M A T H 2 1 B
Mathematics Math21b Spring 2009
Linear Algebra and Differential Equations
Syllabus
Course Head: Oliver Knill
Office: SciCtr 434

Syllabus Broshure [PDF] , Slides intro meeting [PDF], and [Ipod 100 Meg!] Day to Day lecture plan

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:
• Oliver Knill
Course assistants: See the Section page
Lecture times:
• Mo-We-Fr 10-11
• Mo-We-Fr 11-12
• Mo-We-Fr 12-1
• Tu-Th 10-11:30
• Tu-Th 11:30-1:00
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. Prentice-Hall, Upper Saddle River, NJ, 2008. This is the latest edition.
• 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. Tue-Thu 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 7-8:30pm Hall C 2. Midterm: Tue 4/7 7-8:30pm Hall C
```                                          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 21-March 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 Gauss-Jordan 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  2.3-4 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  Gram-Schmidt 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  6.2-3 determinants 2
Lect 21  3/19  7.1-2 eigenvalues

Spring break 3/22-3/30

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 5/1-5/12
Spring exam    period 5/12-5/21
```
Please send questions and comments to math21b@fas.harvard.edu
Math21b (Exam Group 1)| Oliver Knill | Spring 2009 | Department of Mathematics | Faculty of Art and Sciences | Harvard University