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.

Course head:


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 takes place in room 309.
For details, see the MQC page.

Website:

http://www.courses.fas.harvard.edu/~math21b bookmark this!
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Text:

We recommend Otto Bretscher, Linear Algebra with Applications
but it is not required.
Any edition work as we post homework independent of editions.

About this course:

 teaches methods to solve systems of linear equations.
 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 quantum mechanics, 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. Homework is online
and no book is required.
TTh sections submit two homework sets 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: (they need still be confirmed)
1. Midterm:  TBA  78:30pm  Hall 
2. Midterm:  TBA  78:30pm  Hall 
Final exam:  May, 2018  TBA  Hall 

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

21 22 23 24 25 26 27 0 Jan 22: 8:30AM SC B, Jan 25/26 lectures start
28 29 30 31 1 2 3 1
4 5 6 7 8 9 10 2
11 12 13 14 15 16 17 3
18 19 20 21 22 23 24 4 Mon Feb 19 Presidents day
25 26 27 28 1 2 3 5 First midterm: Feb 27
4 5 6 7 8 9 10 6
11 12 13 14 15 16 17 Spring recess Mar 1018
18 19 20 21 22 23 24 7
25 26 27 28 29 30 31 8
1 2 3 4 5 6 7 9 Second midterm: April 3
8 9 10 11 12 13 14 10
15 16 17 18 19 20 21 11
22 23 24 25 26 27 28 12 April 25 Wed, last class day
29 30 1 2 3 4 5 Apr 26 May 2: reading period
6 7 8 9 10 11 12 May 312 exam period


Day to day syllabus:

Lecture Date Book Topic
Week 0: Systems of linear equations Jan 25/26
Lect 1 F 1.1 introduction to linear systems
Week 1: Systems of linear equations Jan 29Feb 2
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
Week 2: Matrix Algebra Feb 5  9
Lect M 2.2 linear transformations in geometry
Lect 5 W 2.3 matrix product
Lect 6 F 3.1 image and kernel
Week 3: Basis, dimension Feb 12  16
Lect M Presidents day (no classes)
Lect 7 W 3.2 basis
Lect 8 F 3.3 dimension
Week 4: Coordinates, Projections Feb 19  23
Lect 9 M 3.4 coordinates
Lect 10 W 4.1 linear spaces
Lect 11 F 5.1 orthonormal basis and projection
Week 5: Orthogonality Feb 26Feb 30
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 Mar 5 Mar 9
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 Mar 12 Mar 16
Week 7: Eigenvalues Eigenvectors Mar 19 Mar 23
Lect 18 7.12 eigenvalues and eigenvectors
Lect 19 7.3 eigenspaces
Lect 20 7.4 diagonalization
Week 8: Complex eigenvalues, Stability Mar 26 Mar 30
Lect 21 7.5 complex eigenvalues
Lect 22 7.6 stability
Lect 23 8.1 symmetric matrices
Week 9: Differential equations Mar 2  Apr 6
Lect 24 review for second midterm
Lect 25 9.1 differential equations I
Lect 26 9.2 differential equations II
Week 10: Function spaces, nonlinear systems Apr 9  Apr 13
Lect 27 9.4 nonlinear systems
Lect 28 4.2 operator method
Lect 29 9.3 cookbook for Differential equations
Week 11: Fourier series Apr 16  Apr 20
Lect 30 HH Fourier series I
Lect 31 HH Fourier series II Parseval
Lect 32 HH PDE I
Week 12: Partial differential equations Apr 23  Apr 25
Lect 33 HH PDE II
Lect 34 HH Overview
