Math 455 – Numerical Analysis
Semester: 1/2557

Instructor: Dr. Nattapol Ploymaklam
Office: MB 2306
Office Hours: Tu F at 4-5 pm, or by appointment
Email: nploymaklam at gmail dot com

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Final

Time: Tuesday, 7 December 2014 at 3:30-6:30 p.m. (15:30-18:30 น.)

Location: MB 2213-14

Recap

Date	Topics	Note
Friday, August 15	Chapter 1: Interpolation Theory Polynomial interpolation: Lagrange method and Newton method	Syllabus, Homework 1, Plot sample
Tuesday, August 19	No class (National Science day activities)
Friday, August 22	Divided difference, Hermite interpolation	Homework 2
Tuesday, August 26	Cubic spline, group exercise	Project 1
Friday, August 29	Group project presentation Intro to MATLAB: Xsquared, Commands	Homework 3
Tuesday, September 2	Cubic spline (continued), Cubic B-Spline Function in MATLAB: DD2 DD2b	Homework 4
Friday, September 5	Chapter 2: Approximation of functions Bernstein polynomial Recursive function in MATLAB: DD2new, DD3new, Fibonacci, FibonacciR, Commands	Homework 5
Tuesday, September 9	Proof of Weierstrass Theorem, General approximation problem, Uniform (minimax) approximation by polynomial
Friday, September 12	Uniform approximation (continued), Least square, Approximation in pre-Hilbert space
Tuesday, September 16	Normal equation, Orthogonal polynomials	Homework 6 due Friday, September 26, 2014 Use f(x) = e^xcos(2πx)
Friday, September 19	General least square, orthogonal polynomials For loop in MATLAB: DividedDiff, Commands
Tuesday, September 23	Chapter 3: Numerical analysis for ODE ODE review, Euler’s method	Homework 7
Friday, September 26	Truncation error, numerical error MATLAB: Euler1, Commands	Ch1: some exam problems HW 5 extra credit
Tuesday, September 30	Derivations and orders of Euler, Trapezoidal, and Midpoint methods. In-class exercise	HW 6 solution Midterm review
Friday, October 3	Problem session and review	Ch2: some exam problems
Tuesday, October 7	No class
Wednesday, October 8	Midterm 8:00-11:00 a.m.
Friday, October 10	No class
Tuesday, October 14	Multistep method, Adams methods Matrices in MATLAB: Commands	Homework 8
Friday, October 17	Adam-Bashforth and Adam-Moulton methods, Stability and convergence, Root condition
Tuesday, October 21	Strong root condition, relative stability, region of absolute stability
Friday, October 24	Runge-Kutta methods, Second order ODE, Boundary value problems, Shooting method	Homework 9 16-point Gauss-Legendre Project 2
Tuesday, October 28	Chapter 4: Numerical methods for PDE Forward/backward/central difference. Intro to PDE, Heat equation
Friday, October 31	Finite difference for Heat equation, stability In-line function and diag commands in MATLAB: Commands
Tuesday, November 4	More on heat equation, advection equation	Slideshow from 11/3 Colloquium HW 8 solution
Friday, November 7	Wave equation, Laplace equation Mathematica: Function definition and its integral
Tuesday, November 11	Eigenvalue
Friday, November 14	Location of eigenvalues, power method MATLAB: Commands Mathematica: Commands	Homework 10 Due Tuesday, November 25, 2014
Tuesday, November 18	Power iteration, Rayleigh iteration MATLAB: Commands, RQIteration
Friday, November 21	QR factorization and QR algorithm	HW 9 solution
Tuesday, November 25	Application of Numerical analysis
Friday, November 28
Tuesday, December 2	Final week	HW 10 solution Correction Final review
Friday, December 5	Final week
Sunday, December 7	Final 3:30-6:30 p.m. Location: MB 2213-14

Lecture notes

Tentative schedule

Scores