M A T H 2 1 B
Mathematics Math21b Fall 2010
Linear Algebra and Differential Equations
Syllabus
Office: SciCtr 434

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.
• 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 TBA
                                          Grade1  Grade2
First hourly                              20     20
Second hourly                             20     20
Homework                                  20     20
Lab                                        5
Final exam                                35     40
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Total                                    100    100


Calendar: (Registrar)
 --------------------------------------------------------
So Mo Tu We Th Fr Sa
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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
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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