| Instructor: | Steven
J. Leon , Department of Mathematics Office: Group I-394D Office hours: Tu,Wed,Th 2:00-3:15, Email: sleon@umassd.edu phone: 999-8320 You can link to the MTH 353 Spring 2008 Webpage from the instructor's homepage: http://www.umassd.edu/cas/mathematics/people/leon/ |
|---|---|
| Textbooks: | Linear Algebra With Applications, 7th
ed.,
by S. J. Leon, ATLAST Computer Exercises for Linear Algebra, 2nd ed. |
| Homework: | Homework assignments are listed below for each of the sections. Homework will be collected and graded. |
| Exams: | There will be 2 in-class exams worth 100 points each and possibly a third exam worth 50 points. There will be a final exam worth 200 points. No makeups unless you have a note from your doctor. The exams will be closed book. You are not allowed to use notes during the exam. Hand calculators may be used for arithmetic and to check your answers, but you must show all of your work in solving exam problems. If you have a correct answer to a problem, but have not shown your work, you may not receive any credit for the problem. Exams are not graded on a curve. |
| Grading: |
Your grade for the course
will be based on how well you score on the homework, in-class exams,
and
the final exam. |
| Academic integrity: | Academic dishonesty will not be tolerated. Any student caught cheating on an exam will receive an F for the course and a note will be sent to the Dean regarding the incident. This could result in the expulsion of the student from the university. Academic dishonesty includes using crib notes, copying from another student or letting another student copy from you during an exam. |
| UNIT 1: | Orthogonality | |
|---|---|---|
| Topics: | 1 - Scalar Product and Orthogonality in R n | |
| 2 - Orthogonal Subspaces | ||
| 3 - Least Squares Problems | ||
| 4 - Inner Products and Norms | ||
| 5 - Orthonormal Sets | ||
| 6 - Orthogonal Matrices | ||
| 7 - Gram-Schmidt Process | ||
| 8 - QR Factorization from Gram-Schmidt Process | ||
| Assignments: | Chapter 5 | |
| Section: | 5.1 Exercises 1 - 3 parts a and c, 4 , 5, 12, 13, 15, 18 | |
| 5.2 Exercises 1 - 4, 6 - 9, 12 - 17 | ||
| 5.3 Exercises 1 - 6, 9 -14 | ||
| 5.4 Exercises 1 - 4,
7 - 9, 15, 16, 19 - 24,
26,
28, 30 |
||
| 5.5 Exercises 1 - 8, 11, 12, 14, 16, 17, 19 - 25, 28, 31 | ||
| 5.6 Exercises 1 - 5, 7, 8, 11, 12 | ||
| MATLAB Exercises or projects | ||
| Review of Unit 1 | ||
| Test 1 | Exam covering Sections 5.1-5.6 | |
| UNIT 2: | Eigenvalues | |
| Topics: | 9 - Review of Eigenvalues, Eigenvectors and Diagonalization | |
| 10 - The Matrix Exponential | ||
| 11 - Applications to Linear Systems of Differential Equations | ||
| 12 - Hermitian Matrices | ||
| 13 - Singular Value Decomposition | ||
| 14 - Quadratic Forms and Optimization | ||
| 15 - Positive Definite Matrices | ||
| Assignments: | Chapter 6 | |
| Section: | 6.2 Exercises 1a, c, e, 2 a, c, 3, 4, 5a | |
| 6.3 Exercises
20, 22, 24, 26, 27
a, c, 28a, c, 30, 31 |
||
| 6.4 Exercises 1 - 4, 5 a, c, e, g, 6, 9, 12b, c, 15, 18, 22, 23 | ||
| 6.5 Exercises 1 - 7,
8, 10 |
||
| 6.6 Exercises 1,6, 7a,c,e,f, 8 - 14 | ||
| 6.7 Exercises 1a, c, 2, 3, 4 a, c, 5 a, c, 6, 8 - 11, 13 | ||
| MATLAB Exercises | ||
| Review of Unit 2 | ||
| Test 2 | Exam covering all of unit 2 | |
| UNIT 3: | Numerical Linear Algebra | |
| Topics: | 15 - Solving Linear Systems with Pivoting | |
| 16 - Matrix Norms and Condition Numbers | ||
| 17 - Householder Transformations | ||
| 18 - Rotations and Reflections | ||
| 19 - The Eigenvalue Problem | ||
| 20 - Least Squares Problems | ||
| Assignments: | Chapter 7 | |
| Section: | 7.4 Exercises
1, 7 - 18, 24, 28-30, 33, 34 |
|
| 7.5 Exercises 1, 2 a, c, 3 a, c, 4 - 6, 7a, c, 11-16 | ||
| 7.6 Exercises 1- 8, 11, 12a | ||
| 7.7 Exercises 1 - 3, 6 - 11 | ||
| MATLAB Exercises | ||
| Test 3 | Exam covering all or part of unit 3 (if time allows) | |
|
Final exam:
|
Comprehensive exam over all sections covered during the semester |