Week

Topics covered

Chapter

1

Triple Integrals in Cylindrical and Spherical Coordinates

Substitutions in Multiple Integrals

Thomas Calc.

15.6

15.7

2

Line Integrals, Vector Fields, Work, Flow, Circulation, Flux

Path Independence, Potential Functions and Conservative Fields, Green’s Theorem

16.1-16.2

 

 

16.3-16.4

3

Surface Area and Surface Integrals, Parametrized Surfaces

Stoke’s Theorem, Divergence Theorem

16.5-16.6

 

16.7-16.8

4

Systems of Linear Equations, Matrices

Determinants

El. Lin. Alg

1

2

5

Vectors in 2-space and 3-space

Real Vector Spaces, Subspaces, Linear Independence

3

5.1 – 5.3

6

Basis and Dimension, Row Space, Rank and Nullity

Inner Product Spaces, Gram-Schmidt Process, Orthogonal Matrices

5.4 – 5.6

6

7

Eigenvalues and Eigenvectors

Diagonalization

7.1

7.2-7.3