Math21b: Linear Algebra and Differential Equations

is an introduction to linear algebra, including linear
transformations, determinants, eigenvectors, eigenvalues,
inner products and linear spaces. As applications, the
course introduces discrete dynamical systems, differential
equations, Fourier series as well as some partial differential
equations. This course is taught in 6 sections.

Instructors:

 Samik Basu
 Veronique Godin
 David Helm
 Thomas Lam
 Matt Leingang
 Oliver Knill

Course assistants:

See the Section page

Lecture times:

 MoWeFr 910
 MoWeFr 1011
 MoWeFr 1112
 TuTh 1011:30
 TuTh 11:301:00

Problem Sections:

See the Sections page.

Website:

http://www.courses.fas.harvard.edu/~math21b/

Text:

We use
Otto Bretscher, Linear Algebra with Applications,
third edition. PrenticeHall, Upper Saddle River,
NJ, 2001. This great book has been used for many years here.

About this course:

 teaches methods to solve systems of linear equations Ax = b,
 allows you to analyze and solve systems of linear differential equations,
 you learn to solve discrete linear dynamical systems like Markov processes
 you will master the technique of least square fit with arbitrary function sets
and know why it works,
 you will learn the basics of Fourier series and how to use it to solve linear
partial differential equations,
 prepares you for the further study in other scientific fields
like for example quantum mechanics, combinatorics
 it improves thinking skills, problem solving skills, algorithmic and the
ability to use more abstract tools.

Homework:

HW will be assigned in each class and is due
the next lecture. TueThu section HW is splitted
usually 1/3 from Tue to Thu and 2/3 from Thu to Tue.

Exams:

We have two midterm exams and one final exam. Here are the
midterm exam dates:
1. Midterm:  Wed 3/7  78:30pm  Hall C 
2. Midterm:  Tue 4/10  78:30pm  Hall C 

Grades:

Grade1 Grade2
First hourly 20 20
Second hourly 20 20
Homework 20 20
Lab 5
Final exam 35 40

Total 100 100
Grade = Max(Grade1,Grade2)
Doing the mathematica project will soften a bit the final
exam.

Calendar:


So Mo Tu We Th Fr Sa

S M T W T F S
31 1 2 3 31. Jan Plenary introduction
4 5 6 7 8 9 10 1 5. Feb Lectures start
11 12 13 14 15 16 17 2
18 19 20 21 22 23 24 3
25 26 27 28 1 2 3 4 March
4 5 6 7 8 9 10 5 March 7. First midterm Hall C
11 12 13 14 15 16 17 6
18 19 20 21 22 23 24 7
25 26 27 28 29 30 31 Spring recess
1 2 3 4 5 6 7 8 April
8 9 10 11 12 13 14 9 April 10 Second midterm Hall C
15 16 17 18 19 20 21 10
22 23 24 25 26 27 28 11
29 30 1 2 3 4 5 12 May
6 7 8 9 10 11 12
13 14 15 16 17 18 19


Day to day syllabus: A more detailed lecture plan.

Lecture Date Book Topic
1. Week: Systems of linear equations
Lect 1 2/5 1.1 introduction to linear systems
Lect 2 2/7 1.2 matrices and GaussJordan elimination
Lect 3 2/9 1.3 on solutions of linear systems
2. Week: Linear transformations
Lect 4 2/12 2.1 linear transformations and their inverses
Lect 5 2/14 2.2 linear transformations in geometry
Lect 6 2/16 2.34 matrix product and inverse
3. Week: Linear subspaces
Lect 7 2/19 Presidents day, no class
Lect 8 2/21 3.1 image and kernel
Lect 9 2/23 3.2 bases and linear independence
4. Week: Dimension and linear spaces
Lect 10 2/26 3.3 dimension
Lect 11 2/28 3.4 coordinates
Lect 12 3/2 4.1 linear spaces
5. Week: Orthogonality
Lect 13 3/5 review for first midterm
Lect 14 3/7 4.1 linear spaces II
Lect 15 3/9 5.1 orthonormal bases and orthogonal projections
6. Week: Datafitting
Lect 16 3/12 5.2 GramSchmidt and QR factorization
Lect 17 3/14 5.3 orthogonal transformations
Lect 18 3/16 5.4 least squares and data fitting
7. Week: Determinants
Lect 19 3/19 6.1 determinants 1
Lect 20 3/21 6.2 determinants 2
Lect 21 3/23 7.12 eigenvalues
Spring break
8. Week: Diagonalization
Lect 22 4/2 7.3 eigenvectors
Lect 23 4/4 7.4 diagonalization
Lect 24 4/6 7.5 complex eigenvalues
9. Week: Stability and symmetric matrices
Lect 25 4/9 Review for second midterm
Lect 26 4/11 7.6 stability
Lect 27 4/13 8.1 symmetric matrices
10. Week: Differential equations
Lect 27 4/16 9.1 differential equations I
Lect 28 4/18 9.2 differential equations II
Lect 29 4/20 9.4 nonlinear systems
11. Week: Function spaces
Lect 30 4/23 4.2 function spacess
Lect 31 4/25 9.3 linear differential operators
Lect 32 4/27 5.5 inner product spaces
12. Week: Partial differential equations
Lect 33 4/30 5.5 Fourier theory I
Lect 34 5/2 5.5 Fourier theory II
Lect 35 5/4 Partial differential equations
