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### Advanced Calculus, Theory and Practice by John Srdjan Petrovic

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Advanced Calculus, Theory and Practice written by John Srdjan Petrovic .
This text was written for a one-semester or a two-semester course in advanced calculus. It has several goals: To expand the material covered in elementary calculus, and to present it in a rigorous fashion; to improve problem-solving and proof-writing skills of students; to make the reader aware of the historical development of calculus concepts and the reasons behind it; and to point out the connection between various topics.
Sequences and Their Limits Computing the LimitsDefinition of the Limit Properties of Limits Monotone Sequences The Number e Cauchy Sequences Limit Superior and Limit Inferior Computing the Limits-Part II Real Numbers The Axioms of the Set R Consequences of the Completeness Axiom Bolzano-Weierstrass Theorem Some Thoughts about RContinuity Computing Limits of Functions A Review of Functions Continuous Functions: A Read more...
Abstract: Sequences and Their Limits Computing the LimitsDefinition of the Limit Properties of Limits Monotone Sequences The Number e Cauchy Sequences Limit Superior and Limit Inferior Computing the Limits-Part II Real Numbers The Axioms of the Set R Consequences of the Completeness Axiom Bolzano-Weierstrass Theorem Some Thoughts about RContinuity Computing Limits of Functions A Review of Functions Continuous Functions: A Geometric Viewpoint Limits of Functions Other Limits Properties of Continuous Functions The Continuity of Elementary Functions Uniform Continuity Two Properties of Continuous Functions

Book Detail :-
Title: Advanced Calculus, Theory and Practice
Edition:
Author(s): John Srdjan Petrovic
Publisher: CRC Press
Series: Textbooks in Mathematics
Year: 2013
Pages: 564
Type: PDF
Language: English
ISBN: 978-1-4665-6564-7,1466565640,135-138-143-1,259-264-269-2
Country: US
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The author John Srdjan Petrovic is a professor of mathematics in the Department of Mathematics at Western Michigan University, Kalamazoo MI 49008-5248, USA.

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Book Contents :-
Advanced Calculus, Theory and Practice written by John Srdjan Petrovic cover the following topics.
Preface
1. Sequences and Their Limits
2. Real Numbers
3. Continuity
4. Derivative
5. Indefinite Integral
6. Definite Integral
7. Infinite Series
8. Sequences and Series of Functions
9. Fourier Series
10. Functions of Several Variables
11. Derivatives
12. Implicit Functions and Optimization
13. Integrals Depending on a Parameter
14. Integration in Rn
15. Fundamental Theorems
16. Solutions and Answers to Selected Problems
Bibliography
Subject Index
Author Index

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