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**About this book :- **
**Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra, 2E ** written by
** Tom M. Apostol **.

The approach in this book has been suggested by the historical and philosophical development of calculus and analytic geometry. For example, integration is treated before differentiation. Although to some this may seem unusual, it is historically correct and pedagogically sound. Moreover, it is the best way to make meaningful the true connection between the integral and the derivative.

The concept of the integral is defined first for step functions. Since the integral of a step function is merely a finite sum, integration theory in this case is extremely simple. As the student learns the properties of the integral for step functions, he gains experience in the use of the summation notation and at the same time becomes familiar with the notation for integrals. This sets the stage SO that the transition from step functions to more general functions seems easy and natural.

(Tom M. Apostol)

**Book Detail :- **
** Title: ** Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra
** Edition: ** 2nd
** Author(s): ** Tom M. Apostol, Greg Hurst
** Publisher: ** John Wiley & Sons
** Series: **
** Year: ** 1967
** Pages: ** 686
** Type: ** PDF
** Language: ** English
** ISBN: ** 0471000051,9780471000051
** Country: ** US
**Download Similar Books from Amazon **

**About Author :- **
The author ** Tom M. Apostol ** joined the Caltech faculty in 1950 and is Professor of Mathematics, Emeritus. He is internationally known for his books on Calculus, Analysis, and Analytic Number Theory, (translated into 7 languages), and for creating Project MATHEMATICS!, a video series that brings mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international festivals, and were translated into Hebrew, Portuguese, French, and Spanish. Apostol has published 102 research papers, has written two chapters for the Digital Library of Mathematical Functions (2010), and is coauthor of three texts for the physics telecourse.

He has received several awards for research and teaching. In 1978 he was a visiting professor at the University of Patras, Greece, and in 2001 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek. In 2012 he was selected to be a Fellow of the American Mathematical Society.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Mathematical Analysis, 2E, Tom M. Apostol **

** • Download PDF Mathematical Analysis, 2E, Solution Manual, Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory (2E) by Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory (Solutions Manual) by Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory by Tom M. Apostol **

** • Download PDF Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol **

** • Download PDF New Horizons in Geometry, Tom M. Apostol, Mamikon A Mnatsakanian **

** • Download PDF Selected Papers on Precalculus, Tom M. Apostol **

** • Download PDF Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra, 2E, Tom M. Apostol **

** • Download PDF Calculus II: Multi-Variable Calculus & Linear Algebra, with Applications to Diff. Equations & Probability, Tom M. Apostol **

** • Download PDF Multimedia Tools for Communicating Mathematics by Tom M. Apostol, Jonathan Borwein, Maria H. Morales, José F. Rodrigues, Konrad Polthier **

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**Book Contents :- **
**Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra, 2E ** written by
** Tom M. Apostol **
cover the following topics.
'

0. INTRODUCTION

Part 1. Historical Introduction

Part 2. Some Basic Concepts of the Theory of Sets

Part 3. A Set of Axioms for the Real-Number System

Part 4. Mathematical Induction, Summation Notation, and Related Topics

1. THE CONCEPTS OF INTEGRAL CALCULUS

2. SOME APPLICATIONS OF INTEGRATION

3. CONTINUOUS FUNCTIONS

4. DIFFERENTIAL CALCULUS

5. THE RELATION BETWEEN INTEGRATION AND DIFFERENTIATION

6. THE LOGARITHM, THE EXPONENTIAL, AND THE INVERSE TRIGONOMETRIC FUNCTIONS

7. POLYNOMIAL APPROXIMATIONS TO FUNCTIONS

8. INTRODUCTION TO DIFFERENTIAL EQUATIONS

9. COMPLEX NUMBERS

10. SEQUENCES, INFINITE SERIES, IMPROPER INTEGRALS

11. SEQUENCES AND SERIES OF FUNCTIONS

12. VECTOR ALGEBRA

13. APPLICATIONS OF VECTOR ALGEBRA TO ANALYTIC GEOMETRY

14. CALCULUS OF VECTOR-VALUED FUNCTIONS

15. LINEAR SPACES

16. LINEAR TRANSFORMATIONS AND MATRICES

Answers to exercises

Index

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