The schedule below is tentative. Please check the class website (Announcements) for changes/updates.
NM –
Numerical Methods Design, Analysis, and Computer
Implementation of Algorithms by Greenbaum
& Chartier
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Date
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Lecture Notes
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Week 1
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June 16 |
Lecture 1: Introduction, Numbers, Operators, Numerical Error [.pdf] NM Chp 5 (except 5.5) |
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June 17 |
Lecture 1: continued |
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June 18 |
Lecture 1: continued
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June 19 |
Lecture 2: Taylor Series, Rate of Convergence ,Condition Number , Stability [.pdf] NM Chps 4.2,5.5, 6, Appendix B |
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June 20 |
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Week 2
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June 23 |
Lecture 2: continued |
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June 24 |
Lecture 3: continued |
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June 25 |
Lecture 3: Root finding, Bracketing, bisection, Newton's method, Rate of Convergence, Condition Number [.pdf] NM Chps 4 (except 4.4.3, 4.5), 6 |
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June 26 |
Lecture 3: continued |
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June 27 |
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Week 3
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June 30 |
Lecture 4: Newton's Method in higher dimensions, Secant Method, Fractals, Matlab's fzero function [.pdf] NM Chp 4.43, 4.6, |
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July 1 |
Lecture 5: Solving systems of linear equations, simple cases. Cramer's Rule. [.pdf] NM Chp 7.1,7.2 (except 7.2.4), 7.3 Review of Linear Algebra [.pdf] NM Appendix A |
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July 2 |
Lecture 5: continued |
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July 3 |
Lecture 6: Gaussian elimination, LU factorization, Inverse of a matrix [.pdf] NM Chp 7.1, 7.2(except 7.2.4) |
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July 4 |
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Week 4
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July 7 |
Lecture 6: continued |
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July 8 |
Lecture 7: GE with pivoting, LUPA, LUPAQ [.pdf] NM Chp 7.4, 7.5 |
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July 9 |
Lecture 7: continued |
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July 10 |
Midterm Exam |
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July 11 |
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Week 5
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July 14 |
Lecture 7:continued |
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July 15 |
Lecture 8: Banded matrices, more LU, orthogonal, symmetric and symmetric positive definite matrices, Cholesky factorization, SVD [.pdf] NM Chp 7.2.4 |
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July 16 |
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July 17 |
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July 18 |
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Week 6
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July 21 |
Lecture 9: Least Square Problems, QR factorization, SVD and least squares [.pdf] NM Chp 7.6.1, 7.6.2 |
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July 22 |
Lecture 9: continued |
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July 23 |
Lecture 10: Sparse matrices. Jacobi, Gauss-Siedel, Conjugate Gradient iterative methods for solving a linear system. Power method, inverse power method for finding eigenvalues. [.pdf] NM Chp 12.1.1, 12.2.1-12.2.4 |
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July 24 |
Lecture 10: continued |
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July 25 |
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Week 7
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July 28 |
Lecture 11: Polynomial
Interpolation , Lagrange and Newton polynomials [.pdf]
NM Chp 8.1-8.5 |
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July 29 |
Lecture 11: continued |
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July 30 |
Lecture 12: Polynomial Interpolation. Piecewise polynomials, Splines [.pdf] NM Chp 8.6 |
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July 31 |
Lecture 12: continued |
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Aug 1 |
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Week 8 |
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Aug 4 |
Lecture 13: Definite Integrals, Newton-Cotes, Monte Carlo, Random Numbers, Gaussian Quadrature [.pdf] NM Chp 10.1-10.3 |
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Aug 5 |
Lecture 13: continued |
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Aug 6 |
Lecture 13: continued |
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Aug 7 |
READINGS DAY 1pm |
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Aug 8 |
Final Exam (Time and location to
be determined) |