ANALYSIS

A GATEWAY TO UNDERSTANDING MATHEMATICS

By: Seán Dineen

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Hardcover | 4 May 2012

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Hardcover
320 Pages

Dimensions(cm)
22.86 x 15.24 x 1.91

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This book shows that it is possible to provide a fully rigorous treatment of calculus for those planning a career in an area that uses mathematics regularly (e.g., statistics, mathematics, economics, finance, engineering, etc.). It reveals to students on the ways to approach and understand mathematics. It covers efficiently and rigorously the differential and integral calculus, and its foundations in mathematical analysis. It also aims at a comprehensive, efficient, and rigorous treatment by introducing all the concepts succinctly. Experience has shown that this approach, which treats understanding on par with technical ability, has long term benefits for students.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Booktopia Publisher Services World Scientific Publishing

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Paperback

Published: 14th May 2012

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Preface	p. xi
Quadratic Equations	p. 1
Quadratic Equations	p. 1
Further Consequences	p. 14
Exercises	p. 19
Diagrams	p. 21
Graphs	p. 21
Exercises	p. 37
Functions	p. 39
Functions	p. 39
Generating New Functions	p. 53
Exercises	p. 57
Inverse Functions	p. 59
Injective and Surjective Functions	p. 60
Bijective Functions and Inverses	p. 63
Increasing, Decreasing, Convex and Indicator Functions	p. 69
Exercises	p. 72
Numbers	p. 77
The Positive Integers	p. 77
The Integers and Rational Numbers	p. 85
Arithmetic and Geometry	p. 93
Exercises	p. 101
Sets of Real Numbers	p. 103
Countable Sets	p. 103
Uncountable Sets	p. 108
Sets Which Are Bounded Above	p. 110
Intervals	p. 114
Exercises	p. 115
Series with Positive Entries	p. 117
Increasing and Decreasing Sequences	p. 117
Series with Positive Entries	p. 124
The Exponential Function	p. 128
Multiplication of Series	p. 130
The Log Function	p. 131
Exercises	p. 135
Review and Transition	p. 137
Review and Preview	p. 137
Convergent Sequences	p. 139
Convergent Series	p. 142
Power Series	p. 148
Exercises	p. 151
Continuous Functions	p. 155
Continuous Functions	p. 155
Intermediate Value Theorem	p. 159
Fundamental Existence Theorem for Maxima and Minima	p. 162
Exercises	p. 166
Differentiable Functions	p. 169
Differentiable Functions	p. 169
Basic Functions and Rules for Differentiation	p. 174
Mean Value Theorem	p. 177
Exercises	p. 185
Applications of Differentiation	p. 189
Sequences	p. 189
Limits	p. 192
Curve Sketching	p. 195
Applications of the Mean Value Theorem	p. 201
In Retrospect	p. 211
Exercises	p. 213
The Real Numbers	p. 219
Upper Bounds	p. 219
Dyadic Sections and the Bisection Principle	p. 222
Foundational Developments	p. 229
Infinitesimals	p. 234
Exercises	p. 235
Integration Theory	p. 237
The Riemann Integral	p. 237
Fundamental Theorem of Calculus	p. 245
Methods of Integration	p. 247
Exercises	p. 251
Applications of Integration Theory	p. 253
Integral Inequalities	p. 254
Integrals over Infinite Intervals	p. 255
Taylor's Theorem	p. 262
Exercises	p. 265
Solutions	p. 269
Bibliography	p. 291
Index	p. 295
Table of Contents provided by Ingram. All Rights Reserved.

ANALYSIS

A GATEWAY TO UNDERSTANDING MATHEMATICS

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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