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Book Cover
E-book
Author Voxman

Title Advanced Calculus : an Introduction to Modern Analysis
Published Bosa Roca : CRC Press, 1981

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Description 1 online resource (697 pages)
Series Chapman and Hall/CRC Pure and Applied Mathematics ; v. 63
Chapman and Hall/CRC Pure and Applied Mathematics
Contents Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Preface -- Table of Contents -- Chapter 1: Preliminaries -- A. Induction -- B. Sets and Functions -- C. Unions, Intersections, and Complements -- D. Countability -- E. sup, lub, inf, and glb -- F. Complex Numbers and Functions -- Problems -- References -- Chapter 2: Introduction to Linear Algebra and Ordinary Differential Equations -- A. Vector Spaces -- B. Matrices, Determinants, and Systems of Equations -- C.* Applications -- D. Introduction to Differential Equations
E. Linear TransformationsProblems -- References -- Chapter 3: Limits and Metric Spaces -- A. Prelude -- B. Metric Spaces -- Problems -- References -- Chapter 4: Continuity, Compactness, and Connectedness -- A. Continuity -- B. Continuity and Compactness -- C. Cauchy Sequences -- D.* A Characterization of Compactness -- E. The Intermediate Value Theorem -- F.* Conclusion -- Problems -- Reference -- Chapter 5: The Derivative: Theory and Elementary Applications -- A. The Derivative -- B. Applications of the Derivative and the Mean Value Theorems
C. Applications of the Mean Value TheoremsD. The Differential -- E.* A Concluding Problem -- Problems -- References -- Chapter 6 : A First Look at Integration -- A. The Definite Integral -- B. Elementary Properties of the Definite Integral -- C. Improper Integrals and the Gamma and Beta Functions -- D.* Some Elementary Applications of the Definite Integral: Buffonâ#x80;#x99;s Needle Problem, Arc Length, and the Picard Existence Theorem -- E.* The Weierstrass Approximation Theorem -- Problems -- References -- Chapter 7: Differentiation of Functions of Several Variables
A. Partial and Directional DerivativesB. The Differential and Differentiability -- C.* Differentiability in a Complex Setting -- D. Generalizations -- E. The Chain Rule -- F. Differentiation Under the Integral Sign -- G.* Implicit Function Theorems -- H.* An Application of the Implicit Function Theorem: Lagrange Multipliers -- I.* The Brachistochrone Problem -- J. The Vibrating String -- Problems -- References -- Chapter 8: Sequences and Series -- A. The Vibrating String (continued) -- B. Infinite Series of Numbers -- C. Infinite Series of Functions
D. Taylor Polynomials and the Taylor ExpansionE. Power Series -- F.* Divergent Series -- Problems -- Chapter 9: Elementary Applications of Infinite Series -- A. The Irrationality of e -- B. Calculation of Limits -- C. The Approximation of Definite Integrals -- D. Infinite Series and Differential Equations -- E. Infinite Series of Matrices and Linear Systems of Differential Equations -- F. Calculation of etA -- G. Infinite Series, Infinite Products, and Probability -- Problems -- References -- Chapter 10: An Introduction to Fourier Analysis
Notes ""A. Introduction""
Print version record
Subject Calculus.
calculus.
Calculus
Form Electronic book
Author Voxman, William L
ISBN 9781351468671
1351468677