A First Course in Differential Equations [electronic resource] / by J. David Logan.

By: David Logan, J [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Undergraduate Texts in Mathematics: Publisher: New York, NY : Springer New York, 2006Description: XV, 290 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387299303Subject(s): Mathematics | Matrix theory | Algebra | Differential equations | Partial differential equations | Mathematics | Ordinary Differential Equations | Linear and Multilinear Algebras, Matrix Theory | Partial Differential EquationsAdditional physical formats: Printed edition:: No titleDDC classification: 515.352 LOC classification: QA372Online resources: Click here to access online
Contents:
Preface -- Differential Equations and Models -- Analytic Solutions and Approximations.-Second-Order Differential Equations -- Laplace Transforms -- Linear Systems -- Nonlinear Systems -- Appendix A: References -- Appendix B: A Brief on MATLAB -- Appendix C: Maple Commands -- Appendix D: Sample Examinations -- Appendix E: Solutions to Selected Exercises.
In: Springer eBooksSummary: This text is designed for the standard post-calculus course in elementary differential equations. It is a brief, one-semester treatment of the basic ideas, models, and solution methods. The book, which serves as an alternative to existing texts for instructors who want more concise coverage, emphasizes graphical, analytical, and numerical approaches, and is written with clear language in a user-friendly format. It provides students with the tools to continue on to the next level in applying differential equations to problems in engineering, science, and applied mathematics. The topics include: * separable and linear first-order equations; * autonomous equations; * second order linear homogeneous and nonhomogeneous equations; * Laplace transforms; * linear and nonlinear systems in the phase plane. Many exercises are provided, in addition to examples from engineering, ecology, physics, economics, and other areas. An expanded section on the required linear algebra is presented, and an appendix contains templates of Maple and MATLAB commands and programs which are useful in differential equations.
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Preface -- Differential Equations and Models -- Analytic Solutions and Approximations.-Second-Order Differential Equations -- Laplace Transforms -- Linear Systems -- Nonlinear Systems -- Appendix A: References -- Appendix B: A Brief on MATLAB -- Appendix C: Maple Commands -- Appendix D: Sample Examinations -- Appendix E: Solutions to Selected Exercises.

This text is designed for the standard post-calculus course in elementary differential equations. It is a brief, one-semester treatment of the basic ideas, models, and solution methods. The book, which serves as an alternative to existing texts for instructors who want more concise coverage, emphasizes graphical, analytical, and numerical approaches, and is written with clear language in a user-friendly format. It provides students with the tools to continue on to the next level in applying differential equations to problems in engineering, science, and applied mathematics. The topics include: * separable and linear first-order equations; * autonomous equations; * second order linear homogeneous and nonhomogeneous equations; * Laplace transforms; * linear and nonlinear systems in the phase plane. Many exercises are provided, in addition to examples from engineering, ecology, physics, economics, and other areas. An expanded section on the required linear algebra is presented, and an appendix contains templates of Maple and MATLAB commands and programs which are useful in differential equations.

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