Syllabus for Math 609-600, Numerical Analysis, Fall 2017
General information:
- Instructor: Dr. Bojan Popov, Blocker 507B
- URL address: /~popov/math609.html
- Time: MW 11:10 -- 12:25 (regular class) and T 3:55 - 4:45 pm (lab)
- Classroom: MW BLOC 605AX; Lab: BLOC 128 by Yanbo Li, Blocker 604A (liy@math.tamu.edu)
- Office Hours: MW 1:30 p.m. -- 2:30 p.m. or by appointment; TA Office Hour: Friday 10am--11am.
- Text: Numerical Analysis by D. Kincaid & W. Cheney, Brooks & Cole Publ., 1996.
- The third edition printed in 2002 is the one I have: ISBN 0-534-38905-8
- Other books about numerical linear algebra: Trefethen-Bau, Golub-VanLoan
- Lectures 1-5 from the Trfethen's book
- Syllabus link
Course description:
- This is a
one-semester course on numerical analysis which gives an introduction
to various topics in numerical methods and provides a firm basis for
future study.
- The Labs provide help in programming and problem solving. Here is the Labs home-page.
Course Outline:
- Direct and Iterative Methods for Solving Linear and Nonlinear Systems
- Polynomial (Lagrange and Hermite) and Spline Interpolation
- Numerical Differentiation and Integration
- Initial Value Problems for Ordinary Differential Equations (ODE)
- Finite Difference Method for Two-Point BVP for ODE's (if time permits)
Exam Schedule:
- Test #1, Wednesday, October 4, 2017, numerical linear algebra
- Test #2, Monday, November 20, 2017, interpolation, numerical differentiation
- Final Exam, December 13, 2017, 10:30-12:30 (cumulative)
Grading Policy:
- Your grade for the course will be computed as follows:
- your MINIMUM grade will be A, B, C, or D, for averages of 90%, 80%, 65%, or 50%, respectively.
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- Final Exam Schedule: http://admissions.tamu.edu/registrar/general/finalschedule.aspx
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Fall 2017 schedule:
Lecture 1. Wednesday, August 30, 2017
Systems of linear equations: basic facts, simple matrices, equivalent systems, inverse, symmetric PD, eigenvalues
Lecture 2. Monday, September 4, 2017
Symmetric PD
matrices, eigenvalues/eigenvectors again; LU-factorization algorithm
and computational cost
Direct methods for linear systems
Lecture 3. Wednesday, September 6, 2017
Direct methods for linear systems again and introductions in vector spaces & operators/matrix norms
Lecture 4. Monday, September 11, 2017
Matrix norms, condition number, basic linear algebra facts
Lecture 5. Wednesday, September 13, 2017
Matrix norms again and some basic iterative methods
Lecture 6. Monday, September 18, 2017
Fundamental theorem for iterative methods; Eigenvalues of some tridiagonal matrices
Lecture 7. Wednesday, September 20, 2017
Matrix norms Fundamental theorem for iterative methods again Gerschgorin's theorem, convergence of Jacobi
Lecture 8. Monday, September 25, 2017
Convergence results for Richardson, Jacobi, Gauss-Seidel using the fundamental
theorem and Gerschgorin's theorem.
Lecture 9. Wednesday, September 27, 2017
Connvergence
of SOR (and GS) for Symmetric PD matrices continued, nonstationary
iterative methods
Lecture 10. Monday, October 2, 2017
Review for Exam
#1 - based on the homework, the sample test, and
sections 4.1-5.2 from the textbook.
Lecture 11. Wednesday, October 4, 2017 Exam 1, Exam 1 solutions
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Lecture 12. Monday, October 9
Variational methods: steepest descent (SD), conjugate gradient (CG), GMRES, MINRES
Lecture 13. Wednesday, October 11
Conjugate Gradient
Lecture 14. Monday, October 16
Convergence of CG
Lecture 15. Wednesday, October 18
Convergence of CG continued and brief introduction to nonlinear problems
Lecture 16. Monday, October 23, 2017
Approximation theory: Section 6.1 and Sections 6.2 from the book. Returned the
exams - check your grade online (ecampus)
Lecture 17. Wednesday, October 25
Section 6.2 and 6.3. Finished the class with approximation by
linear positive operators: Bohman-Korovkin Theorem
Lecture 18. Monday, October 30
Section 6.4 - Note that Homework 4 and Programing assignment are due on November 13.
Lecture 19. Wednesday, November 1
Numerical differentiation and intergation: sections 7.1, 7.2 and 7.3 in the book.
Extra problems: Section 7.1: page477/
7,14,16,18; Section 7.2: page488/2,4,10,13,22;
Section 7.3: page499/11,14,15,17,22,28
Lecture 20. Monday, November 6. Composite rules and Gaussian rules for integration.
Lecture 21. Wednesday, November 8. Error estimates for Gaussian rules, Romberg Integration, Adaptive rquadrature,
Lecture 22. Monday, November 13. Trigonometric interpolation (section 6.12); FFT;
Lecture 23. Wednesday, November 15. Review for Exam 2. Interpolation, Numerical integration and differentiation.
In addition to Homework 3 and 4, please have a look at tone old test: Old Exam2 solutions;
and the solutions of the Chapter 7 extra problems: Extra problems- solutions; Homework 4 solutions;
Lecture 24. Monday, November 20. Exam 2.
Lecture 25. Wednesday, November 22. Chapter 8.1 - existence and uniqueness of solutions of ODEs.
Lecture 26. Monday, November 27. Chapter 8 again: sections 8.1 and 8.2
Sections 8.1 and 8.2 from
the book: Numerical solution of ODEs: existence and uniqueness, Taylor
series methods
Lecture 27. Wednesday, November 29. Chapter 8 - section 8.3.
Numerical solution of ODEs: Runge-Kutta methods, forward Euler error estimate
Suggested problems from
Chapter 8: Section 8.1/1,3,7; Section 8.2/3; Section 8.3/3 -- short
solutions here: page 1, page 2
Lecture 28. Monday, December 4. More on numerical ODE methods - review of Chapter 8.
Solutions of the second exam: page1 page2 page3 page4 page5
Lecture 29. Wednesday, December 6. General review: Final exam format: 3 + 3 + 1 problems from part 1 + part 2 + ODE
Final Exam, December 13, 2017, 10:30 - 12:30 (cumulative)