M A T H 2 1 B
Mathematics Math21b Spring 2015
Linear Algebra and Differential Equations
Syllabus
Course Head: Oliver Knill
Office: SciCtr 432

Math21b: Linear Algebra and Differential Equations This course 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.
Instructors:
• Oliver Knill
Course assistants: Head CA:
Lecture times:
• Mo-We-Fr 9-10
• Mo-We-Fr 10-11
• Mo-We-Fr 11-12
• Mo-We-Fr 12-1
• Tue-Th 10-11:30
• Tue-Th 11:30-1
MQC: This spring the MQC for Math 21b is in room 309. For details, see the MQC page.
Website: http://www.courses.fas.harvard.edu/~math21b bookmark this!
https://canvas.harvard.edu/courses/1803 canvas
http://isites.harvard.edu/icb/icb.do?keyword=k109254 Isites
Text: We use Otto Bretscher, Linear Algebra with Applications. The fourth or 5th edition both should work as we post HW independent of editions.
• 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 class. TTh sections submit two homework on Tuesday's except for the first week.
Exams: We have two midterm exams and one final exam. We plan to have the following midterm exam dates:
 1. Midterm: 7-8:30pm Hall B 2. Midterm: 7-8:30pm Hall B
                                          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 week  Events
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25 26 27 28 29 30 31       Jan 26: 8:30AM SC B, 29/30 start
1  2  3  4  5  6  7    1
8  9 10 11 12 13 14    2
15 16 17 18 19 20 21    3  Feb 16 Presidents day
22 23 24 25 26 27 28    4
1  2  3  4  5  6  7    5  First midterm March 3
8  9 10 11 12 13 14    6
15 16 17 18 19 20 21       Spring break Mar 14-22
22 23 24 25 26 27 28    7
29 30 31  1  2  3  4    8
5  6  7  8  9 10 11    9  Second midterm April 7
12 13 14 15 16 17 18   10
19 20 21 22 23 24 25   11
26 27 28 29 30  1  2   12  April 29 last day of classes
3  4  5  6  7  8  9       Until May 6: reading period
10 11 12 13 14 15 16       May 7-16 exam period
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Day to day syllabus: (updated on February 8 as Feb 9 is a snow day)
    Lecture Date   Book Topic

Week 0: Systems of linear equations

Lect 1  F  1.1   introduction to linear systems

Week 1: Systems of linear equations

Lect 2  M  1.2   matrices and Gauss-Jordan elimination
Lect 3  W  1.3   on solutions of linear systems
Lect 4  F  2.1   linear transformations and inverses

Week 2: Matrix Algebra

Lect    M  Snow day   (classes cancelled)
Lect 5  w  2.2   linear transformations in geometry
Lect 6  F  2.3/4 matrix product and inverse

Week 3: Basis, dimension

Lect    M  Presidents day   (no classes)
Lect  7 W  3.1   image and kernel
Lect  8 F  3.2   basis and linear independence

Week 4: Coordinates, Projections

Lect  9 M  3.3   dimension
Lect 10 W  3.4   coordinates
Lect 11 F  5.1   orthonormal bases and orthogonal projections

Week 5: Orthogonality

Lect 12 M        review for the first midterm
Lect 13 W  5.2   Gram-Schmidt and QR factorization
Lect 14 F  5.3   orthogonal transformations

Week 6: Datafitting and Determinants

Lect 15 M  5.4   least squares and data fitting
Lect 16 W  6.1   determinants 1
Lect 17 F  6.2/3 determinants 2

Spring Break

Week 7: Eigenvalues Eigenvectors

Lect 18    7.1-2 eigenvalues and eigenvectors
Lect 19    7.3   eigenspaces
Lect 20    7.4   diagonalization

Week 8: Complex eigenvalues and Stability

Lect 21    7.5  complex eigenvalues
Lect 22    7.6  stability
Lect 23    8.1  symmetric matrices

Week 9: Differential equations

Lect 24         review for second midterm
Lect 25    9.1  differential equations I
Lect 26    9.2  differential equations II

Week 10: Function spaces and nonlinear systems

Lect 27    9.4  nonlinear systems
Lect 28    4.2  linear trafos on function spaces
Lect 29    9.3  inhomogeneous differential equations

Week 11:  Fourier series

Lect 30   HH    Fourier series I
Lect 31   HH    Fourier series II Parseval
Lect 32   HH    PDE I

Week 12: Partial differential equations

Lect 33   HH    PDE II
Lect 34   HH    Overview


Please send questions and comments to knill@math.harvard.edu
Math21b Harvard College/GSAS: 1771, Exam group 3| Oliver Knill | Spring 2015 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas], [ISites]. Bookmark http://sites.fas.harvard.edu/~math21b/| Twitter