Key Idea

Contents Summary

Title Page
Contents
1. Introduction
2. Key Idea
3. Root finding in one dimension
4. Linear equations
5. Numerical integration
6. First order ordinary differential equations
7. Higher order ordinary differential equations
8. Partial differential equations

2. Key Idea

The central idea behind the majority of methods discussed in this course is the Taylor Series expansion of a function about a point. For a function of a single variable, we may represent the expansion as

.

(1)

In two dimensions we have

.

(2)

Similar expansions may be constructed for functions with more independent variables.

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