Fundamentals of Differential Equations, Global Edition + MyLab Mathematics with Pearson eText (Package)

Name: Fundamentals of Differential Equations, Global Edition + MyLab Mathematics with Pearson eText (Package)
Price: 1332 SEK
Availability: InStock

AvR. Nagle,Edward Saff

2018

1 332 kr

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Produktinformation

Utgivningsdatum:2018-09-13
Höjd:205 x 255 x 20 mm
Vikt:1 220 g
Språk:Engelska
Upplaga:9
Förlag:Pearson Education
EAN:9781292241494

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

1. Introduction1.1 Background1.2 Solutions and Initial Value Problems1.3 Direction Fields1.4 The Approximation Method of Euler 2. First-Order Differential Equations2.1 Introduction: Motion of a Falling Body2.2 Separable Equations2.3 Linear Equations2.4 Exact Equations2.5 Special Integrating Factors2.6 Substitutions and Transformations 3. Mathematical Models and Numerical Methods Involving First Order Equations3.1 Mathematical Modeling3.2 Compartmental Analysis3.3 Heating and Cooling of Buildings3.4 Newtonian Mechanics3.5 Electrical Circuits3.6 Improved Euler's Method3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta 4. Linear Second-Order Equations4.1 Introduction: The Mass-Spring Oscillator4.2 Homogeneous Linear Equations: The General Solution4.3 Auxiliary Equations with Complex Roots4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients4.5 The Superposition Principle and Undetermined Coefficients Revisited4.6 Variation of Parameters4.7 Variable-Coefficient Equations4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations4.9 A Closer Look at Free Mechanical Vibrations4.10 A Closer Look at Forced Mechanical Vibrations 5. Introduction to Systems and Phase Plane Analysis5.1 Interconnected Fluid Tanks5.2 Elimination Method for Systems with Constant Coefficients5.3 Solving Systems and Higher-Order Equations Numerically5.4 Introduction to the Phase Plane5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models5.6 Coupled Mass-Spring Systems5.7 Electrical Systems5.8 Dynamical Systems, Poincaré Maps, and Chaos 6. Theory of Higher-Order Linear Differential Equations6.1 Basic Theory of Linear Differential Equations6.2 Homogeneous Linear Equations with Constant Coefficients6.3 Undetermined Coefficients and the Annihilator Method6.4 Method of Variation of Parameters 7. Laplace Transforms7.1 Introduction: A Mixing Problem7.2 Definition of the Laplace Transform7.3 Properties of the Laplace Transform7.4 Inverse Laplace Transform7.5 Solving Initial Value Problems7.6 Transforms of Discontinuous Functions7.7 Transforms of Periodic and Power Functions7.8 Convolution7.9 Impulses and the Dirac Delta Function7.10 Solving Linear Systems with Laplace Transforms 8. Series Solutions of Differential Equations8.1 Introduction: The Taylor Polynomial Approximation8.2 Power Series and Analytic Functions8.3 Power Series Solutions to Linear Differential Equations8.4 Equations with Analytic Coefficients8.5 Cauchy-Euler (Equidimensional) Equations8.6 Method of Frobenius8.7 Finding a Second Linearly Independent Solution8.8 Special Functions 9. Matrix Methods for Linear Systems9.1 Introduction9.2 Review 1: Linear Algebraic Equations9.3 Review 2: Matrices and Vectors9.4 Linear Systems in Normal Form9.5 Homogeneous Linear Systems with Constant Coefficients9.6 Complex Eigenvalues9.7 Nonhomogeneous Linear Systems9.8 The Matrix Exponential Function 10. Partial Differential Equations10.1 Introduction: A Model for Heat Flow10.2 Method of Separation of Variables10.3 Fourier Series10.4 Fourier Cosine and Sine Series10.5 The Heat Equation10.6 The Wave Equation