Multivariable Calculus

 

Table of Contents

 

Chapter 1: Vectors and Geometry

Chapter 2: Vector-Valued Functions and Curves

Chapter 3: Partial Differentiation and Applications

  1. Functions of Several Variables
  2. Graph of a Function
  3. Level Curves and Level Surfaces
  4. Open and Closed Sets
  5. Limits and Continuity
  6. Partial Derivatives
  7. Higher Partial Derivatives
  8. Tangent Planes
  9. Linear (or Affine) Approximation
  10. Differentiability
  11. The Differential of a Function
  12. The Chain Rule
  13. Directional Derivatives and Gradients
  14. The Direction of the Fastest Increase
  15. Tangent Planes — Revisited
  16. Implicit Functions
  17. Taylor’s Theorem
  18. The Maxima and Minima

  19. The Constrained Extrema and Lagrange Multipliers

Chapter 4: Multiple Integrals

Chapter 5: Vector Calculus