Math2930_Oct17 - Partial Differential Equations and Fourier...

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Unformatted text preview: Partial Differential Equations and Fourier Series Oct 17, 2011 Math 2930 Fourier Series • Will allow us to represent any periodic function as a sum of sin and cos functions • Use solutions to sin and cos functions to build solution to more general problems Partial Differential Equations • PDEs involve equations with more than one independent variable • For example: time and position in 1D, transient heat conduction: Many other applications 1 NODAL SOLUTION • Thermal and Structural Analysis: Example is simulation of re‐entry heating in a ceramic thermal protection system • Diffusion …. (of fluids, medications, pollutants.. • Fluid flow • Electromagnetic fields JUN 27 2006 14:01:06 STEP=1 SUB =17 TIME=929.931 TEMP (AVG) RSYS=0 SMN =312.575 SMX =617.543 MX Y Z X MN 312.575 346.46 thermal-example-2 380.345 448.116 414.231 515.887 482.001 583.657 549.772 617.543 Building blocks 2 point boundary value problems (today) Fourier series Convergence Odd and even series Heat equation – models 1D time dependent heat flow • Wave equation – models 1D waves • Laplace equation – models 2D heat flow, or 2D fluid flow, deflection of a membrane, electric potential …. • • • • • ...
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Math2930_Oct17 - Partial Differential Equations and Fourier...

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