Algebra in the Study of Functions of Several Variables
• Chapter 7: Applications of Linear Algebra to Non-Linear Functions

Textbook: The course makes reference to the out-of-print textbook cited below, but any newer textbook will suffice to expand on topics covered in the video lectures. Thomas, George B. Calculus and Analytic Geometry. Addison-Wesley, 1968. ISBN: 9780201075250.