## Numerical Analysis and Computing

SPRING 2019

Course web page: http://www.math.rutgers.edu/~wz222/teaching/cs323

Instructor: Wujun Zhang
(wujun@math.rutgers.edu)
214 Hill Center
office hrs: TBD by appointment

Teaching assistant: TBA
(luhan@cs.rutgers.edu )
TBA
office hours: to be announced

...recitation starts SECOND week of classes

Text: (recommended)  K. Atkinson & W. Han, Elementary Numerical Analysis, 3rd edition, Wiley
on reserve in SERC reading room

Additional material: The Book authors have a website that provides slides and matlab programs for the course-- CLICK HERE

Prerequisites:  CALC1, CALC2, Math 250 (linear algebra), ability to program in a high level language

Programs will be written in MATLAB language - Matlab tutorial + links to other references

• written homework, QUIZES and computer programs (4-5) ~ 20%
• midterm ~ 40%
• final exam ~ 40%
Objectives:   derivation, analysis, implementation of algorithms for numerical problems

Outline of topics...

• A Rapid Matlab Introduction
• Floating point numbers and roundoff error (Chap. 1-2 of text)
• Solution of nonlinear algebraic equations (Chap. 3)
• bisection method, fixed point iteration, secant method, Newton's method
• roots of polynomials
• Solution of linear algebraic systems (Chap. 6)
• Gaussian elimination, partial pivoting
• matrix inversion
• LU decomposition
• error analysis
• iterative methods
• Least squares approximation (Chap. 7.1)
• Polynomial interpolation (Chap. 4)
• Lagrange and Newton forms of interpolating polynomial
• error term
• interpolation of derivatives
• piecewise polynomial interpolation, splines
• Numerical differentiation and integration (Chap. 5)
• derivation of quadrature formulas and their error terms
• composite formulas