April, 1996

MATH 240 Multivariate Calculus

Course Outline

1. Functions of Many Variables

a. Surface Graphics

b. Contour Diagrams

c. Limits and Continuiity

2. Vectors

a. Displacement Vectors

b. Vectors in General

c. Dot and Cross Products

3. Differentiation of Functions of Many Variables

a. Partial Derivatives

b. The Differential

c. Gradients and Directional Derivatives

d. Chain Rule

e. Second Order Partial Derivatives

f. Taylor Approximations

4. Optimization

a. Local Extrema

b. Global Extrema

c. LaGarange Multipliers

5. Integrating Functions of Many Variables

a. Definite Integral of a Function of Two Variable

b. Iterated Integrals

c. Integrals of Functions of Three Variables

d. Polar Coordinates

e. Cylindrical and Spherical Coordinates

f. Changes of Variables

6. Parametric Curves and Surfaces

a. Parametric Curves

b. Motion, Velocity and Acceleration

c. Parametric Surfaces

d. Implicit Function Theorem

7. Vector Fields

a. Vector Fields

b. Flow of a Vector Field

c. Divergence of a Vector Field

d. Curl of a Vector Field

e. Stoke's Theorem

8. Line Integrals

a. Definition of a Line Integral

b. Computing Line Integrals

c. Gradient Fields

d. Green's Theorem

Prerequisite: MATH 141 with a grade of "C" or better.

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