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Practical analysis in one variable

Author: Donald J Estep
Publisher: New York : Springer, ©2002.
Series: Undergraduate texts in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"The book is well suited for an honors calculus sequence typically taken by first-year undergraduates planning to major in engineering, mathematics, and science and for an introductory course in rigorous real analysis offered to mathematics majors."--Jacket.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Estep, Donald J., 1959-
Practical analysis in one variable.
New York : Springer, ©2002
(DLC) 2002020943
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Donald J Estep
ISBN: 0387226443 9780387226446 0585472327 9780585472324 1280009780 9781280009785
OCLC Number: 559499637
Description: 1 online resource (xx, 621 pages) : illustrations.
Contents: Cover --
Preface --
Table of Contents --
Introduction --
Part I-Numbers and Functions, Sequences and Limits --
1. Mathematical Modeling --
2. Natural NUmbers Just Arent Enough --
3. Infinity and Mathematical Induction --
4. Rational Numbers --
5. Functions --
6. Polynomials --
7. Functions, Functions and More Functions --
8. LIpschitz Continuity --
9. Sequences and Limits --
10. Solving the Muddy Yard Model --
11. Real Numbers --
12. Functions of Real Numbers --
13. The Bisection Algorithm --
14. Inverse Functions --
15. Fixed Points and Contraction Maps --
Part II-Differential and Integral Calculus --
16. The Linearization of a Function at a Point --
17. Analyzing the Behaviour of a Population Model --
18. Interpretations of the Derivative --
19. Differentiability on Intervals --
20. Using Properties of the Derivative --
21. The Mean Value Theorum --
22. Derivative of Inverse Functions --
23. Modeling with Differential Equations --
24. Antidifferentiation --
25. Integration --
26. Properties of the Integral --
27. Applications of the Integral --
28. Rocket Propulsion and the Logarithm --
29. Constant Relative Rate of Change and the Exponential --
30. A Mass Spring System and the Trigonometric Functions --
31. Fixed Point Iteration and Newton's Method --
Calculus Quagmires --
Part III-You Want Anaylsis? We've Got Your Analysis Right Here --
32. Notions Of Continuity and Differentiability --
33. Sequences of Functions --
34. Relaxing Integration --
35. Delicate Limits and Gross Behaviour --
36. The Weierstrass Approximation Theorem --
37. The Taylor Polynomial --
38. Polynomial Interpolation --
39. Nonlinear Differential Equations --
40. The Picard Iteration --
41. The Forward Euler Method --
A Conclusion or an Introduction? --
References.
Series Title: Undergraduate texts in mathematics.
Responsibility: Donald Estep.
More information:

Abstract:

This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students.  Read more...

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From the reviews:MAA ONLINE"I confess that when I first started reading this book I was intrigued by the new approach of real analysis but did not quite see what it might be good for. In the end, Read more...

 
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