Differential Equations (Classic Version)

Häftad, Engelska, 2017

Del i serien Pearson Modern Classics for Advanced Mathematics Series

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Beskrivning

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles.

Combining traditional differential equation material with a modern qualitative and systems approach, this new edition continues to deliver flexibility of use and extensive problem sets. The 2nd Edition’s refreshed presentation includes extensive new visuals, as well as updated exercises throughout.

Produktinformation

Utgivningsdatum:2017-03-14
Mått:201 x 251 x 28 mm
Vikt:1 193 g
Format:Häftad
Språk:Engelska
Serie:Pearson Modern Classics for Advanced Mathematics Series
Antal sidor:672
Upplaga:2
Förlag:Pearson Education
ISBN:9780134689586

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Innehållsförteckning

Chapter 1: Introduction to Differential Equations Differential Equation Models. The Derivative. Integration. Chapter 2: First-Order Equations Differential Equations and Solutions. Solutions to Separable Equations. Models of Motion. Linear Equations.Mixing Problems. Exact Differential Equations. Existence and Uniqueness of Solutions. Dependence of Solutions on Initial Conditions. Autonomous Equations and Stability.Project 2.10 The Daredevil Skydiver. Chapter 3: Modeling and Applications Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3.5 The Spruce Budworm. Project 3.6 Social Security, Now or Later. Chapter 4: Second-Order Equations Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients. Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4.8 Nonlinear Oscillators. Chapter 5: The Laplace Transform The Definition of the Laplace Transform. Basic Properties of the Laplace Transform 241. The Inverse Laplace TransformUsing the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project 5.9 Forced Harmonic Oscillators. Chapter 6: Numerical Methods Euler’s Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.Project 6.6 Numerical Error Comparison. Chapter 7: Matrix Algebra Vectors and Matrices. Systems of Linear Equations with Two or Three Variables. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Determinants. Chapter 8: An Introduction to SystemsDefinitions and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8.6 Long-Term Behavior of Solutions. Chapter 9: Linear Systems with Constant CoefficientsOverview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules. Chapter 10: Nonlinear SystemsThe Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator—Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species. Chapter 11: Series Solutions to Differential EquationsReview of Power Series. Series Solutions Near Ordinary Points. Legendre’s Equation. Types of Singular Points–Euler’s Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points – the General Case. Bessel’s Equation and Bessel Functions.