Differential Equations (inbunden)
Inbunden (Hardback)
Antal sidor
2 New edition
Apple Academic Press Inc.
9 black & white tables 156 black & white illustrations
9 Tables, black and white; 156 Illustrations, black and white
242 x 160 x 35 mm
930 g
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Differential Equations (inbunden)

Differential Equations

Theory, Technique and Practice, Second Edition

Inbunden Engelska, 2014-11-13
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"Krantz is a very prolific writer. He ... creates excellent examples and problem sets." -Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA Designed for a one- or two-semester undergraduate course, Differential Equations: Theory, Technique and Practice, Second Edition educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies. New to the Second Edition Improved exercise sets and examples Reorganized material on numerical techniques Enriched presentation of predator-prey problems Updated material on nonlinear differential equations and dynamical systems A new appendix that reviews linear algebra In each chapter, lively historical notes and mathematical nuggets enhance students' reading experience by offering perspectives on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight rich applications from engineering, physics, and applied science. Problems for review and discovery also give students some open-ended material for exploration and further learning.
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"Retaining many of the strong aspects of the first edition, which received positive feedback from readers, the new edition focuses on clarity of exposition and examples, many of which feature applications of differential equations. ... Being an homage to the excellent writing skills of George Simmons and his well-known text on differential equations written back in 1972, this updated edition maintains the highest standards of mathematics exposition. Warmly recommended as a comprehensive and modern textbook on theory, methods, and applications of differential equations!" -Zentralblatt MATH 1316 "Krantz is a very prolific writer. He...creates excellent examples and problem sets." -Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA

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Övrig information

Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has written more than 65 books and more than 175 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.


Preface What is a Differential Equation? Introductory Remarks The Nature of Solutions Separable Equations First-Order Linear Equations Exact Equations Orthogonal Trajectories and Families of Curves Homogeneous Equations Integrating Factors Reduction of Order Dependent Variable Missing Independent Variable Missing The Hanging Chain and Pursuit Curves The Hanging Chain Pursuit Curves Electrical Circuits Anatomy of an Application: The Design of a Dialysis Machine Problems for Review and Discovery Second-Order Linear Equations Second-Order Linear Equations with Constant Coefficients The Method of Undetermined Coefficients The Method of Variation of Parameters The Use of a Known Solution to Find Another Vibrations and Oscillations Undamped Simple Harmonic Motion Damped Vibrations Forced Vibrations A Few Remarks about Electricity Newton's Law of Gravitation and Kepler's Laws Kepler's Second Law Kepler's First Law Kepler's Third Law Higher Order Equations Historical Note: Euler Anatomy of an Application: Bessel Functions and the Vibrating Membrane Problems for Review and Discovery Qualitative Properties and Theoretical Aspects A Bit of Theory Picard's Existence and Uniqueness Theorem The Form of a Differential Equation Picard's Iteration Technique Some Illustrative Examples Estimation of the Picard Iterates Oscillations and the Sturm Separation Theorem The Sturm Comparison Theorem Anatomy of an Application: The Green's Function Problems for Review and Discovery Power Series Solutions and Special Functions Introduction and Review of Power Series Review of Power Series Series Solutions of First-Order Equations Second-Order Linear Equations: Ordinary Points Regular Singular Points More on Regular Singular Points Gauss's Hypergeometric Equation Historical Note: Gauss Historical Note: Abel Anatomy of an Application: Steady State Temperature in a Ball Problems for Review and Discovery Fourier Series: Basic Concepts Fourier Coefficients Some Remarks about Convergence Even and Odd Functions: Cosine and Sine Series Fourier Series on Arbitrary Intervals Orthogonal Functions Historical Note: Riemann Anatomy of an Application: Introduction to the Fourier Transform Problems for Review and Discovery Partial Differential Equations and Boundary Value Problems Introduction and Historical Remarks Eigenvalues, Eigenfunctions, and the Vibrating String Boundary Value Problems Derivation of the Wave Equation Solution of the Wave Equation The Heat Equation The Dirichlet Problem for a Disc The Poisson Integral Sturm-Liouville Problems Historical Note: Fourier Historical Note: Dirichlet Anatomy of an Application: Some Ideas from Quantum Mechanics Problems for Review and Discovery Laplace Transforms Introduction Applications to Differential Equations Derivatives and Integrals of Laplace Transforms Convolutions Abel's Mechanics Problem The Unit Step and Impulse Functions Historical Note: Laplace Anatomy of an Application: Flow Initiated by an Impulsively-Started Flat Plate Problems for Review and Discovery The Calculus of Variations Introductory Remarks Euler's Equation Isoperimetric Problems and the Like Lagrange Multipliers Integral Side Conditions Finite Side Conditions Historical Note: Newton Anatomy of an Application: Hamilton's Principle and its Implications Problems for Review and Discovery Numerical Methods Introductory Remarks The Method of Euler The Error Term An Improved Euler Method The Runge-Kutta Method Anatomy of an Application: A Constant Perturbation Method for Linear, Second-Order Equations Problems for Review and Discovery Systems of First-Order Equations Introductory Remarks Linear Systems Homogeneous Linear Systems w