| Spring 2023 MAT 211: Introduction to linear algebra | ||
| Schedule | TTh 11:30-12:50pm Earth & Space 79. | |
| Instructor | Robert Hough | |
| Office hours | F 9am-11am in Math Tower 4-118, 6-7pm in MLC. | |
| Description | Introduction to the theory of linear algebra with some applications; vectors, vector spaces, bases and dimension, applications to geometry, linear transformations and rank, eigenvalues and eigenvectors, determinants and inner products. May not be taken for credit in addition to AMS 210. | |
| Textbook | Otto Bretscher. Linear algebra with applications, 5th edition. Pearson (2013). | |
| Final exam | Wednesday, May 10 from 11:15-1:45pm in the usual classroom. | |
| Grading | The course grade is based upon homework 20%, two midterms 20% each and final exam 40%. | |
Syllabus/schedule (subject to change)
| Tues 1/24 | 1. | Linear systems, Gauss-Jordan elimination | Bretscher 1.1-1.2 | Homework 1: due 2/2 p.5 #17, 42, p.18 #10, 18, 35, 38, p.34 #4, 14, 22, 36 |
| Thurs 1/26 | 2. | Matrix algebra | Bretscher 1.3 | |
| Tues 1/31 | 3. | Linear transformations | Bretscher 2.1 | Homework 2: due 2/9 p.53 #7, 13, 16, 20, 44, p.71 #6, 14, 15, 33, 34 |
| Thurs 2/2 | 4. | Geometric interpretation | Bretscher 2.2 | |
| Tues 2/7 | 5. | Matrix products and inverses | Bretscher 2.3-2.4 | Homework 3: due 2/16 p.85 #13, 22, 24, 39, p.97 #8, 12, 35, p.119 #10, 14, 35, p. 131 #18, 32 |
| Thurs 2/9 | 6. | Image, kernel, subspaces and bases Boards. | Bretscher 3.1-3.2 | |
| Tues 2/14 | 7. | Dimension and coordinates Boards. | Bretscher 3.3-3.4 | Homework 4: due 2/23 p.143 #18, 40, 68, p.159 #17, 29, 50, p.176 #15, 22, 34, p. 184 #33, 37, 78 |
| Thurs 2/16 | 8. | Linear spaces, transformations, isomorphisms Boards. | Bretscher 4.1-4.2 | |
| Tues 2/21 | Midterm 1 Practice Midterm. | Homework 5: due 3/2 p.195 #8, 13, 66, 70 | ||
| Thurs 2/23 | 9. | The matrix of a linear transformation Boards. | Bretscher 4.3 | |
| Tues 2/28 | 10. | Orthogonal projection, orthonormal bases, QR factorization | Bretscher 5.1-5.2 | Homework 6: due 3/9 p.214 #8, 17, 31, p.224 #10, 16, 38, p.233 #4, 34, 43, p.245 #8, 21, 29 |
| Thurs 3/2 | 11. | Orthogonal transformations and least squares Boards | Bretscher 5.3-5.4 | |
| Tues 3/7 | 12. | Inner product spaces | Bretscher 5.5 | Homework 7: due 3/23 p.260 #15, 17, 21, 33 p.275 #10, 27, 39, 57 |
| Thurs 3/9 | 13. | Determinants Boards | Bretscher 6.1 | |
| No class - Spring Break 3/13-3/19 | ||||
| Tues 3/21 | 14. | Properties of the determinant Boards | Bretscher 6.2 | Homework 8: due 3/30 p.289 #10, 29, 31, 44, 50, 66 p.305 #8, 10, 13, 26, 32 |
| Thurs 3/23 | 15. | Geometric interpretation of the determinant Boards | Bretscher 6.3 | |
| Tues 3/28 | 16. | Review | ||
| Thurs 3/30 | 17. | Review | ||
| Tues 4/4 | 18. | Diagonalization Boards | Bretscher 7.1 | Homework 9: due 4/11 p.323 #9, 15, 19, 32, 54 p.336 #1, 8, 43 p.345 #10,20, 32, 33 |
| Thurs 4/6 | 19. | Eigenvalues and eigenvectors Boards | Bretscher 7.2-7.3 | |
| Tues 4/11 | 20. | Dynamical systems | Bretscher 7.4 | Homework 10: due 4/20 p.355 #5, 6, 27, 41, 70 |
| Thurs 4/13 | Midterm 2 | |||
| Tues 4/18 | 21. | Complex eigenvalues | Bretscher 7.5 | Homework 11: due 4/27 p.371 #20, 23, 31, 38, 44 p.380 #10, 17, 20, 26, 36 |
| Thurs 4/20 | 22. | Stability | Bretscher 7.6 | |
| Tues 4/25 | 23. | Symmetric matrices | Bretscher 8.1 | Homework 12: due 5/4 p.391 #4, 10, 15, 27, 49 p.400 #10, 17, 25, 55, 71 |
| Thurs 4/27 | 24. | Quadratic forms | Bretscher 8.2 | |
| Tues 5/2 | 25. | Singular values | Bretscher 8.3 | Homework 13: optional p.411 #6, 11, 20, 29, 33 p.425 #3, 31, 32, 36, 52 |
| Thurs 5/4 | 26. | Continuous dynamical systems, linear differential equations | Bretscher 9.1-9.3 |
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