SM313: Engineering Mathematics for Electrical Engineers
Linear Algebra and Probability with Applications Fall 2000-2001
Texts: Richard Bronson, Matrix Operations (Schaum’s Outline Series) and Walpole, Myers, and Myers, Probability and Statistics for Engineers and Scientists, 6th edition.
| LECTURE | TOPIC | CHAPTER | EXERCISES |
| Linear Algebra | |||
| 1 |
Systems of linear equations | ||
| 1,2 | ------------ | ||
| 2 | Matrix operations | 1,2 | Chapter 1: 19-31,34,35 |
| 3 | Elementary row ops, echelon form | 1 | ------------ |
| 4 | Gaussian elimination | 2 | Chapter 2: 17,18,23,25,27,28a,31,32 |
| 5 | Inverses, row echelon method | 4 | Chapter 4: 5(all),16,18,20,26,29,31a |
| 6 | Determinants | Chapter 5: 22(all),24ab,25 | |
| 7 | Determinants, Cramer’s Rule | 5 | Chapter 5: 2.27,4.8,4.9 by C’s Rule |
| 8 | Linear independence, dependence | 6 | Chapter 6: 15,16,19,21,24 |
| 9 | Span | Handout 1 | Handout 1 |
| 10 | Bases, dimension | Handout 1 | Handout 1 |
| 11 | Solutions as subspaces | 1-6 | Handout 2 |
| 12 | Problem session / review | ||
| 13 | Exam Wednesday Sept 20 (Lessons 1-12) | ||
| 14 | Eigenvalues and eigenvectors | 7 | Chapter 7: 18-21,23,24,28,29,32,33 |
| 15 | Linear systems of DE’s | Handout 3 | Handout 3 |
| 16 | Coupled oscillators | Handout 3 | Handout 3 |
| 17 | Coupled oscillators | Handout 3 | Handout 3 |
| Probability | |||
| 18 |
Introduction to probability | ------------- | |
| 19 | Sets | 2.1,2.2 | p. 17: 4,8,10,14,18,19 |
| 20 | Basic counting principles | 2.3 | p. 27: 2,3,6,10,12,20,24,25,27,29 |
| 21 | Probabilities of events | 2.4,2.5 | p. 33: 1,3,5,8,10,13,14, p. 49: 12 |
| 22 | Problem session / review | ||
| 23 | Exam Monday Oct 16 (Lessons 14-22) | ||
| 24 | Conditional probabilities / independence of events | 2.6,2.7 | p. 42: 2,6,7,9,22,14,17,18 |
| 25 | Bayes rule | 2.8 | p. 48: 1,3,5,6, p. 49: 1,10 |
| 26 | Random variables | 3.1 | |
| 27 | Probability distribution functions | 3.2,3.3 | p. 61: 1,3,4,5,7,8,10,12,14,17,21,25 |
| 28 | Joint distributions | 3.5 | p. 79: 2,3,5,8,14,15,16,18,19 |
| 29 |
Mean and variance | 4.1,4.2 | p. 90: 1,2,4,7,9,13,14,17,26; p. 100: 3,4,8,9,11, p. 111: 5,7 |
| 30 | Binomial distribution | 5.3 | p. 122: 5,7,11,16,19,20,25,27 |
| 31 | Hypergeometric distribution | 5.4 | p. 131: 1,3,7,8,11,13,16,18 |
| 32 | Negative binomial and geometric distribution | 5.5 | |
| 33 | Poisson distribution | 5.6 | p. 139: 1,2,4,5,8,10,12,13,14,17a |
| 34 | Exponential and uniform distributions | 6.1,6.2 | p. 158: 20,21,22, p. 178: 2 |
| 35 | Normal distribution | 6.2,6.3 | p. 158: 1,3,4,7,8,9,10,13,14 |
| 36 | Normal distribution | 6.4 | Handout 4 |
| 37 | Central limit theorem | Handout 4 | Handout 4 |
| 38 | Central limit theorem | ||
| 39 | Problem session / review | ------------ | |
| 40 | Problem session / review | ------------ | |
| 41 | Exam Wed Nov 29 (Lessons 24-40) | ||
| 42 | Review linear algebra | ------------ | |
| 43 | Review probability | ------------ | |
| 44 | Problem session / review | ------------ | |
| 45 | Problem session / review | ------------ | |
Here are the due dates for the HW:
| Number | Lesson # | Due Date |
| HW1 |
2,3,4 |
Friday, September 1 |
| HW2 | 5,6,7 | Wednesday, September 13 |
| HW3 | 8,9,10,11 | Friday, September 22 |
| HW4 | 14,15,16,17 | Wednesday, October 4 |
| HW5 | 19,20,21 | Wednesday, October 18 |
| HW6 | 24,25 | Wednesday, October 25 |
| HW7 | 27,28,29 | Friday, November 3 |
| HW8 | 30,31 | Wednesday, November 8 |
| HW9 | 33,34 | Friday, November 17 |
| HW10 | 35,36,37 | Monday, December 4 |