Math 4A Course Topics

 

Multivariable Calculus (7th ed.) by Howard Anton (Wiley)

 

Categories:      1.    Must be covered.

                        2.    Must be covered at least briefly.

                        3.    Do not cover unless you have extra time after doing 1 and 2.

 

Category    Section

Section

Topic

 

1

 12.1

Rectangular Coordinates in 3-Space

1

 12.2

Vectors

1

 12.3

Dot Products; Projections

1

 12.4

Cross Products

1

 12.5

Parametric Equations of Lines

1

 12.6

Planes in 3-Space

1

 12.7

Quadric Surfaces

2

 12.8

Cylindrical and Spherical Coordinates

1

 13.1

Introductions to Vector-Valued Functions

1

 13.2

Calculus of Vector-Valued Functions              

1

 13.3

Change of Parameters; Arc Length

1

 13.4

Unit Tangent and Normal Vectors

1

 13.5

Curvature

1

 13.6

Motion Along a Curve

3

 13.7

Kepler’s Laws of Planetary Motion

1

 14.1

Functions of Two or More Variables

1

 14.2

Limits and Continuity

1

 14.3

Partial Derivatives

1

 14.4

Differentiability, Local Linearity, and Differentials

1

 14.5

The Chain Rule

1

 14.6

Directional Derivatives and Gradients

1

 14.7

Tangent Planes and Normal Vectors

1

 14.8

Maxima and Minima of Functions of Two Variables

1

 14.9

Lagrange Multipliers             

1

 15.1

Double Integrals

1

 15.2

Double Integrals over Nonrectangular Regions

1

 15.3

Double Integrals for Polar Coordinates

1

 15.4

Parametric Surfaces; Surface Areas

1

 15.5

Triple Integrals

1

 15.6

Centroid, Center of Gravity, Theorem of Pappas

1

 15.7

Triple Integrals in Cylindrical and Spherical

3

 15.8

Change of Variables in Multiple Integrals

1

 16.1

Vector Fields                                     

1

 16.2

Line Integrals

1

 16.3

Independence of Path; Conservative Vector Fields

1

 16.4

Green's Theorem

1

 16.5

Introduction to Surface Integrals

1

 16.6

Application of Surface Integrals; Flux

1

 16.7

The Divergence Theorem

1

 16.8

Stoke's Theorem