Math21b, Fall 2007, Linear Algebra and Differential Equations,

Math21b: Linear Algebra and Differential Equations

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:

Evan Bullock
Leila Khatami
Yum-Tong Siu

Course assistants:

See the Section page

Lecture times:

Mo-We-Fr 9-10
Mo-We-Fr 10-11
Mo-We-Fr 11-12

Problem Sections:

See the Sections page.

Website:

http://www.courses.fas.harvard.edu/~math21b/

Text:

We use Otto Bretscher, Linear Algebra with Applications, third edition. Prentice-Hall, Upper Saddle River, NJ, 2001. This great book has been used for many years here.

About this course:

teaches methods to solve systems of linear equations Ax = b,
allows you to analyze and solve systems of linear differential equations,
you learn to solve discrete linear dynamical systems like 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 for example quantum mechanics, combinatorics
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 lecture.

Exams:

We have two midterm exams and one final exam. Here are the midterm exam dates:

1. Midterm:

Wed 10/14

7-8:30pm

Hall C

2. Midterm:

Wed 11/28

7-8:30pm

Hall C

Grades:

                                          Grade1  Grade2
 First hourly                              20     20   
 Second hourly                             20     20
 Homework                                  20     20
 Lab                                        5
 Final exam                                35     40
 -------------------------------------------------------
 Total                                    100    100
 
 Grade = Max(Grade1,Grade2)
 
 Doing the mathematica project will soften a bit the final
 exam.

Calendar:

 --------------------------------------------------------
 So Mo Tu We Th Fr Sa
 --------------------------------------------------------
  S  M  T  W  T  F  S
                    1        September
  2  3  4  5  6  7  8        
  9 10 11 12 13 14 15     
 16 17 18 19 20 21 22        Sept 17 Plenary introduction
 23 24 25 26 27 28 29    1   Sept 24 Lectures start
 30  1  2  3  4  5  6    2   October 
  7  8  9 10 11 12 13    3   Oct 8 Columbus Day
 14 15 16 17 18 19 20    4   Oct  14  First midterm Hall C
 21 22 23 24 25 26 27    5   
 28 29 30 31  1  2  3    6   November
  4  5  6  7  8  9 10    7   
 11 12 13 14 15 16 17    8   Nov 12 Veteran's Day                            
 18 19 20 21 22 23 24    9   Nov 22-25 Thanksgiving Recess
 25 26 27 28 29 30  1   10   Nov 28  Second midterm Hall C  
  2  3  4  5  6  7  8   11   December
  9 10 11 12 13 14 15   12
 16 17 18 19 20 21 22   13   Dec 19 Winter Recess starts
 23 24 25 26 27 28 29
 30 31  1  2  3  4  5        January  Jan 2 Reading Period starts
  6  7  8  9 10 11 12
 13 14 15 16 17 18 19        Jan 13 Reading Period ends, Jan 14 Exam Period starts
 20 21 22 23 24 25 26        Jan 23 Exam Period ends
 27 28 29 30 31 
 ---------------------------------------------------------

Day to day syllabus: A more detailed lecture plan.

    Lecture Date   Book Topic
 
 1. Week:  Systems of linear equations
 
    Lect 1   9/24  1.1   introduction to linear systems  
    Lect 2   9/26  1.2   matrices and Gauss-Jordan elimination
    Lect 3   9/28  1.3   on solutions of linear systems
 
 2. Week:  Linear transformations
 
    Lect 4   10/1  2.1   linear transformations and their inverses
    Lect 5   10/3  2.2   linear transformations in geometry 
    Lect 6   10/5  2.3-4 matrix product and inverse
 
 3. Week:  Linear subspaces
 
    Lect 7   10/8  Columbus Day, no class
    Lect 8   10/10  3.1   image and kernel 
    Lect 9   10/12  3.2   bases and linear independence 
 
 4. Week:  Dimension and linear spaces
 
    Lect 10  10/15 3.3   dimension 
    Lect 11  10/17 3.4   coordinates
    Lect 12  10/19 4.1   linear spaces 
 
 5. Week:  Orthogonality
 
    Lect 13  10/22   review for first midterm        
    Lect 14  10/24 4.1  linear spaces II,  First Midterm Hall C
    Lect 15  10/26 5.1  orthonormal bases and orthogonal projections
 
 6. Week:  Datafitting
 
    Lect 16  10/29 5.2  Gram-Schmidt and QR factorization 
    Lect 17  10/31 5.3  orthogonal transformations
    Lect 18  11/2  5.4  least squares and data fitting
 
 7. Week:  Determinants
 
    Lect 19  11/5  6.1   determinants 1
    Lect 20  11/7  6.2   determinants 2
    Lect 21  11/9  7.1-2 eigenvalues 
 
 8. Week:  Diagonalization
 
    Lect 22  11/12   Veterans's Day, no class
    Lect 23  11/14   7.3  eigenvectors
    Lect 24  11/16   7.4  diagonalization                     
 
 9. Week:  Stability and symmetric matrices
 
    Lect 25  11/19  7.5  complex eigenvalues
    Lect 26  11/21  7.6  stability        
    Lect 27  11/23  Thanksgiving Recess, no class    
 
 10. Week:  Differential equations
 
    Lect 27  11/26  Review for second midterm        
    Lect 28  11/28  8.1  symmetric matrices  Second Midterm Hall C 
    Lect 29  11/30  9.1  differential equations I 
 
 11. Week:  Function spaces
 
    Lect 30  12/3  9.2  differential equations II      
    Lect 31  12/5  9.4  nonlinear systems  
    Lect 32  12/7  4.2  function spaces             
 
 12. Week:  Partial differential equations
 
    Lect 33  12/10  9.3  linear differential operators  
    Lect 34  12/12  5.5  inner product spaces  
    Lect 35  12/14  5.5  Fourier theory I 
    
 13. Week:  Partial differential equations
 
    Lect 36  12/17  5.5  Fourier theory II, Partial differential equations