CS 514 - Numerical Analysis

Textbook:

• Numerical Analysis - an introduction
• Author: Walter Gautschi
• Published by Birkhauser

Grades:

• 25% Homework sets
• 30% Midterm Examinations
• 45% Final Examination
• All examinations are open-book/open-notes.

Instructor:

• Ahmed Sameh CS-222; sameh@cs.purdue.edu
• Office hours -- Tuesday 1:30 to 2:30 p.m.
• Or by appointment

Course Outline:

1. Floating-point Computations
   • Floating-point numbers
   • Floating-point arithmetic (basic operations)
   • Condition of problems
   • Stability of algorithms
2. Approximation of Functions
   • Basic concepts
   • Interpolation
     • Lagrange interpolation
     • Newoton’s interpolation
     • Hermite interpolation
     • Limitation of polynomial interpolation
     • Piecewise interpolation
     • Spline interpolation
     • B-splines
   • Linear least-squares approximation
3. Numerical Integration
   • Interpolatory quadrature
   • Adaptive quadrature
   • Gaussian quadrature
   • Difficulties in numerical integration
4. Nonlinear Equations
   • Single nonlinear equation
   • Systems of nonlinear equations
5. Ordinary Differential Equations
   • Two-point boundary value problems
   • Initial value problems: one-step methods
   • Initial value problems: multistep methods