| 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 3 sections.
|
| Instructors:
|
|
| Course assistants:
|
See the Section page
|
| Lecture times:
|
- Mo-We-Fr 10-11 (Leila Khatami, SC 112)
- Mo-We-Fr 11-12 (Evan Bullock, SC 109)
- Mo-We-Fr 12-1 (Yum-Tong Siu, SC 309a)
|
| 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. Prentice-Hall, 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.
|
| Exams:
|
We have two midterm exams and one final exam. Here are the
midterm exam dates:
| First Midterm | Wed 10/24
| 7-8:30pm | Jefferson 256 |
| Second Midterm | Wed 11/28
| 7-8:30pm | Science
Center Hall A |
|
| Grades:
|
Grade
First hourly 20
Second hourly 20
Homework 20
Final exam 40
-------------------------------------------------------
Total 100
|
| Calendar:
|
--------------------------------------------------------
So Mo Tu We Th Fr Sa
--------------------------------------------------------
S M T W T F S
1 September
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22 Sept 17 Plenary introduction
23 24 25 26 27 28 29 1 Sept 24 Lectures start
30 1 2 3 4 5 6 2 October
7 8 9 10 11 12 13 3 Oct 8 Columbus Day
14 15 16 17 18 19 20 4
21 22 23 24 25 26 27 5 Oct 24 First midterm
28 29 30 31 1 2 3 6 November
4 5 6 7 8 9 10 7
11 12 13 14 15 16 17 8 Nov 12 Veteran's Day
18 19 20 21 22 23 24 9 Nov 22-25 Thanksgiving Recess
25 26 27 28 29 30 1 10 Nov 28 Second midterm
2 3 4 5 6 7 8 11 December
9 10 11 12 13 14 15 12
16 17 18 19 20 21 22 13 Dec 19 Winter Recess starts
23 24 25 26 27 28 29
30 31 1 2 3 4 5 January Jan 2 Reading Period starts
6 7 8 9 10 11 12
13 14 15 16 17 18 19 Jan 13 Reading Period ends, Jan 14 Exam Period starts
20 21 22 23 24 25 26 Jan 23 Exam Period ends
27 28 29 30 31
---------------------------------------------------------
|
| Day to day syllabus: A more detailed lecture plan.
|
Lecture Date Book Topic
1. Week: Systems of linear equations
Lect 1 9/24 1.1 introduction to linear systems
Lect 2 9/26 1.2 matrices and Gauss-Jordan elimination
Lect 3 9/28 1.3 on solutions of linear systems
2. Week: Linear transformations
Lect 4 10/1 2.1 linear transformations and their inverses
Lect 5 10/3 2.2 linear transformations in geometry
Lect 6 10/5 2.3-4 matrix product and inverse
3. Week: Linear subspaces
No class 10/8 Columbus Day
Lect 7 10/10 3.1 image and kernel
Lect 8 10/12 3.2 bases and linear independence
4. Week: Dimension and linear spaces
Lect 9 10/15 3.3 dimension
Lect 10 10/17 3.4 coordinates
Lect 11 10/19 4.1 linear spaces
5. Week: Orthogonality
Review 10/22 Review for first midterm
Lect 12 10/24 4.1 linear spaces II, First Midterm
Lect 13 10/26 5.1 orthonormal bases and orthogonal projections
6. Week: Datafitting
Lect 14 10/29 5.2 Gram-Schmidt and QR factorization
Lect 15 10/31 5.3 orthogonal transformations
Lect 16 11/2 5.4 least squares and data fitting
7. Week: Determinants
Lect 17 11/5 6.1 determinants 1
Lect 18 11/7 6.2 determinants 2
Lect 19 11/9 7.1-2 eigenvalues
8. Week: Diagonalization
No class 11/12 Veterans's Day
Lect 20 11/14 7.3 eigenvectors
Lect 21 11/16 7.4 diagonalization
9. Week: Stability and symmetric matrices
Lect 22 11/19 7.5 complex eigenvalues
Lect 23 11/21 7.6 stability
No class 11/23 Thanksgiving Recess
10. Week: Differential equations
Review 11/26 Review for second midterm
Lect 24 11/28 8.1 symmetric matrices Second Midterm
Lect 25 11/30 9.1 differential equations I
11. Week: Function spaces
Lect 26 12/3 9.2 differential equations II
Lect 27 12/5 Nonlinear systems (from notes of Bretscher)
Lect 28 12/7 4.2 function spaces
12. Week: Partial differential equations
Lect 29 12/10 9.3 linear differential operators
Lect 30 12/12 5.5 inner product spaces
Lect 31 12/14 Fourier theory I (from notes)
13. Week: Partial differential equations
Lect 32 12/17 Fourier theory II, Partial differential equations
(from notes)
|