Math21b: Linear Algebra and Differential Equations

This course 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.

Instructors:


Course assistants:

Head CA:

Lecture times:

 MoWeFr 910
 MoWeFr 1011
 MoWeFr 1112
 MoWeFr 121
 TueTh 1011:30
 TueTh 11:301

MQC:

This spring the MQC for Math 21b is in room 309.
For details, see the MQC page.

Website:

http://www.courses.fas.harvard.edu/~math21b bookmark this!
https://canvas.harvard.edu/courses/1803 canvas
http://isites.harvard.edu/icb/icb.do?keyword=k109254 Isites

Text:

We use
Otto Bretscher, Linear Algebra with Applications.
The fourth or 5th edition both should work as we
post HW independent of editions.

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 class.
TTh sections submit two homework on Tuesday's except for the first week.

Exams:

We have two midterm exams and one final exam. We plan to have the following
midterm exam dates:
1. Midterm:   78:30pm  Hall B 
2. Midterm:   78:30pm  Hall B 

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 week Events

25 26 27 28 29 30 31 Jan 26: 8:30AM SC B, 29/30 start
1 2 3 4 5 6 7 1
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 First midterm March 3
8 9 10 11 12 13 14 6
15 16 17 18 19 20 21 Spring break Mar 1422
22 23 24 25 26 27 28 7
29 30 31 1 2 3 4 8
5 6 7 8 9 10 11 9 Second midterm April 7
12 13 14 15 16 17 18 10
19 20 21 22 23 24 25 11
26 27 28 29 30 1 2 12 April 29 last day of classes
3 4 5 6 7 8 9 Until May 6: reading period
10 11 12 13 14 15 16 May 716 exam period


Day to day syllabus: (updated on February 8 as Feb 9 is a snow day)

Lecture Date Book Topic
Week 0: Systems of linear equations
Lect 1 F 1.1 introduction to linear systems
Week 1: Systems of linear equations
Lect 2 M 1.2 matrices and GaussJordan elimination
Lect 3 W 1.3 on solutions of linear systems
Lect 4 F 2.1 linear transformations and inverses
Week 2: Matrix Algebra
Lect M Snow day (classes cancelled)
Lect 5 w 2.2 linear transformations in geometry
Lect 6 F 2.3/4 matrix product and inverse
Week 3: Basis, dimension
Lect M Presidents day (no classes)
Lect 7 W 3.1 image and kernel
Lect 8 F 3.2 basis and linear independence
Week 4: Coordinates, Projections
Lect 9 M 3.3 dimension
Lect 10 W 3.4 coordinates
Lect 11 F 5.1 orthonormal bases and orthogonal projections
Week 5: Orthogonality
Lect 12 M review for the first midterm
Lect 13 W 5.2 GramSchmidt and QR factorization
Lect 14 F 5.3 orthogonal transformations
Week 6: Datafitting and Determinants
Lect 15 M 5.4 least squares and data fitting
Lect 16 W 6.1 determinants 1
Lect 17 F 6.2/3 determinants 2
Spring Break
Week 7: Eigenvalues Eigenvectors
Lect 18 7.12 eigenvalues and eigenvectors
Lect 19 7.3 eigenspaces
Lect 20 7.4 diagonalization
Week 8: Complex eigenvalues and Stability
Lect 21 7.5 complex eigenvalues
Lect 22 7.6 stability
Lect 23 8.1 symmetric matrices
Week 9: Differential equations
Lect 24 review for second midterm
Lect 25 9.1 differential equations I
Lect 26 9.2 differential equations II
Week 10: Function spaces and nonlinear systems
Lect 27 9.4 nonlinear systems
Lect 28 4.2 linear trafos on function spaces
Lect 29 9.3 inhomogeneous differential equations
Week 11: Fourier series
Lect 30 HH Fourier series I
Lect 31 HH Fourier series II Parseval
Lect 32 HH PDE I
Week 12: Partial differential equations
Lect 33 HH PDE II
Lect 34 HH Overview
