More Calculus of a Single Variable

Peter R. Mercer (Autor)

Buch | Softcover

411 Seiten

2016 | Softcover reprint of the original 1st ed. 2014
Springer-Verlag New York Inc.
978-1-4939-4681-5 (ISBN)

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This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization.

More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations.

Peter R. Mercer is Professor of Mathematics at the State University of New York College at Buffalo.

Preface.- 1 The Real Numbers.- 2 Famous Inequalities.- 3 Continuous Functions.- 4 Differentiable Functions.- 5 The Mean Value Theorem.- 6 The Exponential Function.- 7 Other Mean Value Theorems.- 8 Convex Functions and Taylor's Theorem.- 9 Integration of Continuous Functions.- 10 The Fundamental Theorem of Calculus.- 11 Techniques of Integration.- 12 Classic Examples.- 13 Simple Quadrature Rules.- 14 Error Terms.- A The Proof of Theorem 9.1.- Index.

Erscheinungsdatum	12.08.2016
Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	60 Illustrations, black and white; XVI, 411 p. 60 illus.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	AGM inequality • Continuous functions • mean value theorem • Taylor's theorem
ISBN-10	1-4939-4681-1 / 1493946811
ISBN-13	978-1-4939-4681-5 / 9781493946815
Zustand	Neuware