**For introductory courses in Differential Equations.** This best-selling text by these well-known authors blends the 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 reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

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Differential equations and boundary value problems computing and modeling, 5th ed

C. H. Edwards, David E. Penney, David T. Calvis, Henry Edwards, David Penney, Edwards

Edwards, C., Penney, David, Calvis, David

Addison-Wesley Longman, Incorporated

Longman Publishing

Prentice-Hall

Adobe Press

Fifth edition, Upper Saddle River, New Jersey, 2015

United States, United States of America

Fifth edition, Boston, MA, 2015

5, 2014-09-04

Sep 14, 2014

kolxoz -- 80

lg2130601

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Source title: Differential Equations and Boundary Value Problems: Computing and Modeling (5th Edition) (Edwards, Penney & Calvis, Differential Equations: Computing and Modeling Series)

Content: 1. 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 2. 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 3. 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 Coef cients 3.4 Mechanical Vibrations 3.5 Nonhomogeneous Equations and Undetermined Coef cients 3.6 Forced Oscillations and Resonance 3.7 Electrical Circuits 3.8 Endpoint Problems and Eigenvalues 4. 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 5. 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 6. 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 7. 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 8. Power Series Methods 8.1 Introduction and Review of PowerSeries 8.2 Series Solutions Near Ordinary Points 8.3 Regular Singular Points 8.4 Method of Frobenius: The Exceptional Cases 8.5 Bessel's Equation 8.6 Applications of Bessel Functions 9. Fourier Series Methods and Partial Differential Equations 9.1 Periodic Functions and Trigonometric Series 9.2 General Fourier Series and Convergence 9.3 Fourier Sine and Cosine Series 9.4 Applications of Fourier Series 9.5 Heat Conduction and Separation of Variables 9.6 Vibrating Strings and the One-Dimensional Wave Equation 9.7 Steady-State Temperature and Laplace's Equation 10. Eigenvalue Methods and Boundary Value Problems 10.1 Sturm-Liouville Problems and Eigenfunction Expansions 10.2 Applications of Eigenfunction Series 10.3 Steady Periodic Solutions and Natural Frequencies 10.4 Cylindrical Coordinate Problems 10.5 Higher-Dimensional Phenomena

Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies

2017-10-15