Advanced Calculus

ISBN-10: 0486661032
ISBN-13: 9780486661032
Edition: 2nd 1989 (Revised)
Authors: David V. Widder
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Description: Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral,  More...

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Book details

List price: $22.95
Edition: 2nd
Copyright year: 1989
Publisher: Dover Publications, Incorporated
Publication date: 8/1/1989
Binding: Paperback
Pages: 544
Size: 5.50" wide x 8.75" long x 1.00" tall
Weight: 1.188

Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Numerous graded exercises with selected answers. 1961 edition.

Partial Differentiation
Introduction
Functions of One Variable
Functions of Several Variables
Homogeneous Functions. Higher Derivatives
Implicit Functions
Simultaneous Equations. Jacobians
Dependent and Independent Variables
Differentials. Directional Derivatives
Taylor's Theorem
Jacobians
Equality of Cross Derivatives
Implicit Functions
Vectors
Introduction
Solid Analytic Geometry
Space Curves
Surfaces
A Symbolic Vector
Invariants
Differential Geometry
Arc Length of a Space Curve
Osculating Plane
Curvature and Torsion
Frenet-Serret Formulas
Surface Theory
Fundamental Differential Forms
Mercator Maps
Applications of Partial Differentiation
Maxima and minima
Functions of Two Variables
Sufficient Conditions
Functions of Three Variables
Lagrange's Multipliers
Families of Plane Curves
Families of Surfaces
Stieltjes Integral
Introduction
Properties of the Integral
Integration by Parts
Laws of the Mean
Physical Applications
Continuous Functions
Existence of Stieltjes Integrals
Multiple Integrals
Introduction
Properties of Double Integrals
Evaluation of Double Integrals
Polar Coordinates
Change in Order of Integration
Applications
Further Applications
Triple Integrals
Other Coordinates
Existence of Double Integrals
Line and Surface Integrals
Introduction
Green's Theorem
Application
Surface Integrals
Change of Variable in Multiple Integrals
Line Integrals in Space
Limits and Indeterminate Forms
The Indeterminate Form 0/0
The Indeterminate Form
Other Indeterminate Forms
Other Methods. Orders of Infinity
Superior and Inferior Limits
Infinite Series
Convergence of Series. Comparison Tests
Convergence Tests
Absolute Convergence. Altering Series
Limit Tests
Uniform Convergence
Applications
Divergent Series
Miscellaneous Methods
Power Series
Convergence of Improper Integrals
Introduction
Type I. Limit Tests
Type I. Conditional Convergence
Type III
Combination of Types
Uniform Convergence
Properties of Proper Integrals
Application of Uniform Convergence
Divergent Integrals
Integral Inequalities
The Gamma Function. Evaluation of Definite Integrals
Introduction
The Beta Function
Evaluation of Definite Integrals
Stirling's Formula
Fourier Series
Introduction
Several Classes of Functions
Convergence of a Fourier Series to Its Defining Function
Extensions and Applications
Vibrating String
Summability of Fourier Series
Applications
Fourier Integral
The Laplace Transform
Introduction
Region of Convergence
Absolute and Uniform Convergence
Operational Properties of the Transform
Resultant
Tables of Transforms
Uniqueness
Inversion
Representation
Related Transforms
Applications of the Laplace Transform
Introduction
Linear Differential Equation
The General Homogeneous Case
The Nonhomogeneous Case
Difference Equations
Partial Differential Equations
Selected Answers
Index of Symbols
Index

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