Introductory Analysis A Deeper View of Calculus~tqw~ darksiderg

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Introductory Analysis: A Deeper View of Calculus
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Release NotesIntroductory Analysis: A Deeper View of Calculus addresses the needs of students
taking a course in analysis after completing a semester or two of college level
calculus. Textbooks written at this level often assume mathematics majors as
their primary audience. This book offers a practical alternative. By using a
conversational tone and style that nonetheless does not compromise mathematical
rigor, the author explains real analysis in terms that help the reader gain a
firmer grasp of calculus concepts before studying more rigorous or abstract
mathematics.

Table Of Contents

Table of Contents
Acknowledgments
Preface
I The Real Number System
1 Familiar Number Systems 1
2 Intervals 6
3 Suprema and Infima 11
4 Exact Arithmetic in R 17
5 Topics for Further Study 22
II Continuous Functions
1 Functions in Mathematics 23
2 Continuity of Numerical Functions 28
3 The Intermediate Value Theorem 33
4 More Ways to Form Continuous Functions 36
5 Extreme Values 40
III Limits
1 Sequences and Limits 46
2 Limits and Removing Discontinuities 49
3 Limits Involving [infinity] 53
IV The Derivative
1 Differentiability 57
2 Combining Differentiable Functions 62
3 Mean Values 66
4 Second Derivatives and Approximations 72
5 Higher Derivatives 75
6 Inverse Functions 79
7 Implicit Functions and Implicit Differentiation 84
V The Riemann Integral
1 Areas and Riemann Sums 93
2 Simplifying the Conditions for Integrability 98
3 Recognizing Integrability 102
4 Functions Defined by Integrals 107
5 The Fundamental Theorem of Calculus 112
6 Topics for Further Study 115
VI Exponential and Logarithmic Functions
1 Exponents and Ligarithms 116
2 Algebraic Laws as Definitions 119
3 The Natural Logarithm 124
4 The Natural Exponential Function 127
5 An Important Limit 129
VII Curves and Arc Length
1 The Concept of Arc Length 132
2 Arc Length and Integration 139
3 Arc Length as a Parameter 143
4 The Arctangent and Arcsine Functions 147
5 The Fundamental Trigonometric Limit 150
VIII Sequences and Series of Functions
1 Functions Defined by Limits 153
2 Continuity and Uniform Convergence 160
3 Integrals and Derivatives 164
4 Taylor's Theorem 168
5 Power Series 172
6 Topics for Further Study 177
IX Additional Computational Methods
1 L'Hopital's Rule 179
2 Newton's Method 184
3 Simpson's Rule 187
4 The Substitution Rule for Integrals 191
References 197
Index 198

Product Details

* ISBN: 0120725509
* ISBN-13: 9780120725502
* Format: Textbook Hardcover, 220pp
* Publisher: Elsevier Science & Technology Books
* Pub. Date: June 2000
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