Honours Partial Differential EquationsMATH-375

Lecture notes by Alexandre Tomberg

Prof. Charles Roth RothMcGill University

Fall 2008

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Table of ContentsDecember-03-08

12:16 PM

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Vector SpacesSeptember-09-08

6:39 PM

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Fundamental theorem of ODEsSeptember-09-08

6:51 PM

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Inner Product SpacesSeptember-09-08

6:57 PM

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Fourier ExpansionsSeptember-09-087:04 PM

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Best Approximation in the MeanSeptember-09-08

7:24 PM

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Best Approximation in the MeanSeptember-09-08

7:14 PM

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Bessel's inequalitySeptember-09-08

7:43 PM

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Hermitian operators

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Hermitian operatorsSeptember-09-08

8:21 PM

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Eigens of Hermitian operatorsSeptember-09-088:23 PM

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Eigens of Hermitian operatorsSeptember-09-08

8:33 PM

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Eigens of Hermitian operatorsSeptember-09-088:38 PM

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Eigens of second order differential operatorSeptember-11-08

2:46 PM

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Expansion in terms of Fourier sinesSeptember-11-08

3:08 PM

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Parseval's TheoremSeptember-11-08

3:35 PM

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Complete Fourier SeriesSeptember-16-08

3:24 PM

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Differentiation of F. SeriesSeptember-18-08

2:47 PM

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Integration of F. Series.September-18-08

3:07 PM

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Complex Fourier seriesSeptember-18-08

3:19 PM

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Some PDEs of Applied MathematicsSeptember-18-08

3:26 PM

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Boundary ConditionsSeptember-22-08

7:07 PM

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Uniqueness TheoremsSeptember-23-082:44 PM

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1. Heat in a thin barSeptember-25-08

2:46 PM

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2. Vibrating stringOctober-02-082:38 PM

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3. Steady state temperature/potential/...October-02-08

3:06 PM

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Laplace's Equation in Polar Coordinates

4. Potentials (steady-state temperature, etc.)October-07-08

2:39 PM

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Effect of a cylinder on uniform flowOctober-14-08

2:54 PM

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5. Time independent non-homogeneous aspectsOctober-14-08

3:24 PM

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6. Time dependent non-homogeneous aspectsOctober-16-08

3:09 PM

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7. Three Variable ProblemsOctober-21-08

3:14 PM

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8. Poisson's equationOctober-23-08

3:03 PM

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Sturm-Liouville TheoryOctober-28-08

2:35 PM

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Some PossibilitiesOctober-28-08

3:24 PM

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Sturm - Liouville ExpansionOctober-28-08

3:40 PM

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Constraint Relations in Neumann Problems (Poisson's Equation)November-04-08

2:57 PM

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9. Steady State Potential in Spherical RegionsNovember-04-083:07 PM

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10. Potentials inside finite cylindersNovember-06-08

3:29 PM

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11. Diffusion Equation & Vibrations in a DiskNovember-12-08

11:13 AM

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12. Diffusion of heat in a sphereNovember-13-082:55 PM

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14. Diffusion of heat in a thin rod with a Robin conditionNovember-13-08

3:25 PM

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15. Spherical HarmonicsDecember-08-08

10:24 AM

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16. Potential in a cylinder (θ dependence)December-08-08

10:24 AM

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Fourier Integrals & TransformsNovember-18-08

3:37 PM

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The Fourier TransformNovember-20-08

3:18 PM

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Convolution RuleNovember-25-08

2:50 PM

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Fourier vs. Laplace TransformsNovember-25-083:15 PM

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17. Potential in the upper half planeNovember-25-08

3:31 PM

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Fourier Transforms and PDEsNovember-27-08

2:49 PM

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