Lectures

Date

Section in the book (Lay)

Section in the book (Hardy)

Topic
(click for the notes I use to give my lectures)

Scanned actual notes written in class

Week 1

Tues Jan 8^th

Thurs Jan 10^th

Supp Notes

8.1

8.2

8.3

Intro

Algebraic theory of complex numbers

Geometric theory of complex numbers

Polar forms of complex numbers

Week 1 Lectures 1 and 2

Week 2

Tues Jan 15^th

Thurs Jan 17^th

Supp Notes

Ch 1.1

Ch 1.2

(Ch 4.6)

8.4

1.1

1.2

Complex polynomials and roots

Linear systems of equations

Echelon forms and ranks

Week 2 Lecture 3

Week 2 Lecture 4

Week 3

Tues Jan 22^nd

Thurs Jan 24^th

Ch 1.6 & Ch 1.10

Ch 2.1 & Ch 2.4

1.3

2.1

Applications of linear systems

Matrix algebra

Week 3 Lecture 5

Week 3 Lecture 6

Week 4

Tues Jan 29^th

Thurs Jan 31^st

Ch 2.2-2.3

Ch 2.5

Ch 2.6-2.7

2.2

2.3

2.4

Inverses

LU factorization

Applications

Week 4 Lecture 7

Week 4 Lecture 8

Week 5

Tues Feb 5^th

Thurs Feb 7^th

Ch 3

Ch 1.3-1.4

Ch 1.5 & Ch 1.7

(Ch 4.3)

5

3.1

3.2

Determinants

Spaces of vectors

Span, Linear independence

Mid-term

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

Week 5 Lecture 9

Week 5 Lecture 10 = MIDTERM!

Here is the midterm exam and its solutions

Week 6

Tues Feb 12^th

Thurs Feb 14^th

Ch 2.8-2.9

(Ch 4.2-4.7)

3.2

Span, Linear independence

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

Subspaces: Null space, column space, row space

Week 6 Lecture 11

Week 6 Lecture 12

Week 7

Tues Feb 19^th

Thurs Feb 21^st

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 7 Lecture 13

Week 7 Lecture 14

Week 8

Tues Feb 26^th

Thurs Feb 28^th

Ch 6.5-6.6

4.3

Orthogonal subspaces, projections, bases

Week 8 Lecture 15

Week 8 Lecture 16

Week 9

Tues Mar 5^th

Thurs Mar 7st

Ch 6.7

Ch 5.1-5.2

Ch 5.3

4.4

6.1

6.2

Applications

Eigenvalues

Diagonalization

Week 9 Lecture 17

Week 9 Lecture 18

Week 10

Tues Mar 12^th

Thurs Mar 14^th

Ch 5.6-5.8

(Ch 4.8-4.9)

(Ch 4)

6.3

6.4

(7)

Applications

(General vector spaces)

Review

Week 10 Lecture 19

Review

Week 10 Lecture 20

Finals exam

Weds Mar 20^th

12pm-3pm

Here is an example final

Here are solutions to the example final

DONE!