M A T H 2 1 B
Mathematics Math21b Spring 2016
Linear Algebra and Differential Equations
Syllabus
Office: SciCtr 432

Syllabus Broshure [PDF] ,

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:
Lecture times:
• Mo-We-Fr 9-10
• Mo-We-Fr 10-11
• Mo-We-Fr 11-12
• Mo-We-Fr 12-1
• Tue-Th 10-11:30
• Tue-Th 11:30-1
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.
• 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 7-8:30pm Hall B 2. Midterm: Tuesday,April 5 7-8:30pm Hall B Final exam: May, 2016 TBA Hall B
```                                          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 13-20
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 5-14 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 1-5

Lect 2  M  1.2   matrices and Gauss-Jordan elimination
Lect 3  W  1.3   on solutions of linear systems
Lect 4  F  2.1   linear transformations

Week 2: Matrix Algebra                Feb 8-12

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 15-19

Lect    M  Presidents day   (no classes)
Lect  7 W  3.2   basis
Lect  8 F  3.3   dimension

Week 4: Coordinates, Projections      Feb 22-26

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 29-Mar 4

Lect 12 M        review for the first midterm
Lect 13 W  5.2   Gram-Schmidt 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    7.1-2 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

```