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COS 233-8 : Numerical Methods


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  Notes

Errors
Root-finding methods
Iterative methods
Interpolating polynomials
Matrix methods
Numerical differentiation
Numerical integration
My lectures
Practice problems
UNISA assignments 2001
Exam papers
Links
Download a comprehensive summary of numerical methods

 

 
  Errors

Errors: sources and propagation
Types of errors
Error formula for Simpson's Rule
Error formula for the Trapezoidal Rule

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  Root-finding methods

Bisection method
Fixed-point iteration method
Newton's method
Regula Falsi method
Secant method

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  Iterative methods

Aitken's acceleration formula
Jacobi & Gauss-Siedel methods

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  Interpolating polynomials

Cubic Bezier curves and matrix forms
Cubic Splines
Lagrange interpolating polynomials
Least-squares approximations
Newton's divided difference method
Newton-Gregory polynomials
Piecewise polynomial functions
Taylor's polynomials

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  Matrix methods

Gaussian elimination (with partial pivoting)
L-U decomposition

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  Numerical differentiation

Richardson's interpolation

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  Numerical integration

Gaussian quadrature
Newton-Cotes formulae
Numerical Integration
Romberg integration
Trapezoidal rule
Simpson's rules

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  My lectures

Lecture 1 (Introduction)
Lecture 2 (Bisection method)
Lecture 3 (Errors)
Lecture 4 (The Secant method)
Lecture 5 (Regula falsi and Aitken's acceleration)
Lecture 6 (LU decomposition and Crout reduction)
Lecture 7 (The Jacobi and Gauss-Seidel methods; Southwell overrelexation method)

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  Practice problems

Exercise 1
Exercise 2 and Solutions
Exercise 3
Exercise 4 and Solutions
Exercise 5 and Solutions
Exercise 6 and Solutions
Exercise 7 and Solutions
Exercise 8 and Solutions
Exercise 9 and Solutions
Exercise 10
Exercise 11 and Solutions
Exercise 12 and Solutions
Exercise 13 and Solutions

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  UNISA Assignments 2001

Assignment 1 and Solutions
Assignment 2 and Solutions
Assignment 3 and Solutions
Assignment 4 and Solutions
Assignment 5
Assignment 6

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  Exam papers

UNISA October 2000 Exams and Solutions
June 2001 Mock Exams
September 2001 Mock Exams
August 2002 Mock Exams

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  Links

Introduction to Numerical Analysis (Maple)
Linear Algebra electronic textbook
Numerical Analysis Math 2070
Numerical Analysis Homepage
Freely available software for Linear Algebra
Programming and Numerical Analysis
Applied Linear Algebra
Numerical Analysis handouts
Power Point Slides Galore
Site for practice problems
Links to Numerical Analysis sites

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