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 3 sections.

Instructors:


Course assistants:

Head CA:
See the Section page

Lecture times:

 MoWeFr 1011
 MoWeFr 1112
 MoWeFr 121

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. We plan to have the following
midterm exam dates:
1. Midterm:  Thu 10/7  78:30pm  Hall D 
2. Midterm:  Thu 11/4  78:30pm  Hall D 
Final Exam:  Fri 12/17  TBA  TBA 

Grades:

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

Total 100 100

Calendar: (Registrar)


So Mo Tu We Th Fr Sa

29 30 31 1 2 3 4 0 Sep 1: intro meeting in Hall B
5 6 7 8 9 10 11 1 Sep 6: labour day Sep 8: 1. lect
12 13 14 15 16 17 18 2
19 20 21 22 23 24 25 3
26 27 28 29 30 1 2 4
3 4 5 6 7 8 9 5 Oct 7: first hourly
10 11 12 13 14 15 16 6 Oct 11: Columbus day
17 18 19 20 21 22 23 7
24 25 26 27 28 29 30 8
31 1 2 3 4 5 6 9 Nov 4: second hourly
7 8 9 10 11 12 13 10 Nov 11: Veterans day
14 15 16 17 18 19 20 11
21 22 23 24 25 26 27 12 Nov 2528: thanksgiving holiday
28 29 30 1 2 3 4 13 Dec 3: last day of class
5 6 7 8 9 10 11 14 Dec 412: reading period
12 13 14 15 16 17 18 15 Dec 1321: exam period
19 20 21 22 23 24 25 16


Day to day syllabus:

Lecture Date Book Topic
1. Week: Systems of linear equations
9/6 labour day
Lect 1 9/8 1.1 introduction to linear systems
Lect 2 9/10 1.2 matrices and GaussJordan elimination
2. Week: Linear transformations
Lect 3 9/13 1.3 on solutions of linear systems
Lect 4 9/15 2.1 linear transformations and their inverses
Lect 5 9/17 2.2 linear transformations in geometry
3. Week: Linear subspaces
Lect 6 9/20 2.3 matrix product
Lect 7 9/22 2.4 the inverse
Lect 8 9/24 3.1 image and kernal
4. Week: Dimension and linear spaces
Lect 9 9/27 3.2 bases and linear independence
Lect 10 9/29 3.3 dimension
Lect 11 10/1 3.4 coordinates
5. Week: Orthogonality
Lect 12 10/4 4.1 linear spaces
Lect 13 10/6 review for first midterm
Lect 14 10/8 5.1 orthonormal bases and orthogonal projections
6. Week: Datafitting
10/11 Columbus day
Lect 15 10/13 5.2 GramSchmidt and QR factorization
Lect 16 10/15 5.3 orthogonal transformations
7. Week: Determinants
Lect 17 10/18 5.4 least squares and data fitting
Lect 18 10/20 6.1 determinants 1
Lect 19 10/22 6.23 determinants 2
8. Week: Diagonalization
Lect 20 10/25 7.12 eigenvalues
Lect 21 10/27 7.3 eigenvectors
Lect 22 10/29 7.4 diagonalization
9. Week: Stability and symmetric matrices
Lect 23 11/1 7.5 complex eigenvalues
Lect 24 11/3 review for second midterm
Lect 25 11/5 7.6 stability
10. Week: Differential equations
Lect 26 11/8 8.1 symmetric matrices
Lect 27 11/10 9.1 differential equations I
Lect 28 11/12 9.2 differential equations II
11. Week: Function spaces
Lect 29 11/15 9.4 nonlinear systems
Lect 30 11/17 4.2 linear trafos on function spaces
Lect 31 11/19 9.3 inhomogeneous differential equations
12. Week: Inner product spaces
Lect 32 11/22 9.3 inhomogeneous differential equations
Lect 33 11/24 4.2 inner product spaces
11/25 Thanksgiving
13. Week: Partial differential equations
Lect 34 11/29 HH Fourier series
Lect 35 12/1 HH Parseval identity
Lect 36 12/3 HH Partial differential equations
12/412/12 Fall reading period
12/1312/21 Fall exam period
