Course in Calculus and Real Analysis

Name: Course in Calculus and Real Analysis
Availability: OutOfStock
ISBN: 9780387305301

ISBN-10: 0387305300

ISBN-13: 9780387305301

Edition: 2006

Authors: Sudhir R. Ghorpade, Balmohan V. Limaye

List price: $99.99

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Description:

Real analysis may be regarded as a formidable counterpart to calculus. It is a subject where one revisits notions encountered in calculus, but with greater rigor and sometimes with greater generality. Here, the authors provide a self-contained and rigorous introduction to the calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications.

Book details

List price: $99.99
Copyright year: 2006
Publisher: Springer New York
Publication date: 6/5/2006
Binding: Hardcover
Pages: 432
Size: 6.30" wide x 9.50" long x 0.80" tall
Weight: 1.672
Language: English




Numbers and Functions



Properties of Real Numbers



Inequalities



Functions and Their Geometric Properties


Exercises



Sequences



Convergence of Sequences



Subsequences and Cauchy Sequences


Exercises



Continuity and Limits



Continuity of Functions



Basic Properties of Continuous Functions



Limits of Functions of a Real Variable


Exercises



Differentiation



The Derivative and Its Basic Properties



The Mean Value and Taylor Theorems



Monotonicity, Convexity, and Concavity



L'Hopital's Rule


Exercises



Applications of Differentiation



Absolute Minimum and Maximum



Local Extrema and Points of Inflection



Linear and Quadratic Approximations



The Picard and Newton Methods


Exercises



Integration



The Riemann Integral



Integrable Functions



The Fundamental Theorem of Calculus



Riemann Sums


Exercises



Elementary Transcendental Functions



Logarithmic and Exponential Functions



Trigonometric Functions



Sine of the Reciprocal



Polar Coordinates



Transcendence


Exercises


Revision Exercises



Applications and Approximations of Riemann Integrals



Area of a Region Between Curves



Volume of a Solid



Arc Length of a Curve



Area of a Surface of Revolution



Centroids



Quadrature Rules


Exercises



Infinite Series and Improper Integrals



Convergence of Series



Convergence Tests for Series



Power Series



Convergence of Improper Integrals



Convergence Tests for Improper Integrals



Related Integrals


Exercises


References


List of Symbols and Abbreviations


Index