Week |
Date |
Topic |
Homework/Test |
1 |
January 4 |
Introduction |
The Definition of Numerical Analysis |
| | Part I: Fundamentals |
|
January 5 |
1: Matrix-Vector Multiplication |
|
|
|
January 7 |
2: Orthogonal Vectors and Matrices |
Mathematical autobiography using the
Layout skill (LaTeX template) |
|
January 8 |
3: Norms |
Problems 1.1 and 1.3 |
2 |
January 11 |
4: The Singular Value Decomposition |
Problems 2.2 and 2.6 |
|
January 12 |
|
January 14 |
5: More on the SVD |
Problems 3.3 and 3.4 |
|
January 15 |
3 |
January 18 |
Martin Luther King, Jr. Day, no class |
| | Part II: QR Factorization and Least Squares |
|
January 19 |
6: Projectors |
Problem 4.1; Problem 4.2 using the Flow skill (drop deadline) |
|
January 21 |
7: QR Factorization |
Problem 5.3 |
|
January 22 |
|
Problems 6.2 and 6.4 |
4 |
January 25 |
| Test on Part I |
|
January 26 |
8: Gram-Schmidt Orthogonalization |
|
January 28 |
9 Matlab |
Problem 7.1 and 7.4 |
|
January 29 |
10: Householder Triangularization |
Problem 8.2; Problem 8.1 using the Logic skill |
5 |
February 1 |
11: Least-Squares Problems |
Problems 9.1 and 9.3 |
|
February 2 |
| | Part III: Conditioning and Stability |
|
February 4 |
12: Conditioning and Condition Numbers |
Problems 10.2 and 10.3 |
|
February 5 |
13: Floating Point Arithmetic |
Problems 11.1 and 11.3 |
6 |
February 8 |
| (drop deadline with WP/WF) |
|
February 9 |
|
Test on Part II |
|
February 11 |
14: Stability |
|
February 12 |
15: More on Stability |
Problem 12.2 using the Graphs skill |
7 |
February 15 | |
Problems 13.2 and 13.3 |
|
February 16 |
16: Stability of Householder Triangularization |
Problems 14.1 and 14.2 |
|
February 18 |
17: Stability of Back Substitution |
Problem 15.1 and 15.2 |
|
February 19 |
8 |
February 22 |
18: Conditioning of Least Squares Problems |
Problem 16.2 using the Intros skill |
|
February 23 |
|
Problems 17.1 and 17.2 |
|
February 25 |
19: Stability of Least Squares Algorithms |
| | Part IV: Systems of Equations |
|
February 26 |
20: Gaussian Elimination |
9 |
March 1 | |
Problems 18.1 and 18.2 |
|
March 2 |
21: Pivoting |
Problems 19.1 and 19.2 |
|
March 4 |
|
March 5 |
|
Test on Part III |
10 |
March 8 |
22: Stability of Gaussian Elimination
(Presentation) |
Problems 20.1 and 20.3 |
|
March 9 |
23: Cholesky Factorization (Presentation) |
Problems 21.1 and 21.6 |
| | Part V: Eigenvalues |
|
March 11 |
24: Eigenvalue Problems (Presentation) |
Problem 22.1 using the
Symbols skill |
|
March 12 |
Problems 23.1 and 23.3 |
11 |
March 17 |
Wednesday at 12:20 pm in our regular classroom |
Final Exam |