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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
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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
thermalexample2 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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 '07
 TERRELL,R
 Partial Differential Equations, Fourier Series, 1941, 1931, 1958

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