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    1. Naturvetenskap och teknik
    2. Matematik och naturvetenskap
    3. Matematik

    Elementary Differential Equations with Boundary Value Problems

    AvWerner Kohler,Lee Johnson

    Häftad, Engelska, 2014

    2 627 kr

    Beställningsvara. Skickas inom 3-6 vardagar. Fri frakt över 249 kr.

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    Häftad

    1 079 kr

    Beskrivning

    Elementary Differential Equations with Boundary Value Problems integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order equations, higher-order equations, systems of differential equations, etc.) the text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it. The Table of Contents is comprehensive and allows flexibility for instructors.

    Produktinformation

    • Utgivningsdatum:2014-07-01
    • Mått:10 x 10 x 10 mm
    • Vikt:1 600 g
    • Format:Häftad
    • Språk:Engelska
    • Antal sidor:800
    • Upplaga:2
    • Förlag:Pearson Education
    • ISBN:9780321288356

    Utforska kategorier

    • Matematik inom Naturvetenskap och teknik

    Innehållsförteckning

    • Table of Contents INTRODUCTION TO DIFFERENTIAL EQUATIONS 1.1 Examples of Differential Equations1.2 Direction FieldsFIRST ORDER DIFFERENTIAL EQUATIONS 2.1 Introduction2.2 First Order Linear Differential Equations2.3 Introduction to Mathematical Models2.4 Population Dynamics and Radioactive Decay2.5 First Order Nonlinear Differential Equations2.6 Separable First Order Equations2.7 Exact Differential Equations2.8 The Logistic Population Model2.9 Applications to Mechanics2.10 Euler’s Method2.11 Review ExercisesSECOND AND HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS 3.1 Introduction3.2 The General Solution of Homogeneous Equations3.3 Constant Coefficient Homogeneous Equations3.4 Real Repeated Roots; Reduction of Order3.5 Complex Roots3.6 Unforced Mechanical Vibrations3.7 The General Solution of a Linear Nonhomogeneous Equation3.8 The Method of Undetermined Coefficients3.9 The Method of Variation of Parameters3.10 Forced Mechanical Vibrations, Electrical Networks, and Resonance3.11 Higher Order Linear Homogeneous Differential Equations3.12 Higher Order Homogeneous Constant Coefficient Differential Equations3.13 Higher Order Linear Nonhomogeneous Differential Equations3.14 Review ExercisesFIRST ORDER LINEAR SYSTEMS 4.1 Introduction4.2 Existence and Uniqueness4.3 Homogeneous Linear Systems4.4 Constant Coefficient Homogeneous Systems and the Eigenvalue Problem4.5 Real Eigenvalues and the Phase Plane4.6 Complex Eigenvalues4.7 Repeated Eigenvalues4.8 Nonhomogeneous Linear Systems4.9 Numerical Methods for Systems of Differential Equations4.10 The Exponential Matrix and Diagonalization4.11 Review ExercisesLAPLACE TRANSFORMS 5.1 Introduction5.2 Laplace Transform Pairs5.3 The Method of Partial Fractions5.4 Laplace Transforms of Periodic Functions and System Transfer Functions5.5 Solving Systems of Differential Equations5.6 Convolution5.7 The Delta Function and Impulse ResponseNONLINEAR SYSTEMS 6.1 Introduction6.2 Equilibrium Solutions and Direction Fields6.3 Conservative Systems6.4 Stability6.5 Linearization and the Local Picture6.6 Two-Dimensional Linear Systems6.7 Predator-Prey Population ModelsNUMERICAL METHODS 7.1 Euler’s Method, Heun’s Method, the Modified Euler’s Method7.2 Taylor Series Methods7.3 Runge-Kutta MethodsSERIES SOLUTION OF DIFFERENTIAL EQUATIONS 8.1 Introduction8.2 Series Solutions near an Ordinary Point8.3 The Euler Equation8.4 Solutions Near a Regular Singular Point and the Method of Frobenius8.5 The Method of Frobenius Continued; Special Cases and a SummarySECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES 9.1 Heat Flow in a Thin Bar. Separation of Variables9.2 Series Solutions9.3 Calculating the Solution9.4 Fourier Series9.5 The Wave Equation9.6 Laplace’s Equation9.7 Higher-Dimensional Problems; Nonhomogeneous EquationsFIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS AND THE METHOD OF CHARACTERISTICS 10.1 The Cauchy Problem10.2 Existence and Uniqueness10.3 The Method of CharacteristicsLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS 11.1 Existence and Uniqueness11.2 Two-Point Boundary Value Problems for Linear Systems11.3 Sturm-Liouville Boundary Value Problems