Department of Mathematics
Stony Brook University
office: Math Tower 5-111
phone: (631) 632-8287
e-mail: leon.takhtajan@stonybrook.edu
Dates | Sections
covered and assigned reading |
Homework All problems are from Powers, 6th edition, in page:number format |
Week 1: Aug 22-26 |
Introduction to Fourier series. Examples. Fourier sine and cosine series. Complex form of Fourier series (pp. 108-109). Ch. 1, §§ 1.1-1.2 and § 1.10. |
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Week 2: Aug 29-Sep 2 |
Convergence and uniform convergence of Fourier series. Basic operation on Fourier series. Ch.1, §§1.3-1.4. |
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Week 3: Sep 5-9 |
Basic operation on Fourier series, cont. The heat equation. Steady-state and transient solutions. Ch.1, § 1.5 & Ch.2, §§2.1-2.2. |
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Week 4: Sep 12-16 |
Fixed-end temperatures and separation of variables. Insulated bar and different boundary conditions. Ch.2, §§2.3-2.5. |
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Week 5: Sep 19-24 |
Example: Convection. Summary of separation of variables method. Eigenvalues and eigenfunctions. Ch.2, §§ 2.6-2.7. |
Due: Sep 28 |
Week 6: Sep 26-30 |
Sturm-Liouville problems &
relation to Fourier series. Series of eigenfunctions, examples.
Fourier integral.
Ch 1, §§1.9 and Ch 2, §§2.7-2.8.
Sep 28, Midterm 1 in class. Covers Ch. 1, §§1.1-1.5, 1.10 and Ch. 2, §§2.1-2.5. |
Due: Oct 5 |
Week 7: Oct 3-7 |
Fourier integral & applications to PDEs.
Semi-infinite and infinite rod.
Ch 2, §§2.10-2.11. |
Due Oct 12 |
Week 8: Oct 10-14 |
Wave equation, D'Alembert solution.
Ch 3, §§3.1-3.3. |
Due: Oct 19 |
Week 9: Oct 17-21 |
Wave equation in unbounded regions.
Laplace's equation. Dirichlet problem in a rectangle.
Ch. 3, §3.6 & Ch 4, §§4.1-4.2. |
Due: Oct 26 |
Week 10: Oct 24-28 |
Laplace equation in a rectangle and in unbounded regions. Polar
coordinates and Dirichlet problem in a disk.
Ch 4, §§ 4.3-4.5. |
Due: Nov 7 |
Week 11: Oct 31 - Nov 4 |
Dirichlet problem in a disk cont.
Two-dimensional heat equation: double series solution. Problems in
polar coordinates.
Ch. 5, §§5.2-5.4.
Nov 2, Midterm 2 in class. Covers Ch. 2, §§2.6-2.7, 2.10-2.11 and Ch. 3, §§3.1-3.3, 3.6. |
Due: Nov 14 |
Week 12: Nov 7-11 |
Two-dimensional heat equation: double series solution. Problems in
polar coordinates and Bessel equation.
Ch. 5, §§5.3-5.5. |
Due: Nov 21 |
Week 13: Nov 14-18 |
Bessel equation.
Fourier-Bessel series and heat equation in cylinder. Vibrations of a
circular membrane.
Ch. 5, §§5.5-5.7. |
Due: Nov 28 |
Week 14: Nov 28 - Dec 2 |
Spherical coordinates and Legendre polynomials.
Ch. 5, §5.9. |
Due: Dec 5 |