Harvard University,FAS
Fall 2004

Mathematics Math21b
Fall 2004

Linear Algebra
and Differential Equations

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu
New Syllabus Calendar Homework Exams Exhibits Handouts Cas Faq Links

Syllabus

-  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, SC-434, 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: 
           Mo-We-Fr 10-11  
           Mo-We-Fr 11-12  
           Tu-Th  10-11:30

-  Problem Sections: 
           Tue, in SciC 111   7:00-8:00pm   (Goutham)
           Wed, in SciC 101B  8:30-10:00pm  (Philip)
           Thu, in SciC 116   8:30-9:30pm   (Tien Anh)
           Sun, in SciC 222   8:30-9:30pm   (Aki)

-  Office hours: 
           Oliver:   Mo,We,Fr 15-16
           Janet:    Mo,Th    15-16

-  Website: http://www.courses.fas.harvard.edu/~math21b/
      Section page of Janet

-  Text: 
           Otto Bretscher, Linear Algebra with Applications, 
           third edition. Prentice-Hall, 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. Tue-Thu 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  25-27. 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 Gauss-Jordan 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   2.3-4 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  Gram-Schmidt 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  7.1-2 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



Please send comments to knill@math.harvard.edu


Sun Jan 23 23:10:54 EST 2005