Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version

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1 Brochure More information from Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version Description: The 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 10th edition includes new problems, updated figures and examples to help motivate students. The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two?(or three) semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. Contents: Chapter 1 Introduction Some Basic Mathematical Models; Direction Fields Solutions of Some Differential Equations Classification of Differential Equations Historical Remarks 26 Chapter 2 First Order Differential Equations Linear Equations; Method of Integrating Factors Separable Equations Modeling with First Order Equations Differences Between Linear and Nonlinear Equations Autonomous Equations and Population Dynamics Exact Equations and Integrating Factors Numerical Approximations: Euler s Method The Existence and Uniqueness Theorem First Order Difference Equations 122 Chapter 3 Second Order Linear Equations Homogeneous Equations with Constant Coefficients Solutions of Linear Homogeneous Equations; the Wronskian Complex Roots of the Characteristic Equation 158

2 3.4 Repeated Roots; Reduction of Order Nonhomogeneous Equations; Method of Undetermined Coefficients Variation of Parameters Mechanical and Electrical Vibrations Forced Vibrations 207 Chapter 4 Higher Order Linear Equations General Theory of nth Order Linear Equations Homogeneous Equations with Constant Coefficients The Method of Undetermined Coefficients The Method of Variation of Parameters 241 Chapter 5 Series Solutions of Second Order Linear Equations Review of Power Series Series Solutions Near an Ordinary Point, Part I Series Solutions Near an Ordinary Point, Part II Euler Equations; Regular Singular Points Series Solutions Near a Regular Singular Point, Part I Series Solutions Near a Regular Singular Point, Part II Bessel s Equation 296 Chapter 6 The Laplace Transform Definition of the Laplace Transform Solution of Initial Value Problems Step Functions Differential Equations with Discontinuous Forcing Functions Impulse Functions The Convolution Integral 350 Chapter 7 Systems of First Order Linear Equations Introduction Review of Matrices Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors Basic Theory of Systems of First Order Linear Equations Homogeneous Linear Systems with Constant Coefficients Complex Eigenvalues 408

3 7.7 Fundamental Matrices Repeated Eigenvalues Nonhomogeneous Linear Systems 440 Chapter 8 Numerical Methods The Euler or Tangent Line Method Improvements on the Euler Method The Runge Kutta Method Multistep Methods Systems of First Order Equations More on Errors; Stability 482 Chapter 9 Nonlinear Differential Equations and Stability The Phase Plane: Linear Systems Autonomous Systems and Stability Locally Linear Systems Competing Species Predator Prey Equations Liapunov s Second Method Periodic Solutions and Limit Cycles Chaos and Strange Attractors: The Lorenz Equations 577 Chapter 10 Partial Differential Equations and Fourier Series Two Point Boundary Value Problems Fourier Series The Fourier Convergence Theorem Even and Odd Functions Separation of Variables; Heat Conduction in a Rod Other Heat Conduction Problems TheWave Equation: Vibrations of an Elastic String Laplace s Equation 658 AppendixA Derivation of the Heat Conduction Equation 669 Appendix B Derivation of thewave Equation 673 Chapter 11 Boundary Value Problems and Sturm Liouville Theory 677

4 11.1 The Occurrence of Two Point Boundary Value Problems Sturm Liouville Boundary Value Problems Nonhomogeneous Boundary Value Problems Singular Sturm Liouville Problems Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion Series of Orthogonal Functions: Mean Convergence 728 Answers to Problems 739 Index 799 Ordering: Order Online - Order by Fax - using the form below Order by Post - print the order form below and send to Research and Markets, Guinness Centre, Taylors Lane, Dublin 8, Ireland.

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