"Mathematics, rightly viewed, possesses not only truth, but supreme beauty." --Bertrand Russell

- Math 2080: Differential equations, which is a prerequestite for this course
- Linear Partial Differential Equations and Fourier Theory, by Marcus Pivato
- Fourier Series applet
- Wave Equation applet

__Editor's note__: Any YouTube link with (??:??) means I haven't
made the video yet.

**Section 1: Some linear algebra**. (4 lectures: 2 hr 55 min).

- Lecture 1.1: Vector spaces [YouTube (32:49) | Slides]
- Lecture 1.2: Linear independence and spanning sets [YouTube (46:33) | Slides]
- Lecture 1.3: Linear maps. [YouTube (41:08) | Slides]
- Lecture 1.4: Inner products and orthogonality [YouTube (47:46) | Slides]

- Lecture 2.1: The fundamental theorem of linear ODEs [YouTube (45:07) | Slides]
- Lecture 2.2: Linear independence and the Wronskian [YouTube (39:35) | Slides]
- Lecture 2.3: Inhomogeneous ODEs and affine spaces [YouTube (37:53) | Slides]
- Lecture 2.4: Undetermined coefficients [YouTube (45:51) | Slides]
- Lecture 2.5: Power series solutions to ODEs [YouTube (44:24) | Slides]
- Lecture 2.6: Singular points and the Frobenius method [YouTube (43:21) | Slides]
- Lecture 2.7: Bessel's equation [YouTube (36:34) | Slides]

- Lecture 3.1: Fourier series and orthogonality. [YouTube (29:29) | Slides]
- Lecture 3.2: Computing Fourier series and exploiting symmetry. [YouTube (50:09) | Slides]
- Lecture 3.3: Solving ODEs with Fourier series [YouTube (31:48) | Slides]
- Lecture 3.4: Fourier sine and cosine series. [YouTube (35:07) | Slides]
- Lecture 3.5: Complex inner products and Fourier series. [YouTube (51:14) | Slides]
- Lecture 3.6: Real vs. complex Fourier series. [YouTube (37:03) | Slides]
- Lecture 3.7: Fourier transforms. [YouTube (49:37) | Slides]
- Lecture 3.8: Pythagoras, Parseval, and Plancherel. [YouTube (31:32) | Slides]

- Lecture 4.1: Boundary value problems. [YouTube (56:59) | Slides]
- Lecture 4.2: Symmetric and Hermitian matrices. [YouTube (32:46) | Slides]
- Lecture 4.3: Self-adjoint linear operators. [YouTube (46:44) | Slides]
- Lecture 4.4: Sturm-Liouville theory [YouTube (42:30) | Slides]
- Lecture 4.5: Generalized Fourier series [YouTube (26:12) | Slides]
- Lecture 4.6: Some special orthogonal functions [YouTube (35:43) | Slides]

- Lecture 5.1: Fourier's law and the diffusion equation [YouTube (44:28) | Slides]
- Lecture 5.2: Boundary conditions for the heat equation [YouTube (51:23) | Slides]
- Lecture 5.3: The transport and wave equations [YouTube (40:32) | Slides]
- Lecture 5.4: The Schrödinger equation [YouTube (??:??) | Slides]

- Lecture 6.1: Cauchy problems for the heat and wave equations. [YouTube (??:??) | Slides]
- Lecture 6.2: Semi-infinite domains and the reflection method. [YouTube (??:??) | Slides]
- Lecture 6.3: Solving PDEs with Laplace transforms. [YouTube (??:??) | Slides]
- Lecture 6.4: Solving PDEs with Fourier transforms. [YouTube (??:??) | Slides]

- Lecture 7.1: Harmonic functions and Laplace's equation. [YouTube (53:53) | Slides]
- Lecture 7.2: Eigenfunctions of the Laplacian. [YouTube (29:06) | Slides]
- Lecture 7.3: The heat and wave equations in higher dimensions. [YouTube (54:04) | Slides]
- Lecture 7.4: The Laplacian in polar coordinates. [YouTube (51:53) | Slides]
- Lecture 7.5: Three PDEs on a disk [YouTube (48:02) | Slides]

HW 1: pdf | tex. Topics:

HW 2: pdf | tex. Topics:

HW 3: pdf | tex. Topics:

HW 4: pdf | tex. Topics:

HW 5: pdf | tex. Topics:

HW 6: pdf | tex. Topics:

HW 7: pdf | tex. Topics:

HW 8: pdf | tex. Topics:

HW 9: pdf | tex. Topics:

HW 10: pdf | tex. Topics:

HW 11: pdf | tex. Topics:

HW 12: pdf | tex. Topics: