COURSE DESCRIPTION
Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Credit is not given in both Mathematics 310 and 320.
TEXTBOOK
Steven J. Leon, Linear Algebra with Applications (8th edition), Prentice-Hall, 2009.
SCHEDULE
This is a suggested course schedule. Individual sections may vary somewhat in their precise content and schedules.
| CHAPTER 1: LINEAR EQUATIONS | ||
| Week 1. | § 1.1 | Linear Systems & Row Operations |
| § 1.2 | Gauss-Jordan Operation on Matrices | |
| Week 2. | § 1.2 | |
| § 1.3 | Matrix Arithmetic | |
| Week 3. | § 1.3 | |
| § 1.4 | Matrix Algebra | |
| § 1.5 | Elementary matrices; LU-decomposition | |
| CHAPTER 2: DETERMINANTS | ||
| Week 4. | § 2.1 | Computation by elimination and/or cofactors |
| § 2.2 | Properties | |
| § 2.3 | Cramer's rule | |
| CHAPTER 3: VECTOR SPACES | ||
| Week 5. | § 3.1 | Examples |
| § 3.2 | Subspaces (how to verify), span | |
| Week 6. | § 3.3 | Linear independence |
| § 3.4 | Basis and dimension | |
| Week 7. | § 3.5 | Change of basis (coordinates, transition matrix) |
| § 3.6 | Row space & column space | |
| CHAPTER 4: LINEAR TRANSFORMATIONS | ||
| Week 8. | § 4.1 | Linear transformations - definition & examples |
| § 4.2 | Matrix representation | |
| § 4.3 | Similarity, look ahead to diagonalization in § 6.3 | |
| CHAPTER 5: ORTHOGONALITY | ||
| Week 9. | § 5.1 | Dot product |
| § 5.2 | Orthogonal subspaces | |
| Week 10. | § 5.3 | Least squares, pseudo-inverses |
| § 5.4 | General inner product spaces, Cauchy-Schwarz inequality | |
| Week 11. | § 5.5 | Orthonormal basis and projection |
| § 5.6 | Gram-Schmidt process and QR-factorization | |
| CHAPTER 6: EIGENVALUES | ||
| Week 12. | § 6.1 | Definition: Eigenvalues and eigenvectors; example: Markov Matrices |
| § 6.2 | Linear differential systems | |
| Week 13. | § 6.3 | Diagonalization, matrix exponential; "defective" (or non-diagonalizable) matrices |
| § 6.4 | Hermitian matrices: including symmetric matrices | |
| Week 14. | § 6.6 | General quadratic forms ( as time permits) |
| § 6.7 | Positive definite matrices (as time permits) | |
| Week 15. | § 6.8 | Nonnegative matrices (as time permits) |
HOMEWORK
| Gregory-Canning | Prendergast-Smith | ||
| § 1.1 | 1c,4c,5c,10 | due: Fri Jan 20 | due: Fri Jan 20 |
| § 1.2 | 1,2,3,5acdhjl,6d,8,9,15,19 | due: Mon Jan 30 | due: Fri Jan 27 |
| § 1.3 | 1,2,10,11 | due: Mon Jan 30 | due: Fri Jan 27 |
| § 1.4 | 3,5,7,12,13,32,33 | due: Mon Feb 13 | due: Mon Feb 13 |
| § 1.5 | 1,2,3a,4a,6,8ac,9ab(iii),10aceg | due: Mon Feb 13 | due: Mon Feb 13 |
| § 2.1 | 1,3cfh,4 | Not due | Not due |
| § 2.2 | 2a,3ace,4,7 | Not due | Not due |
| § 2.3 | 1,2ac,5,6 | Not due | Not due |
QUIZZES/EXAMS
| Gregory-Canning | |
| Q1 | 1.1 Fri Jan 20 |
| Q2 | 1.2 Mon Jan 30 |
| Q3 | 1.4 Mon Feb 6 |
| E1 | Ch. 1 & 2 Mon Feb 13 |
STUDENTS WITH DISABILITIES
Students with disabilities who require special accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Students who need exam accommodations must contact ODS in the first week of the term to arrange a meeting with a Disability Specialist.
Please contact ODS at (312)-413-2183 (voice) or (312)-413-0123 (TTY).
