Math 300 – Numerical Analysis.


T 12-1:50, room 412 Matheson, R 12-1:50, room 105D Korman.

Instructor: Anatolii Grinshpan
Current office hours:  TR 3:30-5 or by appointment, 270 Korman

Course information.   Math resource center.   Academic Calendar.

Textbook supplements (Atkinson’s website).

MATLAB tutorial.   Numerical Computing with MATLAB (Moler’s book).

Outline

Apr 3. Introduction. Taylor polynomials.

           Reading: Chapter 1.

 

Apr 5. Basics of  MATLAB. Polynomial evaluation.

           Approximation by Taylor polynomials. Example.

           Problems: 2 a), 4, 14 (1.1),  1, 4, 9 a),  13 (1.2),  7 (1.3).  

 

Apr 10. Decimal and binary number systems. Floating-point numbers.

             Reading: 2.1, 2.2, Appendix E. Subnormal numbers and biased exponents.

             Discussion of IEEE (Goldberg’s paper).

 

Apr 12. Quiz: decimal and binary arithmetic (appendix E, problems on page 531).

             LAB: error arithmetic. Extra credit.

             Reading 2.3, 2.4.

    

Apr 17. Rootfinding.

             Reading: 3.1-3.3.

             Problems 1 a), d), g), 11 (3.1),  2 a), d), 3, 13 (3.2).

 

Apr 19. Quiz: bisection and Newton’s method.

             LAB: rootfinding. Example from class.

             Strang’s paper on Newton’s method and iterations.

 

Apr  24. Secant method. Fixed point iterations.

              Reading: 3.3, 3.4. Extra credit.

              Problems: 8 (3.3), 3-7 (3.4)

 

Apr 26. LAB: fixed point iterations, ill-behaving rootfinding.

             Examples: multiple root slow down (newton1, newton2),

                             root instability for polynomials (wilkin).

 

May 1.   Quiz: fixed point iterations.

              Polynomial interpolation. Review.

            

May 3.   Test 1:  Chapters 1-3.  Important topics.

              Focus: homework and quiz questions, in class examples.

              Sample test. Exam answers.

 

May 8.  Lagrange and Newton interpolation.

             Reading: 4.1-4.3.

             Problems: 3, 4, 7, 12, 20, 24 (4.1).

 

May 10. Error in polynomial interpolation. Minimax problem.

              Chebyshev polynomials.

              Animations for Chebyshev interpolation (by John Mathews).

              Reading: 4.4, 4.5.

              Problems:  2, 9 (4.2).

 

May 15. Quiz: Lagrange and Newton interpolation.

              Splines. Legendre polynomials. Least squares approximation.

              Reading: 4.3, 4.7.

              Problems: Example 4.3.1; 2, 5 (4.5); Example 4.7.1; check formula (4.118) for i, j=0, 1, 2, 3.

 

May 17. Spline interpolation, Legendre polynomials. Legendre nodes.

              Applet: natural cubic splines (by Tim Lambert).

              Least squares approximation (continued).

              Reading: 5.1, 5.2.

              Problems: 2 (4.7).

 

May 22. Quiz: least squares approximation.

              Numerical integration, error formulas.

              Gaussian quadrature.

              Reading: 5.2, 5.3.

              Problems: 6, 8 (5.3).

 

May 24.  Richardson extrapolation. Numerical differentiation.

               Review.

               Reading: 5.4.

               Problems: 6, 8, 10 (5.4).

 

May 29.  Test 2:  Chapters 4 & 5.  Important topics. Sample. Sample test answers.

               Focus: homework, examples (textbook, class), quizzes. Test 2 answers.    

 

May 31.  Linear systems, Gaussian elimination.

               Lab: Legendre nodes, natural cubic spline.

               Reading: 6.1-6.3.   

 

June 5.    Solving systems of  linear equations: LU factorization.

               Early final for graduating seniors.     

               Reading: 6.4.

               Problems: Gaussian elimination, LU factorization for 3x3 systems (try your own examples).

 

June 7.   Quiz: Gaussian elimination, LU factorization.

              Solving linear systems: stability, error analysis.

              Iteration methods (Jacobi and Gauss-Seidel).     

              Reading: 6.5, 6.6.

              Problems: 4-6 (6.5), 3, 5 (do several iteration steps by hand) (6.6).

 

June 12. Questions session 3:30-5 (office).

 

June 14. Final exam: 8-10 A.M., Matheson 307.