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Chapter 9 Application of PDEs

Chapter 9 Application of Partial Differential Equations in Mechanical Engineering Analysis( Chapter 9 Application of PDEs) Tai-Ran Hsu*Based on the book of Applied Engineering Analysis , by Tai-Ran Hsu, published byJohn Wiley & Sons, 2018 (ISBN 9781119071204)Applied Engineering Analysis- slides for class teaching*1 Chapter Learning Objectives Learn the physical meaning of partial derivatives of functions. Learn that there are different order of partial derivatives describing the rate of changes of functions representing real physical quantities. Learn the two commonly used technique for solving partial differential equations by (1) Integral transform methods that include the Laplace transform for physical problems covering half-space, and the Fourier transform method for problems that cover the entire space; (2) the separation of

9.3 Solution Methods for Partial Differential Equations (PDEs) (p.287) There are a number ways to solve PDEs analytically; Among these are: (1) using integral transform methods by “transforming one variable to parametric domain after another in the equations that involve partial derivatives with multi-variables. Fourier transform and Laplace

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