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

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

Calculus II: Multi-Variable Calculus & Linear Algebra, with Applications to Differential Equations & Probability, Tom M. Apostol

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About this book :-
Calculus II: Multi-Variable Calculus & Linear Algebra, with Applications to Differential Equations & Probability written by Tom M. Apostol .
This book is a continuation of the author’s Calculus, Volume I, Second Edition. The present volume has been written with the same underlying philosophy that prevailed in the first. Sound training in technique is combined with a strong theoretical development. Every effort has been made to convey the spirit of modern mathematics without undue emphasis on formalization. As in Volume I, historical remarks are included to give the student a sense of participation in the evolution of ideas.
The second volume is divided into three parts, entitled Linear Analysis, Nonlinear Ana!ysis, and Special Topics. The last two chapters of Volume I have been repeated as the first two chapters of Volume II so that all the material on linear algebra will be complete in one volume.
Part 1 contains an introduction to linear algebra, including linear transformations, matrices, determinants, eigenvalues, and quadratic forms. Applications are given to analysis, in particular to the study of linear differential equations. Systems of differential equations are treated with the help of matrix calculus. Existence and uniqueness theorems are proved by Picard’s method of successive approximations, which is also cast in the language of contraction operators.
Part 2 discusses the calculus of functions of several variables. Differential calculus is unified and simplified with the aid of linear algebra. It includes chain rules for scalar and vector fields, and applications to partial differential equations and extremum problems. Integral calculus includes line integrals, multiple integrals, and surface integrals, with applications to vector analysis. Here the treatment is along more or less classical lines and does not include a formal development of differential forms.
(Tom M. Apostol)

Book Detail :-
Title: Calculus II: Multi-Variable Calculus & Linear Algebra, with Applications to Differential Equations & Probability
Edition:
Author(s): Tom M. Apostol
Publisher: John Wiley
Series:
Year: 1969
Pages: 696
Type: PDF
Language: English
ISBN: 9780471000075,0-471-00007-8
Country: US
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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 II: Multi-Variable Calculus & Linear Algebra, with Applications to Differential Equations & Probability written by Tom M. Apostol cover the following topics. '
PART 1. LINEAR ANALYSIS
1. LINEAR SPACES
2. LINEAR TRANSFORMATIONS AND MATRICES
3. DETERMINANTS
4. EIGENVALUES AND EIGENVECTORS
5. EIGENVALUES OF OPERATORS ACTING ON EUCLIDEAN SPACES
6. LINEAR DIFFERENTIAL EQUATIONS
7. SYSTEMS OF DIFFERENTIAL EQUATIONS
PART 2. NONLINEAR ANALYSIS
8. DIFFERENTIAL CALCULUS OF SCALAR AND VECTOR FIELDS
9. APPLICATIONS OF THE DIFFERENTIAL CALCULUS
10. LINE INTEGRALS
11. MULTIPLE INTEGRALS
12. SURFACE INTEGRALS
PART 3. SPECIAL TOPICS
13. SET FUNCTIONS AND ELEMENTARY PROBABILITY
14. CALCULUS OF PROBABILITIES
15. INTRODUCTION TO NUMERICAL ANALYSIS
Suggested References
Answers to exercises
Index

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