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.
It is becoming a common feature of mathematics books to include a large list of applications. Usually the students are presented with the mathematical model and they are required to apply it to a variety of cases. The derivation of the model is not done. There is some sense in this. After all, mathematics does not include all of the many application areas, and the derivation of the models is the subject of the application areas. Furthermore, the derivations are very time consuming.
However, mathematicians and mathematics are part of the modeling process. It should be a greater part of our teaching. This book takes a novel approach to the teaching of modeling. While a large number of applications are covered as examples, in some cases the applications are covered in more detail than is usual. There is a historical study of the models of motion, which demonstrates to students how models continue to evolve as knowledge increases. There is an in-depth study of several population models, including their derivation. Included are historical examples of how such models were applied both where they were appropriate and where they were not. This demonstrates to students that it is necessary to understand the assumptions that lie behind a model before using them, and that any model must be checked by experiments or observations before it is accepted.
About the Author
John Polking received his PhD in 1966 for a thesis on partial differential equations.
Solutions Manual of Differential Equations With Boundary Value Problems by Polking & Arnold | 2nd edition ISBN 9780131862364
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Solutions Manual of Differential Equations With Boundary Value Problems by Polking & Arnold
|Authors||Polking J.; Arnold D.|