Math21b, Fall 2010, 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 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. The course is taught in 3 sections.

Instructors:

Course assistants:

Head CA: See the Section page

Lecture times:

Mo-We-Fr 10-11
Mo-We-Fr 11-12
Mo-We-Fr 12-1

Problem Sections:

See the Sections page. MQC:

Website:

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

Text:

We use Otto Bretscher, Linear Algebra with Applications, fourth edition. Prentice-Hall, Upper Saddle River, NJ, 2008. This is the latest edition.

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 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 for example quantum mechanics or 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 lecture. Tue-Thu section HW is split usually 1/3 from Tue to Thu and 2/3 from Thu to Tue.

Exams:

We have two midterm exams and one final exam. We plan to have the following midterm exam dates:

1. Midterm:

Thu 10/7

7-8:30pm

Hall D

2. Midterm:

Thu 11/4

7-8:30pm

Hall D

Final Exam:

Fri 12/17

TBA

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
 --------------------------------------------------------
 29 30 31  1  2  3  4    0  Sep 1: intro meeting in Hall B
  5  6  7  8  9 10 11    1  Sep 6: labour day Sep 8: 1. lect
 12 13 14 15 16 17 18    2
 19 20 21 22 23 24 25    3
 26 27 28 29 30  1  2    4  
  3  4  5  6  7  8  9    5  Oct 7:  first hourly  
 10 11 12 13 14 15 16    6  Oct 11: Columbus day
 17 18 19 20 21 22 23    7
 24 25 26 27 28 29 30    8
 31  1  2  3  4  5  6    9  Nov 4:  second hourly  
  7  8  9 10 11 12 13   10  Nov 11: Veterans day
 14 15 16 17 18 19 20   11
 21 22 23 24 25 26 27   12  Nov 25-28: thanksgiving holiday
 28 29 30  1  2  3  4   13  Dec 3: last day of class
  5  6  7  8  9 10 11   14  Dec 4-12: reading period
 12 13 14 15 16 17 18   15  Dec 13-21: exam period
 19 20 21 22 23 24 25   16
 ---------------------------------------------------------

Day to day syllabus:

    Lecture Date   Book Topic
 
 1. Week:  Systems of linear equations
 
             9/6         labour day                       
    Lect 1   9/8   1.1   introduction to linear systems  
    Lect 2   9/10  1.2   matrices and Gauss-Jordan elimination
 
 2. Week:  Linear transformations
 
    Lect 3   9/13  1.3   on solutions of linear systems
    Lect 4   9/15  2.1   linear transformations and their inverses
    Lect 5   9/17  2.2   linear transformations in geometry 
 
 3. Week:  Linear subspaces
 
    Lect 6   9/20  2.3   matrix product
    Lect 7   9/22  2.4   the inverse 
    Lect 8   9/24  3.1   image and kernal               
 
 4. Week:  Dimension and linear spaces
 
    Lect  9  9/27  3.2   bases and linear independence
    Lect 10  9/29  3.3   dimension   
    Lect 11  10/1  3.4   coordinates   
 
 5. Week:  Orthogonality
 
    Lect 12  10/4   4.1  linear spaces
    Lect 13  10/6        review for first midterm        
    Lect 14  10/8   5.1  orthonormal bases and orthogonal projections
 
 6. Week:  Datafitting
 
             10/11       Columbus day                                      
    Lect 15  10/13  5.2  Gram-Schmidt and QR factorization 
    Lect 16  10/15  5.3  orthogonal transformations
 
 7. Week:  Determinants
 
    Lect 17  10/18  5.4   least squares and data fitting
    Lect 18  10/20  6.1   determinants 1
    Lect 19  10/22  6.2-3 determinants 2
 
 8. Week:  Diagonalization
 
    Lect 20  10/25  7.1-2 eigenvalues 
    Lect 21  10/27  7.3   eigenvectors
    Lect 22  10/29  7.4   diagonalization
 
 9. Week:  Stability and symmetric matrices
 
    Lect 23  11/1   7.5  complex eigenvalues
    Lect 24  11/3        review for second midterm
    Lect 25  11/5   7.6  stability          
 
 10. Week:  Differential equations
 
    Lect 26  11/8   8.1  symmetric matrices
    Lect 27  11/10  9.1  differential equations I
    Lect 28  11/12  9.2  differential equations II
 
 11. Week:  Function spaces
 
    Lect 29  11/15  9.4  nonlinear systems
    Lect 30  11/17  4.2  linear trafos on function spaces
    Lect 31  11/19  9.3  inhomogeneous differential equations
 
 12. Week:  Inner product spaces           
 
    Lect 32  11/22  9.3  inhomogeneous differential equations
    Lect 33  11/24  4.2  inner product spaces 
             11/25       Thanksgiving 
 
 13. Week:  Partial differential equations
 
    Lect 34  11/29 HH   Fourier series
    Lect 35  12/1  HH   Parseval identity 
    Lect 36  12/3  HH   Partial differential equations
 
             12/4-12/12  Fall reading period  
             12/13-12/21 Fall exam    period