Numerical Methods
Online Course/Slides
Instructor:
Dr. Aaron Naiman
<naiman@math.jct.ac.il>
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About the course
Change log
13-week lesson plan
Course slides
first slide
last slide
thumbnails
Detailed outline
Taylor Series
Definitions and Theorems
Examples
Proximity of
x
to
c
Additional Notes
Base Representations
Definitions
Conversions
Computer Representation
Loss of Significant Digits
Nonlinear Equations
Motivation
Bisection Method
Newton's Method
Secant Method
Summary
Interpolation and Approximation
Motivation
Polynomial Interpolation
Numerical Differentiation
Additional Notes
Numerical Quadrature
Introduction
Riemann Integration
Composite Trapezoid Rule
Composite Simpson's Rule
Gaussian Quadrature
Linear Systems
Introduction
Naive Gaussian Elimination
Limitations
Operation Counts
Additional Notes
Approximation by Splines
Motivation
Linear Splines
Quadratic Splines
Cubic Splines
Summary
Ordinary Differential Equations
Introduction
Euler Method
Higher Order Taylor Methods
Runge-Kutta Methods
Summary
Least Squares Method
Motivation and Approach
Linearly Dependent Data
General Basis Functions
Polynomial Regression
Function Approximation
Simulation
Random Numbers
Monte Carlo Integration
Problems and Games
For the HTML and PostScript sources, see the
readme
file.
© The material of theses slides copyright by A. E. Naiman, 2003
Page preparation assistance by Gavrie Philipson