-  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 tought in 2 or 3 sections. 

-  Instructors: Oliver Knill, SC-434, knill@math
                Izzett Coskun, SC 333b, coskun@math
-  Course assistants: will be announced
-  Lectures: Mo-We-Fr, times will be announced
-  Place:  will be announced
-  Problem Sections: will be announced
-  Office hours: will be announced
-  Website: http://www.courses.fas.harvard.edu/~math21b/
-  Text: Otto Bretscher. Linear Algebra with Applications, 
      second 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. An example are Markov 
         processes.
       - 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. 
- 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)
  Su Mo Tu We Th Fr Sa   Week
--------------------------------------------------------
  14 15 16 17 18 19 20        16. Sep: Orientation
     +------+----+
  21 22 23 24 25 26 27    1   22. Sep: First day of class
  28 29 30  1  2  3  4    2   
   5  6  7  8  9 10 11    3   October
  12 13 14 15 16 17 18    4   13. Oct: Columbus day
  19 20 21 22 23 24 25    5   Oct 22:  1. Midterm 7:30-9 PM
  26 27 28 29 30 31  1    6
   2  3  4  5  6  7  8    7   November
   9 10 11 12 13 14 15    8   11. Nov Veterans day
  16 17 18 19 20 21 22    9   Nov 19:  2. Midterm 7:30-9 PM
  23 24 25 26 27 28 29   10
  30  1  2  3  4  5  6   11   December
   7  8  9 10 11 12 13   12
  14 15 16 17 18 19 20   13   17. Dec -3. Jan. Recess
     +------+----+
  21 22 23 24 25 26 27     
  28 29 30 31  1  2  3  
   4  5  6  7  8  9 10         5. Jan -16. Jan Reading
  11 12 13 14 15 16 17     
  18 19 20 21 22 23 24        17. Jan -27. Jan Exams
  25 26 27 28 29 30 31     
---------------------------------------------------------

- Day to day syllabus:  

   Lecture Date   Book Topic

1. Week:   Systems of linear equations
   Lect 1   9/22  1.1  introduction to linear systems  
   Lect 2   9/24  1.2  matrices and Gauss-Jordan elimination
   Lect 3   9/26  1.3  on solutions of linear systems

2. Week:   Linear transformations
   Lect 4   9/29  2.1  linear transformations and their inverses
   Lect 5  10/1   2.2  linear transformations in geometry 
   Lect 6  10/3   2.3  inverse of a linear transformation

3. Week:  Linear subspaces
   Lect 7  10/6   2.4  matrix products
   Lect 8  10/8   3.1  image and kernel 
   Lect 9  10/10  3.2  subspaces, bases and linear independence 

4. Week:  Dimension
           10/13  COLUMBUS DAY, no class
   Lect 10 10/15  3.3  dimension 
   Lect 11 10/17  3.4  coordinates

5. Week:  Orthogonality
   Lect 12  10/20 5.1  orthonormal bases and orthogonal projections
   Lect 13  10/22 *** Review for first midterm
   Lect 14  10/24 5.2  Gram-Schmidt and QR factorization  Midterm

6. Week:  Determinants
   Lect 15  10/27 5.3  orthogonal transformations
   Lect 16  10/29 5.4  least squares and data fitting
   Lect 17  10/31 6.2  determinants I

7. Week:  Eigensystems
   Lect 18  11/3  6.3  determinants II Cramer
   Lect 19  11/5  7.1  Eigenvalues introduction
   Lect 20  11/7  7.2  Eigenvalues

8. Week:  Diagonalization
   Lect 21  11/10 7.3  Eigenvectors
   Lect 22  11/12 7.4  Diagonalization
   Lect 23  11/14 7.5  Complex eigenvalues

9. Week:  Stability and symmetric matrices
   Lect 24  11/17 7.6  Stability
   Lect 25  11/29 ***   Review for second midterm
   Lect 26  11/31 8.1  Symmetric matrices 

10. Week:  Differential equations
   Lect 27  11/24 9.1  Continuous dynamical systems
   Lect 28  11/26 9.2  Complex case: Euler formula
   Lect 29  11/28 9.3  Nonlinear systems

11. Week:  Function spaces
   Lect 30  12/1  10.1 Function spaces (also 4.1,4.2)
   Lect 31  12/3  10.2 Ordinary differential equations (also 9.3)
   Lect 32  12/5  10.3 Fourier series

12. Week:  Partial differential equations
   Lect 33  12/8  10.4 The heat equation
   Lect 34  12/10 10.5 The Laplace and wave equation
   Lect 35  12/12  ***  Catchup and Review