Course in Calculus and Real Analysis

ISBN-10: 0387305300

ISBN-13: 9780387305301

Edition: 2006

Authors: Sudhir R. Ghorpade, Balmohan V. Limaye

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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.
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Book details

List price: $79.99
Copyright year: 2006
Publisher: Springer
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
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