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 309a (subject to change).
For details, see the MQC page.

Website:

http://www.courses.fas.harvard.edu/~math21b bookmark this!
https://canvas.harvard.edu/courses/1803 canvas

Text:

We recommend 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.
 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:  Tuesday,March 1  78:30pm  Hall B 
2. Midterm:  Tuesday,April 5  78:30pm  Hall B 
Final exam:  May, 2016  TBA  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

24 25 26 27 28 29 30 0 Jan 25: 8:30AM SC B, 28/29 Lecture
31 1 2 3 4 5 6 1
7 8 9 10 11 12 13 2
14 15 16 17 18 19 20 3 Mon Feb 15 Presidents day
21 22 23 24 25 26 27 4
28 29 1 2 3 4 5 5 First midterm March 1 (planned)
6 7 8 9 10 11 12 6
13 14 15 16 17 18 19 Spring break Mar 1320
20 21 22 23 24 25 26 7
27 28 29 30 31 1 2 8
3 4 5 6 7 8 9 9 Second midterm April 5 (planned)
10 11 12 13 14 15 16 10
17 18 19 20 21 22 23 11
24 25 26 27 28 29 30 12 April 27: last day of classes
1 2 3 4 5 6 7 Until May 4: reading period
8 9 10 11 12 13 14 May 514 exam period


Day to day syllabus:

Lecture Date Book Topic
Week 0: Systems of linear equations Jan 28/29
Lect 1 F 1.1 introduction to linear systems
Week 1: Systems of linear equations Feb 15
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 812
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 1519
Lect M Presidents day (no classes)
Lect 7 W 3.2 basis
Lect 8 F 3.3 dimension
Week 4: Coordinates, Projections Feb 2226
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 29Mar 4
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 7 Mar 11
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 14 Mar 18
Week 7: Eigenvalues Eigenvectors Mar 21 Mar 25
Lect 18 7.12 eigenvalues and eigenvectors
Lect 19 7.3 eigenspaces
Lect 20 7.4 diagonalization
Week 8: Complex eigenvalues and Stabilitya Mar 28 Apr 1
Lect 21 7.5 complex eigenvalues
Lect 22 7.6 stability
Lect 23 8.1 symmetric matrices
Week 9: Differential equations Mar 4  Apr 8
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 Apr 11  Apr 15
Lect 27 9.4 nonlinear systems
Lect 28 4.2 differential operators
Lect 29 9.3 inhomogeneous differential equations
Week 11: Fourier series Apr 18  Apr 22
Lect 30 HH Fourier series I
Lect 31 HH Fourier series II Parseval
Lect 32 HH PDE I
Week 12: Partial differential equations Apr 25  Apr 27
Lect 33 HH PDE II
Lect 34 HH Overview
