For students enrolled in MATH 546, the above syllabus is modified as follows:
Week | Date | Topic/Materials | Homework/Test | ||
---|---|---|---|---|---|
Text | Wikipedia | Other | |||
1 | March 30 | Introduction | 344: 1, 2, 3, 4, 5 | ||
Direct Methods for Solving Linear Systems | |||||
March 31 | 6.1 | System of linear equations; Gaussian elimination | 344: 8, 9, 10 | ||
April 2 | 6.2 | Pivoting | 344: 11 | ||
April 3 | 6.3 | Linear algebra; Invertible matrix | |||
2 | April 6 | 6.4 | Determinant | Homework 1, using Layout | |
April 7 | 6.5 | LU decomposition | 344: 12 | ||
April 9 | 6.6 | Diagonally dominant matrix; Positive-definite matrix; Cholesky decomposition; Band matrix; Tridiagonal matrix | |||
April 10 | |||||
Iterative Techniques in Matrix Algebra | |||||
3 | April 13 | 7.1 | Norm; Normed vector space; Matrix norm | Homework 2, using Flow (drop deadline) | |
April 14 | |||||
April 16 | study guide | Test on Chapter 6 | |||
April 17 | 7.2 | Eigenvalue, eigenvector and eigenspace; Characteristic polynomial; Spectral radius | |||
4 | April 20 | 7.3 | Jacobi method; Gauss-Seidel method; Successive over-relaxation | ||
April 21 | 7.4 | Condition number | Homework 3, using Logic | ||
April 23 | |||||
April 24 | 7.5 | Conjugate gradient method | |||
5 | April 27 | ||||
Approximating Eigenvalues | |||||
April 28 | 9.1 | Eigenvalue, eigenvector and eigenspace; Linear independence; Orthonormal basis; Orthogonal matrix; Unitary matrix; Similar matrix; Gershgorin circle theorem | 344: 14 | Homework 4, using Symbols | |
April 30 | |||||
May 1 | study guide | Test on Chapter 7 | |||
6 | May 4 | (drop deadline with WP/WF) | |||
May 5 | 9.2 | Power iteration; Inverse iteration | 344: 16 | ||
May 7 | |||||
May 8 | 9.3 | Householder transformation; Hessenberg matrix | Homework 5, using Graphs | ||
7 | May 11 | 9.4 | Rotation matrix; Givens rotation; QR algorithm; QR decomposition | 344: 17 | |
May 12 | |||||
Numerical Solutions of Nonlinear Systems of Equations | |||||
May 14 | 10.1 | Fixed point; Contraction mapping; Jacobian matrix | Homework 6, using Intros | ||
May 15 | |||||
8 | May 18 | study guide | Test on Chapter 9 | ||
May 19 | 10.2 | Newton's method | 344: 13 | ||
May 21 | 10.3 | Quasi-Newton method; Broyden's method; Sherman-Morrison formula | |||
May 22 | |||||
9 | May 25 | Memorial Day, no class | |||
May 26 | 10.4 | Gradient descent | |||
May 28 | 10.5 | Homotopy | |||
May 29 | Homework 7 due | ||||
10 | June 1 | Project presentations | |||
June 2 | Project presentations | ||||
June 4 | Project presentations | ||||
June 5 | Review | Project reports due | |||
11 | June 11 | Thursday at 8:00am in our regular classroom | study guide | Final Exam | |