Description
Book SynopsisFor one-semester sophomore- or junior-level courses in Differential Equations.
Fosters the conceptual development and geometric visualization students neednow available with MyLab Math
Differential Equations: Computing and Modeling blends traditional algebra problem-solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomenaa comprehensive approach that makes accessible a wider range of more realistic applications.
The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout. For
Table of Contents
Table of Contents
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First-Order Differential Equations
- 1.1 Differential Equations and Mathematical Models
- 1.2 Integrals as General and Particular Solutions
- 1.3 Slope Fields and Solution Curves
- 1.4 Separable Equations and Applications
- 1.5 Linear First-Order Equations
- 1.6 Substitution Methods and Exact Equations
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Mathematical Models and Numerical Methods
- 2.1 Population Models
- 2.2 Equilibrium Solutions and Stability
- 2.3 Acceleration—Velocity Models
- 2.4 Numerical Approximation: Euler’s Method
- 2.5 A Closer Look at the Euler Method
- 2.6 The Runge—Kutta Method
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Linear Equations of Higher Order
- 3.1 Introduction: Second-Order Linear Equations
- 3.2 General Solutions of Linear Equations
- 3.3 Homogeneous Equations with Constant Coefficients
- 3.4 Mechanical Vibrations
- 3.5 Nonhomogeneous Equations and Undetermined Coefficients
- 3.6 Forced Oscillations and Resonance
- 3.7 Electrical Circuits
- 3.8 Endpoint Problems and Eigenvalues
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Introduction to Systems of Differential Equations
- 4.1 First-Order Systems and Applications
- 4.2 The Method of Elimination
- 4.3 Numerical Methods for Systems
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Linear Systems of Differential Equations
- 5.1 Matrices and Linear Systems
- 5.2 The Eigenvalue Method for Homogeneous Systems
- 5.3 A Gallery of Solution Curves of Linear Systems
- 5.4 Second-Order Systems and Mechanical Applications
- 5.5 Multiple Eigenvalue Solutions
- 5.6 Matrix Exponentials and Linear Systems
- 5.7 Nonhomogeneous Linear Systems
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Nonlinear Systems and Phenomena
- 6.1 Stability and the Phase Plane
- 6.2 Linear and Almost Linear Systems
- 6.3 Ecological Models: Predators and Competitors
- 6.4 Nonlinear Mechanical Systems
- 6.5 Chaos in Dynamical Systems
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Laplace Transform Methods
- 7.1 Laplace Transforms and Inverse Transforms
- 7.2 Transformation of Initial Value Problems
- 7.3 Translation and Partial Fractions
- 7.4 Derivatives, Integrals, and Products of Transforms
- 7.5 Periodic and Piecewise Continuous Input Functions
- 7.6 Impulses and Delta Functions
