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View larger. 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. Practical uses of DEs today are not single equations but rather looking at several DEs using a computer.
The text is platform-neutral. Includes revised coverage of exact first order equations Ch. The most geometric text available. The Derivative. 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.
Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3. 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. The Definition of the Laplace Transform. Basic Properties of the Laplace Transform The Inverse Laplace Transform. Discontinuous Forcing Terms. The Delta Function. Project 5. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale. Project 6.
Vectors and Matrices. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Geometric Interpretation of Solutions.
Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8. Overview 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. Chapter Nonlinear System s. The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Conserved Quantities. Nonlinear Mechanics.
The Method of Lyapunov. Predator—Prey Systems. Project Chapter Series Solutions to Differential Equations. Review of Power Series. Series Solutions Near Ordinary Points. Pearson offers special pricing when you package your text with other student resources. If you're interested in creating a cost-saving package for your students, contact your Pearson rep.
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This title is out of print. Differential Equations, 2nd Edition. Availability This title is out of print. Description 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.
New to This Edition. Chapter 7: Matrix Algebra Vectors and Matrices. Share a link to All Resources. Instructor Resources.
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Differential Equations with Boundary Value Problems (Subscription), 2nd Edition
Differential Equations, 2nd Edition
Differential Equations with Boundary Value Problems