Elementary Analysis
Subtitle: The Theory of Calculus
By: by Kenneth A. Ross
Contributors: SpringerLink (Online service)
Edition: 2nd ed. 2013.
Series: Undergraduate Texts in Mathematics
Publisher: Springer New York; Imprint: Springer
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource]
Number of pages: 409
ISBN-13: 9781461462712
Subjects: Mathematics; Global analysis (Mathematics); Analysis; Real Functions
Description: For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs.  Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus.  Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs.  New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."—MATHEMATICAL REVIEWS
Table of contents: title: Preface; title: 1 Introduction; title: 2 Sequences; title: 3 Continuity; title: 4 Sequences and Series of Functions; title: 5 Differentiation; title: 6 Integration; title: 7 Capstone; title: Appendix on Set Notation; title: Selected Hints and Answers; title: References; title: Index.