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calculus 1 one-variable linear algebra 2nd ed tom apostol [pdf]

# Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra, 2E, Tom Apostol

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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

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.

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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