Mathematical Analysis and Applications: An Introduction

Front Cover
Alpha Science Int'l Ltd., 2004 - Mathematics - 341 pages
Mathematical Analysis and Applications is a first introduction to higher mathematics for students. Starting with a discussion of real numbers and functions, the text introduces standard topics of differential and integral calculus together with their applications such as differential equations, numerical analysis, and approximation methods.The subject is developed in an integrated manner, bringing out its essential unity and the interrelationship between these topics. The text is written in an informal manner and in lively language, but without sacrificing rigour in thinking and precision in writing, so essential in mathematics.

The book is divided in four Parts and seventeen Chapters, described below. A brief Historical Note is included at the end of each Part that describes the contributions of the mathematicians mentioned in the Text. The Book is ideally suited for class-room teaching and also for self-study to undergraduate students of Mathematics and of other disciplines such as Statistics, Physics, Computer Sciences or Engineering that use Mathematical Methods extensively. It is also a handy reference to teachers of Mathematics.
 

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Contents

RATIONAL NUMBERS
5
INDUCTION PRINCIPLE
19
REAL NUMBER SYSTEM
33
SETS AND FUNCTIONS
49
SEQUENCES
69
CONTINUOUS FUNCTIONS I
89
CONTINUOUS FUNCTIONS II
107
INFINITE SERIES
131
MEAN VALUE THEOREMS
171
TAYLORS THEOREM APPROXIMATION
189
POWER SERIES MAPS
205
RIEMANN INTEGRATION I
277
RIEMANN INTEGRATION II
301
RIEMANN INTEGRATION III
313
INDEX
338
Copyright

DIFFERENTIABLE FUNCTIONS
157

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