Applied Partial Differential Equations – David L. Logan – 1st Edition

Description

This concise and up-­to-­date textbook is designed for the standard sophomore course in equations. It treats the basic ideas, models, and methods in a user friendly format that is accessible to engineers, scientists, economists, and majors.

It emphasizes analytical, , and numerical techniques, and it provides the tools needed by 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 , , biology, economics, chemical reactors, and other areas. Moreover, the text contains a new, elementary chapter on systems of differential equations, both 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.

Table of Content



  1. The Physical Origins of Partial Differential Equations

  2. Partial Differential Equations on Unbounded Domains

  3. Orthogonal Expansions

  4. Partial Differential Equations on Bounded Domains

  5. PDE Models in Biology


Appendix: Ordinary Differential Equations
Table of Laplace Transforms
References
Index

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