LEADER 05581nam 22007333u 450 001 9911007194403321 005 20230801231638.0 010 $a9780486135137 010 $a0486135136 010 $a9781621985747 010 $a1621985741 035 $a(CKB)2670000000525551 035 $a(EBL)1894758 035 $a(SSID)ssj0001002738 035 $a(PQKBManifestationID)12461041 035 $a(PQKBTitleCode)TC0001002738 035 $a(PQKBWorkID)11014885 035 $a(PQKB)10557178 035 $a(MiAaPQ)EBC1894758 035 $a(Au-PeEL)EBL1894758 035 $a(OCoLC)868270084 035 $a(MiAaPQ)EBC7294210 035 $a(Au-PeEL)EBL7294210 035 $a(OCoLC)1402813072 035 $a(EXLCZ)992670000000525551 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to Differential Equations and Their Applications 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (1408 p.) 225 1 $aDover Books on Mathematics 300 $aDescription based upon print version of record. 311 08$a9780486445953 311 08$a048644595X 327 $aCover; 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 Equations 327 $a3.2 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 Solutions 327 $a4.1 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 Integral 327 $aChapter 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 Equations 327 $a7.3 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 Equations 327 $a9.4 The Vibrating String: Separation of Variables 330 $aIntended for use in a beginning one-semester course in differential equations, this text is designed for students of pure and applied mathematics with a working knowledge of algebra, trigonometry, and elementary calculus. Its mathematical rigor is balanced by complete but simple explanations that appeal to readers' physical and geometric intuition.Starting with an introduction to differential equations, the text proceeds to examinations of first- and second-order differential equations, series solutions, the Laplace transform, systems of differential equations, difference equations, nonlinear 410 0$aDover Books on Mathematics 606 $aDifferential equations 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aCalculus$2HILCC 615 0$aDifferential equations. 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aCalculus 676 $a515/.35 700 $aFarlow$b Stanley J$042263 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911007194403321 996 $aAn Introduction to Differential Equations and Their Applications$94389975 997 $aUNINA