Syllabus for Math 609-600, Numerical Analysis, Fall 2017


General information:

Course description:

Course Outline:

Exam Schedule:

Grading Policy:

Americans with Disabilities Act (ADA) Policy Statement

Academic Integrity Statement and Policy

Helpful links:

==========================================================================================================



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

-----------------------------------------------------------------------------------------------

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)