 Math21b: Linear Algebra and Differential Equations
This 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: Oliver Knill, SC434, knill@math
Janet Chen, SC 321g, jjchen@math
Section page of Janet
 Course assistants:
Philip Powell ppowell@fas
Tien Anh Nguyen tanguyen@fas
Goutham Seshadri seshadri@fas
Azra Pravdic pravdic@fas
 Lectures:
MoWeFr 1011
MoWeFr 1112
TuTh 1011:30
 Problem Sections:
Tue, in SciC 111 7:008:00pm (Goutham)
Wed, in SciC 101B 8:3010:00pm (Philip)
Thu, in SciC 116 8:309:30pm (Tien Anh)
Sun, in SciC 222 8:309:30pm (Aki)
 Office hours:
Oliver: Mo,We,Fr 1516
Janet: Mo,Th 1516
 Website: http://www.courses.fas.harvard.edu/~math21b/
Section page of Janet
 Text:
Otto Bretscher, Linear Algebra with Applications,
third edition. PrenticeHall, Upper Saddle River,
NJ, 2001.
 About this course:
 teaches methods to solve systems of linear equations Ax = b,
 allows you to analyze and solve systems of linear
differential equations,
 solve discrete linear dynamical systems. Example:
Markov processes,
 learn to do least square fit with arbitrary function sets
and also 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 fields of
mathematics and its applications, like for example quantum
mechanics, combinatorics,
 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
differently but the total homework is the same.
 Exams:
Two midterm exams and one final exam.
 Grades:
First and second hourly 20 % each
Homework 20 %
Final exam 40 %
 Calendar: (12 weeks of class)

So Mo Tu We Th Fr Sa

19 20 21 22 23 24 25 20. September, Orientation
+++
  
26 27 28 29 30 1 2 1 27. Start of classes
3 4 5 6 7 8 9 2
10 11 12 13 14 15 16 3
17 18 19 20 21 22 23 4
24 25 26 27 28 29 30 5 27. Oct, 1. Hourly 6:30 SciC D
31 1 2 3 4 5 6 6 November
7 8 9 10 11 12 13 7 11. Columbus day
14 15 16 17 18 19 20 8
21 22 23 24 25 26 27 9 2527. Thanksgiving, no class
28 29 30 1 2 3 4 10 1. Dec. 2. Hourly 6:00 SciC D
5 6 7 8 9 10 11 11
12 13 14 15 16 17 18 12
19 20 21 22 23 24 25 13 winter break 22.  3. Jan
  
+++
26 27 28 29 30 31 1
2 3 4 5 6 7 8 4. Jan 14. Jan Reading period
9 10 11 12 13 14 15
16 17 18 19 20 21 22 20. January Final: 9:15AM
23 24 25 26 27 28 29 Boylson Hall 110
30 31

 Day to day syllabus:
Lecture Date Book Topic
1. Week: Systems of linear equations
Lect 1 9/27 1.1 introduction to linear systems
Lect 2 9/29 1.2 matrices and GaussJordan elimination
Lect 3 10/1 1.3 on solutions of linear systems
2. Week: Linear transformations
Lect 4 10/4 2.1 linear transformations and their inverses
Lect 5 10/6 2.2 linear transformations in geometry
Lect 6 10/8 2.34 matrix algebra (product and inverse)
3. Week: Linear subspaces
Lect 7 10/11 Columbus day, no class
Lect 8 10/13 3.1 image and kernel
Lect 9 10/15 3.2 subspaces, bases and linear independence
4. Week: Dimension
Lect 10 10/18 3.3 dimension
Lect 11 10/20 3.4 coordinates
Lect 12 10/22 4.1 linear spaces
5. Week: Orthogonality
Lect 13 10/25 4.1 linear spaces II and review
Lect 14 10/27 *** Review for first midterm Midterm
Lect 15 10/29 5.1 orthonormal bases and orthogonal projections
6. Week: Datafitting
Lect 16 11/1 5.2 GramSchmidt and QR factorization
Lect 17 11/3 5.3 orthogonal transformations
Lect 18 11/5 5.4 least squares and data fitting
7. Week: Determinants
Lect 19 11/8 6.1 determinants 1
Lect 20 11/10 6.2 determinants 2
Lect 21 11/12 7.12 eigenvalues
8. Week: Diagonalization
Lect 22 11/15 7.3 eigenvectors
Lect 23 11/17 7.4 diagonalization
Lect 24 11/19 7.5 complex eigenvalues
9. Week: Stability and symmetric matrices
Lect 25 11/22 7.6 stability
Lect 26 11/24 8.1 symmetric matrices
11/26 THANKSGIVING, no class
10. Week: Differential equations
Lect 27 11/29 9.1 Differential equations I
Lect 28 12/1 *** Review for second midterm
Lect 29 12/3 9.2 Differential equations II
11. Week: Function spaces
Lect 30 12/6 9.4 Nonlinear systems
Lect 31 12/8 4.2 Function spaces
Lect 32 12/10 9.3 Linear differential operators
12. Week: Partial differential equations
Lect 33 12/13 5.5 Inner product spaces
Lect 34 12/15 5.5 Fourier theory
Lect 35 12/17 (handout) Partial differential equations
13. Week: Review and Vacation
Lect 36 12/20 Review Last homework due
