The How And Why Of One Variable Calculus
by Amol Sasane
Wiley | August 2015 | ISBN-10: 1119043387 | PDF | 464 pages | 19.2 mb

First course calculus texts have traditionally been either engineering/ science-oriented with too little rigour, or have thrown students in the deep end with a rigorous analysis text. The How and Why of One Variable Calculus closes this gap in providing a rigorous treatment that takes an original and valuable approach between calculus and analysis.Logically organized and user-friendly, it covers 6 main topics; real numbers, sequences, continuity, differentiation, integration, and series. Primarily concerned with developing an understanding of the tools of calculus, it features numerous examples and exercises that illustrate how the techniques of calculus have universal application. Key features:
-  Provides a user-friendly text with more attention to rigour than is usually found in traditional calculus texts.
-  Can be used both as a first course and as a text for a bridge course between calculus and upper level mathematics.
-  Presents numerous illustrations, examples, exercises and detailed solutions to aid the reader’s understanding.

The How and Why of One Variable Calculus presents an excellent text for a first course in calculus for students in the mathematical sciences, statistics and business analytics. It can also be used as a text for a bridge course between single and multi-variable calculus, as well as between single variable calculus and upper level theory courses for math majors.

About the Author 
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Dr Amol Sasane is Associate Professor at Department of Mathematics, London School of Economics
Education: 1997-2001 PhD in Mathematics, University of Groningen, The Netherlands
1993-1997 Bachelor of Technology in Electrical Engineering, Indian Institute of Technology Bombay
Books published: Algebras of Holomorphic Functions and Control Theory (Dover, New York, 2009)
Hankel Norm Approximation for Infinite-Dimensional Systems
Lecture Notes in Control and Information Sciences 277, Springer, Berlin, 2002.


CONTENTS
Preface ix
Introduction xi
Preliminary notation xv
1 The real numbers 1
2 Sequences 44
3 Continuity 86
4 Differentiation 125
5 Integration 183
6 Series 297
Appendix 335
Notes 337
Solutions 338
Bibliography 493
Index 495
 
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