A First Course in Differential Equations / Edition 2 by J David Logan | 9781461427223 | Paperback | Barnes & Noble
A First Course in Differential Equations / Edition 2

A First Course in Differential Equations / Edition 2

by J David Logan
     
 

ISBN-10: 1461427223

ISBN-13: 9781461427223

Pub. Date: 12/28/2012

Publisher: Springer New York

This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed

Overview

This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed by students to continue to the next level in applying the methods to more advanced problems. There is a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics, chemical reactors, and other areas. Moreover, the text contains a new, elementary chapter on systems of differential equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent chapters treat systems in a more formal way. Briefly, the topics include: First-order equations: separable, linear, autonomous, and bifurcation phenomena; Second-order linear homogeneous and non-homogeneous equations; Laplace transforms; and Linear and nonlinear systems, and phase plane properties.

Product Details

ISBN-13:
9781461427223
Publisher:
Springer New York
Publication date:
12/28/2012
Series:
Undergraduate Texts in Mathematics Series
Edition description:
Softcover reprint of hardcover 2nd ed. 2011
Pages:
386
Product dimensions:
6.14(w) x 9.21(h) x 0.83(d)

Table of Contents

Preface to the Second Edition.- To the Student.- 1. Differential Equations and Models.- 1.1 Introduction.- 1.2 General Terminology.- 1.2.1 Geometrical Interpretation.- 1.3 Pure Time Equations.- 1.4 Mathematical Models.- 1.4.1 Particle Dynamics.- 1.5 Separation of Variables.- 1.6 Autonomous Differential Equations.- 1.7 Stability and Bifurcation 1.8 Reactors and Circuits.- 1.8.1 Chemical Reactors.- 1.8.2 Electrical Circuits 2. Linear Equations and Approximations.- 2.1 First-Order Linear Equations.- 2.2 Approximation of Solutions.- 2.2.1 Picard Iteration*.- 2.2.2 Numerical Methods.- 2.2.3 Error Analysis.- 3. Second-Order Differential Equations.- 3.1 Particle Mechanics 3.2 Linear Equations with Constant Coefficients.- 3.3 The Nonhomogeneous Equation
3.3.1 Undetermined Coefficients.- 3.3.2 Resonance.- 3.4 Variable Coefficients.- 3.4.1 Cauchy–Euler Equation.- 3.4.2 Power Series Solutions*.- 3.4.3 Reduction of Order*.- 3.4.4 Variation of Parameters.- 3.5 Boundary Value Problems and Heat Flow*.- 3.6 Higher-Order Equations.- 3.7 Summary and Review.- 4. Laplace Transforms.- 4.1 Definition and Basic Properties.- 4.2 Initial Value Problems.- 4.3 The Convolution Property.- 4.4 Discontinuous Sources.- 4.5 Point Sources.- 4.6 Table of Laplace Transforms.- 5. Systems of Differential Equations.- 5.1 Linear Systems.- 5.2 Nonlinear Models.- 5.3 Applications.- 5.3.1 The Lotka–Volterra Model.- 5.3.2 Models in Ecology.- 5.3.3 An Epidemic Model.- 5.4 Numerical Methods.- 6. Linear Systems.- 6.1 Linearization and Stability.- 6.2 Matrices*.- 6.3 Two-Dimensional Linear Systems.- 6.3.1 Solutions and Linear Orbits.- 6.3.2 The Eigenvalue Problem.- 6.3.3 Real Unequal Eigenvalues.- 6.3.4 Complex Eigenvalues.- 6.3.5 Real, Repeated Eigenvalues.- 6.3.6 Stability.- 6.4 Nonhomogeneous Systems*.- 6.5 Three-Dimensional Systems*.- 7. Nonlinear Systems.- 7.1 Linearization Revisited.- 7.1.1 Malaria*.- 7.2 Periodic Solutions.- 7.2.1 The Poincaŕe–Bendixson Theorem.- Appendix A. References.- Appendix B. Computer Algebra Systems.- B.1 Maple.- B.2 MATLAB.- Appendix C. Sample Examinations.- D. Index.-

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