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View larger. Additional order info. Buy an eText. This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. 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. Chapter Fourier Series. Computation of Fourier Series. Convergence of Fourier Series. Fourier Cosine and Sine Series. The Complex Form of a Fourier Series. Chapter Partial Differential Equations. Derivation of the Heat Equation. Separation of Variables for the Heat Equation. The Wave Equation. Sturm Liouville Problems. Orthogonality and Generalized Fourier Series.
Temperature in a Ball—Legendre Polynomials. Domains with Circular Symmetry—Bessel Functions. Appendix: Complex Numbers and Matrices. Answers to Odd-Numbered Problems. 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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Overview Contents Order Overview. Description This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. 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. Chapter 7: Matrix Algebra Vectors and Matrices. Previous editions.
Differential Equations with Boundary Value Problems (Subscription), 2nd Edition
View larger. Additional order info. Buy an eText. This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. The Derivative.
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. This book strikes a balance between the traditional and the modern combining the traditional material with a modern systems emphasis. Chapter topics cover an introduction to differential equations, first-order equations, modeling and applications, second-order equations, the Laplace Transform, numerical methods, matrix algebra, an introduction to systems, linear systems with constant coefficients, nonlinear systems, power series solutions, Fourier series methods, and partial differential equations. This book started in , when the first author began to reorganize the teaching of ODEs at Rice University. It soon became apparent that a textbook was needed that brought to the students the expanded outlook that modern developments in the subject required, and the use of technology allowed. Over the ensuing years this book has evolved.
ISBN 13: 9780131862364
View larger. 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.
Differential Equations with Boundary Value Problems, 2nd Edition