Introduction (And Things You

Lecture Notes For
Numerical Analysis 
M315

Prof. Paul A. Gray Fall, 1998  

• Introduction

(And Things You Should Know)
• Errors Which We Encounter
• Sources of Errors
• Definitions
• Representing Numbers
• Floating-Point Representation
• Representational Limitations
• The Hidden Bit
• Finite Representability Set
• Rounding and Chopping
• Overflow and Underflow
• Loss of Significance Errors
• Roots of a Single-Variable Equation
• The Bisection Method
• Bisection Error Analysis
• Newton's Method
• Convergence of Newton's Method
• The Secant Method
• Secant Method Convergence
• Fixed-Point Iterations
• Numerical O.D.E.'s
• Background
• Notation
• Euler's Method
• Convergence and Error Analysis of Euler's Method
• Alternative Derivations of Euler's Method
• Derivation via Taylor's Theorem
• Derivation via Numerical Integration
• Derivation via Tangent Line Approximation
• Higher-Order Methods
• Taylor Series Expansion
• Runge-Kutte Methods
• Mathematica and Solutions to Ordinary Differential Equations
• Summary
• References
• About this document ...

Wed Oct 28 11:42:13 EST 1998