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Revised and updated second edition with new material
Text for a transition course between calculus and more advanced analysis courses
Contains new material on topics such as irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions
Includes new examples and improved proofs
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."
Content Level »Lower undergraduate
Keywords »Bolzano-Weierstrass theorem - L'Hospital's rule - Riemann integral - Riemann-Stieltjes integral - Taylor's theorem - continuous functions - differentiation - elementary analysis - fundamental theorem of calculus - integration - limits of sequences - mean value theorem - monotone subsequences - nowhere-differentiable functions - power series - rational zeros theorem
Preface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.
Distribution rights for India: Researchco Book Centre, New Delhi, India