Lectures

Date

Section in the book (Lay)

Section in the book (Hardy)

Topic

Week 1

Tues Apr 4^th

Thurs Apr 6th

Supp Notes

8.1

8.2

8.3

8.4

Intro

Algebraic theory of complex numbers

Geometric theory of complex numbers

Polar forms of complex numbers

Complex polynomials and roots

Week 2

Tues Apr 11^th

Thurs Apr 13th

Ch 1.1

Ch 1.2

(Ch 4.6)

1.1

1.2

Linear systems of equations

Echelon forms and ranks

Week 3

Tues Apr 18^th

Thurs Apr 20th

Ch 1.6 & Ch 1.10

Ch 2.1 & Ch 2.4

Ch 2.2-2.3

1.3

2.1

2.2

Applications of linear systems

Matrix algebra

Inverses

Week 4

Tues Apr 25^th

Thurs Apr 27th

Ch 2.5

Ch 2.6-2.7

Ch 1.3-1.4

(Ch 4.1)

2.3

2.4

3.1

LU factorization

Applications

Spaces of vectors

Week 5

Tues May 2^th

Thurs May 4th

Ch 1.5 & Ch 1.7

(Ch 4.3)

3.2

Span, Linear independence

Mid-term

(here is a sample midterm) (here are the sample midterm solns)

Week 6

Tues May 9^th

Thurs May 11th

Ch 2.8-2.9

(Ch 4.2-4.7)

3.2

Bases, dimension, co-ordinate systems, change of basis

Subspaces: Null space, column space, row space

Week 7

Tues May 16^th

Thurs May 18th

Ch 1.8-1.9

(Ch 4.2)

Ch 6.1

Ch 6.2-6.4

3.3

3.4

5.2

4.2

Linear transformations in Rn

Dot products, norms of vectors

Orthogonality

Week 8

Tues May 23^th

Thurs May 25th

Ch 6.5-6.6

Ch 6.7

4.3

4.4

Orthogonal subspaces, projections, bases

Applications

Week 9

Tues May 30^th

Thurs Jun 1st

(Ch 3)??

Ch 5.1-5.2

Ch 5.3

Ch 5.6-5.8

(Ch 4.8-4.9)

(5.1)??

6.1

6.2

6.3

6.4

(Determinants)??

Eigenvalues

Diagonalization

Applications

Week 10

Tues Jun 6^th

Thurs Jun 8th

(Ch 4)

7

General vector spaces

Review

Finals exam

Tues Jun 13^th

4pm-7pm

Here is an example final

Here are solutions to the example final

DONE!