Math21b: Linear Algebra and Differential Equations

is an introduction to linear algebra, including linear
transformations, determinants, eigenvectors, eigenvalues,
inner products and linear spaces. As for applications, the
course introduces discrete dynamical systems, differential
equations, Fourier series as well as some partial differential
equations. Other highlights are applications in statistics like
Markov chains or data fitting with arbitrary functions.
The course is taught in 6 sections.

Instructors:


Course assistants:

See the Section page

Lecture times:

 MoWeFr 1011
 MoWeFr 1112
 MoWeFr 121
 TuTh 1011:30
 TuTh 11:301:00

Problem Sections:

See the Sections page.
MQC:

Website:

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

Text:

We use
Otto Bretscher, Linear Algebra with Applications,
fourth edition. PrenticeHall, Upper Saddle River,
NJ, 2008. This is the latest edition.

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 discrete 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 or combinatorics or statistics
 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 split
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:  Tue 3/3  78:30pm  Hall C 
2. Midterm:  Tue 4/7  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

Calendar:


So Mo Tu We Th Fr Sa

25 26 27 28 29 30 31 0 Jan 28 intro meeting in hall B
1 2 3 4 5 6 7 1 Feb 2 first day of 21a lectures
8 9 10 11 12 13 14 2
15 16 17 18 19 20 21 3 Feb 16, presidents day
22 23 24 25 26 27 28 4
1 2 3 4 5 6 7 5 March 3, first midterm
8 9 10 11 12 13 14 6
15 16 17 18 19 20 21 March 21March 29 spring break
22 23 24 25 26 27 28 7
29 30 31 1 2 3 4 8
5 6 7 8 9 10 11 9 April 7, second midterm
12 13 14 15 16 17 18 10
19 20 21 22 23 24 25 11
26 27 28 29 30 1 2 12 May 2, reading period starts


Day to day syllabus:

Lecture Date Book Topic
1. Week: Systems of linear equations
Lect 1 2/2 1.1 introduction to linear systems
Lect 2 2/4 1.2 matrices and GaussJordan elimination
Lect 3 2/6 1.3 on solutions of linear systems
2. Week: Linear transformations
Lect 4 2/9 2.1 linear transformations and their inverses
Lect 5 2/11 2.2 linear transformations in geometry
Lect 6 2/13 2.34 matrix product and inverse
3. Week: Linear subspaces
Lect 7 2/16 Presidents day, no class
Lect 8 2/18 3.1 image and kernel
Lect 9 2/20 3.2 bases and linear independence
4. Week: Dimension and linear spaces
Lect 10 2/23 3.3 dimension
Lect 11 2/25 3.4 coordinates
Lect 12 2/27 4.1 linear spaces
5. Week: Orthogonality
Lect 13 3/1 review for first midterm
Lect 14 3/3 4.1 linear spaces II
Lect 15 3/5 5.1 orthonormal bases and orthogonal projections
6. Week: Datafitting
Lect 16 3/8 5.2 GramSchmidt and QR factorization
Lect 17 3/10 5.3 orthogonal transformations
Lect 18 3/12 5.4 least squares and data fitting
7. Week: Determinants
Lect 19 3/15 6.1 determinants 1
Lect 20 3/17 6.23 determinants 2
Lect 21 3/19 7.12 eigenvalues
Spring break 3/223/30
8. Week: Diagonalization
Lect 22 3/29 7.3 eigenvectors
Lect 23 4/31 7.4 diagonalization
Lect 24 4/2 7.5 complex eigenvalues
9. Week: Stability and symmetric matrices
Lect 25 4/5 Review for second midterm
Lect 26 4/7 7.6 stability
Lect 27 4/9 8.1 symmetric matrices
10. Week: Differential equations
Lect 28 4/12 9.1 differential equations I
Lect 29 4/14 9.2 differential equations II
Lect 30 4/16 9.4 nonlinear systems
11. Week: Function spaces
Lect 31 4/19 4.2 linear trafos on function spaces
Lect 32 4/21 9.3 linear differential operators
Lect 33 4/23 5.5 inner product spaces
12. Week: Partial differential equations
Lect 34 4/26 5.5 Fourier theory I
Lect 35 4/28 5.5 Fourier theory II
Lect 36 4/30 Partial differential equations
Spring reading period 5/15/12
Spring exam period 5/125/21
