05581nam 22007333u 450 991100719440332120230801231638.09780486135137048613513697816219857471621985741(CKB)2670000000525551(EBL)1894758(SSID)ssj0001002738(PQKBManifestationID)12461041(PQKBTitleCode)TC0001002738(PQKBWorkID)11014885(PQKB)10557178(MiAaPQ)EBC1894758(Au-PeEL)EBL1894758(OCoLC)868270084(MiAaPQ)EBC7294210(Au-PeEL)EBL7294210(OCoLC)1402813072(EXLCZ)99267000000052555120141222d2012|||| u|| |engur|n|---|||||txtccrAn Introduction to Differential Equations and Their Applications1st ed.Newburyport Dover Publications20121 online resource (1408 p.)Dover Books on MathematicsDescription based upon print version of record.9780486445953 048644595X Cover; Title Page; Copyright Page; Dedication; Contents; Preface; Chapter 1: Introduction to Differential Equations; Prologue; 1.1 Basic Definitions and Concepts; 1.2 Some Basic Theory; Chapter 2: First-Order Differential Equations; 2.1 First-Order Linear Equations; 2.2 Separable Equations; 2.3 Growth and Decay Phenomena; 2.4 Mixing Phenomena; 2.5 Cooling and Heating Phenomena; 2.6 More Applications; 2.7 The Direction Field and Euler's Method; 2.8 Higher-Order Numerical Methods; Chapter 3: Second-Order Linear Equations; 3.1 Introduction to Second-Order Linear Equations3.2 Fundamental Solutions of the Homogeneous Equation3.3 Reduction of Order; 3.4 Homogeneous Equations with Constant Coefficients: Real Roots; 3.5 Homogeneous Equations with Constant Coefficients: Complex Roots; 3.6 Nonhomogeneous Equations; 3.7 Solving Nonhomogeneous Equations: Method of Undetermined Coefficients; 3.8 Solving Nonhomogeneous Equations: Method of Variation of Parameters; 3.9 Mechanical Systems and Simple Harmonic Motion; 3.10 Unforced Damped Vibrations; 3.11 Forced Vibrations; 3.12 Introduction to Higher-Order Equations (Optional); Chapter 4: Series Solutions4.1 Introduction: A Review of Power Series4.2 Power Series Expansions about Ordinary Points: Part I; 4.3 Power Series Expansions about Ordinary Points: Part II; 4.4 Series Solutions about Singular Points: The Method of Frobenius; 4.5 Bessel Functions; Chapter 5: The Laplace Transform; 5.1 Definition of the Laplace Transform; 5.2 Properties of the Laplace Transform; 5.3 The Inverse Laplace Transform; 5.4 Initial-Value Problems; 5.5 Step Functions and Delayed Functions; 5.6 Differential Equations with Discontinuous Forcing Functions; 5.7 Impulse Forcing Functions; 5.8 The Convolution IntegralChapter 6: Systems of Differential Equations6.1 Introduction to Linear Systems: The Method of Elimination; 6.2 Review of Matrices; 6.3 Basic Theory of First-Order Linear Systems; 6.4 Homogeneous Linear Systems with Real Eigenvalues; 6.5 Homogeneous Linear Systems with Complex Eigenvalues; 6.6 Nonhomogeneous Linear Systems; 6.7 Nonhomogeneous Linear Systems: Laplace Transform (Optional); 6.8 Applications of Linear Systems; 6.9 Numerical Solution of Systems of Differential Equations; Chapter 7: Difference Equations; 7.1 Introduction to Difference Equations; 7.2 Homogeneous Equations7.3 Nonhomogeneous Equations7.4 Applications of Difference Equations; 7.5 The Logistic Equation and the Path to Chaos; 7.6 Iterative Systems: Julia Sets and the Mandelbrot Set (Optional); Chapter 8: Nonlinear Differential Equations and Chaos; 8.1 Phase Plane Analysis of Autonomous Systems; 8.2 Equilibrium Points and Stability for Linear Systems; 8.3 Stability: Almost Linear Systems; 8.4 Chaos, Poincare Sections and Strange Attractors; Chapter 9: Partial Differential Equations; 9.1 Fourier Series; 9.2 Fourier Sine and Cosine Series; 9.3 Introduction to Partial Differential Equations9.4 The Vibrating String: Separation of VariablesIntended for use in a beginning one-semester course in differential equations, this text is designed for students of pure and applied mathematics with a working knowledge of algebra, trigonometry, and elementary calculus. Its mathematical rigor is balanced by complete but simple explanations that appeal to readers' physical and geometric intuition.Starting with an introduction to differential equations, the text proceeds to examinations of first- and second-order differential equations, series solutions, the Laplace transform, systems of differential equations, difference equations, nonlinear Dover Books on MathematicsDifferential equationsMathematicsHILCCPhysical Sciences & MathematicsHILCCCalculusHILCCDifferential equations.MathematicsPhysical Sciences & MathematicsCalculus515/.35Farlow Stanley J42263AU-PeELAU-PeELAU-PeELBOOK9911007194403321An Introduction to Differential Equations and Their Applications4389975UNINA