Advanced Calculus: An Introduction to Modern Analysis

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CRC Press, Mar 1, 1981 - Mathematics - 696 pages
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Introduction to linear algebra and ordinary differential equations; Limits and metric spaces; Continuity, compactness and connectedness; The derivative: theory and elementary applications; A first look at integration; Differentiation of functions of several variables; An introduction to fourier analysis; An introduction to modern integration theory; An introduction to complex integration.
 

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Contents

Preliminaries
1
a A a is a member of the set A
5
I B complement of B relative to A
11
complex plane
18
1ntroduction to Linear Algebra
27
jC norm or length of x
37
PA B conditional probability
43
Limits and Metric Spaces
67
Differentiation of Functions of Several Variables
187
Sequences and Series
249
Elementary Applications of 1nfinite Series
293
An 1ntroduction to Fourier Analysis
329
An 1ntroduction to Modern 1ntegration Theory
395
An lntroduction to Complex 1ntegration
465
The Fourier and Laplace Transforms
537
A Sampling of Numerical Analysis
589

Continuity Compactness and Connectedness
91
The Derivative Theory and Elementary Applications
125
A First Look at 1ntegration
147
Answers to Selected Problems
647
Table of Laplace Transforms
662
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