Do not worry about your difficulties in mathematics; I can assure
you that mine are still greater. -Albert Einstein (1879-1955)
- Montana State University
- Department of Mathematical Sciences
- Registrar:
- Term Calendar
- Math Course Catalog
- Search classes.
- Registratiion Handbook including the Final Exam Schedule
- MATLAB's on-line help
- 12/16 Final Exam 3 from 2-3:50pm in Wilson 1-144. Topics: First part of course to exam 1; second part of course.
You are allowed to bring a two pages of notes and a calculator.
- 11/18 DUE date for Take Home Exam 2 on least squares, Chapter 3. Helpful Examples.
- 10/7 Exam 1, list of topics. You are allowed to bring a single page of notes (one sided). Solutions.
- DUE: 12/16 (day of the final exam) Consider some problem that interests you and apply some idea that you learned in this course to model, solve, and/or analyze the problem. The first requirement that you must satisfy in order to qualify for the extra credit: get approval from Al on your idea. Second requirement: your write-up must be typed.
- DUE: 12/11 project 9. All relevant code is below under 11/25-12/9 course schedule. Data: A10x10.mat, A100x100.mat and AIDS cases. Solutions
- DUE: 12/2 project 8 on §5.4-5.6 and 6.2. fftAnal2.m for data analysis using the Fourier Transform, electricity data. Solutions: #1, #2, #5, #6 and #7
- DUE: 11/25 Project 7 on §5.2-5.3. Solutions: Power Method and Shift and Invert (Inverse Iteration is just Shift and Invert run with shift = 0).
- DUE 10/30 Project 6 on chapters 2, 3, and 4. Solutions
- DUE: 10/23 Project 5 on chapter 2. Code: ZoomInPoly, TSVDOneD, Eigenfaces, Face Data. Solutions
- DUE: 10/2 Project 4 on §1.4-1.6. Solutions
- DUE: 9/25 Project 3 on §1.7-1.8. Solutions
- DUE: 9/18 Project 2 on §1.2-1.3. Optional MATLAB lab1. Taylor series m-file. Solutions
- DUE: 9/11 Project 1: In §1.1, do exercises 1.1.8, 1.1.9, 1.1.10, 1.1.14 from the textbook. Print off the appropriate output from MATLAB and hand in. Be sure to organize your work and solutions.
- 12/11 Review
- 12/9 Non-linear
least squares; Gauss
Newton Example for exponential
fit.
- 12/4 Optimization: Newtons Method in 2-D for the Rosenbrock function.
- 12/2 §6.5 Sensitivity of Eigenvalue problems and
stability of QR algorithm; Newton's Method.
mfiles: numint.m,
newton.m. Apply these to any of MATLAB's
built-in functions (exp, log, sqrt ...), or try a Gaussian,
a 6th
order polynomial or its 5th order derivative.
- 11/27 HAPPY TURKEY DAY. No class.
- 11/25 §6.3 An eigensolver for large sparse matrices: Lanczos;
Numerical Integration review. mfiles:
Lanczos.m (Big version, saves
everything), lanczos2.m (only tridiagonal T is
saved).
- 11/25 §5.6,6.2 Proof of Convergence: QR Algorithm is Simultaneous Power Iteration. Cost and Hessenberg preconditioning
- 11/18 §5.4,5.6 Schurs Lemma and the QR Algorithm for finding
eigenvalues and eigenvectors.
- 11/13 § 5.3 The Power, Inverse Power and Shift and Invert Methods
- 11/11 VETERANS DAY. No class today.
- 11/6 § 5.1 A hopeless algorithm (for big problems): finding eigenvalues via roots of the characteristic polynomial; Continuous, Discrete and Fast Fourier Transforms.
- 11/4 GO VOTE! No class today.
- 10/30 § 3.3, 4.4, 5.1 More on sensitivity, QR-LS cost, Eigenvalue problems. Data Analysis using the Fourier Transform: fftAnal
- 10/28 § 3.3, 3.5, 4.4 Calculating the QR factorization via
Householder reflections;
Legendre Polynomials; sensitivity of least squares methods. reflect.m and ZeroOut
- 10/23 §3.2-3.3 When is the QR factorization unique; when is the least squares solution unique; Gram-Schmidt, Givens rotations and Householder reflections.
- 10/21 §3.5 and 4.1 Least Squares Solutions and Orthogonal Projections; full and partial (or
condensed) SVD
- 10/16 §3.3-4.3, 3.5 Least Squares via classic method, QR factorization or SVD: lab2, data: crime, ultrasound, global warming.
- 10/14 §2.5, 2.7,3.1 Stability Analysis; Backward Stability of
Gauss Elimination; Least Squares; Eigenfaces: code, data
- 10/9 §2.4 Residuals; and an example of an ill conditioned problem: Image blurring due to the atmosphere and deblurring using the truncated singular value decomposition. Code: 1D problem, 2 D problem
- 10/7 Exam 1
- 10/2 Review
- 9/30 §2.2 Matrix norms and the condition number
- 9/25 §2.1 Sensitivity Analysis, Error models, vector norms
- 9/23 §1.5-1.6 Sparse and banded matrices
- 9/18 §1.4 Cholesky factorization
- 9/15 §1.4,1.8 Calculating inverses; postive definite matrices;
covariance matrices; principle component analysis.
- 9/11§1.7-1.8 Gaussian Elimination
- 9/9 §1.2-1.3 Review of linear algebra concepts such as
linear
independence, range and null spaces, basis and spanning sets; solving
triangular systems
- 9/4 §1.1 and 2.5 Matrix multiplication; floating point numbers and FLOP's,
- 9/2 Overview of the course
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