General Information
For a description of the course, including the grading policy, consult the course syllabus. Students are responsible for reading the syllabus and being aware of all the course and university policies. Students taking this course for graduate credit should consult the MATH 5120 syllabus.

Textbook: No textbook will be required. See the course syllabus for suggested references.

Classes meet on TR, 2:45-4pm at Stevenson Center 1308.

We will be following the COVID-19-related guidelines stipulated by Vanderbilt.

Contact Information and Office Hours
Instructor's office: Stevenson Center 1515 (5th floor of the Mathematics Building).
Instructor's email: marcelo.disconzi@vanderbilt.edu.
Instructor's office hours: Tuesdays, 4-6pm, Thursdays, 1-2pm, or by appointment.
Instructor's office phone: (615) 322-7147.

Schedule
Below is an ongoing schedule for the course (for the academic calendar, click here). Click here for the class notes, and here for the class notes in handwritten form. The class notes will be updated and typeset as the course progress. Since typesetting them might take some time, typically the most up-to-date version of the notes will be in the handwritten form. Non-math majors taking the course can consult these notes on preliminary notions for some background on mathematical concepts, conventions, and notation that will be used in the course.

Date	Material covered	Remarks
Jan 18	Introduction. Examples of PDEs.	HW1 is posted on Brightspace. Due: 1/25, 12pm.
Jan 21	More examples. Notations and conventions.
Jan 25	Separation of variables for the Schrödinger equation with a radially symmetric potential. Solutions to the Θ equation.	HW2 is posted on Brightspace. Due: 2/1, 12pm. Solutions to HW1 are posted on Brightspace.
Jan 27	Schrödinger equation: solutions to the Φ equation. Legendre polynomials and spherical harmonics.
Feb 1	Schrödinger equation: solutions to the radial equation. Final solution to the Schrödinger equation for the hydrogen atom.	HW3 is posted on Brightspace. Due: 2/8, 12pm. Solutions to HW2 are posted on Brightspace.
Feb 3	Separation of variables for the 1d wave equation. Fourier series.
Feb 8	Properties and convergence of Fourier series.	HW4 is posted on Brightspace. Due: 2/15, 12pm. Solutions to HW3 are posted on Brightspace.
Feb 10	Sine and cosine Fourier series. Fourier series of periodic functions. Back to the wave equation: existence of solutions.
Feb 15	The 1d wave equation on the real line. D'Alembert's formula.	HW5 is posted on Brightspace. Due: 2/22, 12pm. Solutions to HW4 are posted on Brightspace.
Feb 17	The characteristics of the 1d wave equation. Domains of dependence and influence. Singularities and generalized solutions.
Feb 22	Some formal aspects of PDEs.	HW6 is posted on Brightspace. Due: 3/1, 12pm. Solutions to HW5 are posted on Brightspace.
Feb 24	Laplace's and Poisson's equation in ℝn: fundamental solution.
Mar 1	Existence of solutions to Poisson's equation in ℝn.	HW7 is posted on Brightspace. Due: 3/15, 12pm. Solutions to HW6 are posted on Brightspace.
Mar 3	Harmonic functions, mean value, and maximum principle.
Mar 8	Spring break, no class.
Mar 10	Spring break, no class.
Mar 15	The wave equation in ℝn. Domains of dependence and influence. Euler-Poisson-Darboux equation.	HW8 is posted on Brightspace. Due: 3/22, 12pm. Solutions to HW7 are posted on Brightspace.
Mar 17	Existence and uniqueness of solutions to the Cauchy problem for the wave equation in ℝn. Kirchhoff's and Poisson's formulas.
Mar 22	The inhomogeneous wave equation; Duhamel's principle. Lorentz field and decay estimates for the wave equation.	HW9 is posted on Brightspace. Due: 3/29, 12pm. Solutions to HW8 are posted on Brightspace.
Mar 24	The Cauchy problem for the heat equation in ℝn.
Mar 29	The method of characteristics: derivation of the characteristic system of ODEs.	HW10 is posted on Brightspace. Due: 4/5, 12pm. Solutions to HW9 are posted on Brightspace.
Mar 31	The method of characteristics: examples and the transversality condition.
Apr 5	Existence and uniqueness of solutions to first-order quasilinear PDEs in one dimension satisfying the transversality condition.	HW11 is posted on Brightspace. Due: 4/12, 12pm. Solutions to HW10 are posted on Brightspace.
Apr 7	The Burgers equation.
Apr 12	Blow-up of solutions to Burgers' equation; shock waves. Scalar conservations laws in one dimension.	HW12 is posted on Brightspace. Due: 4/19, 12pm. Solutions to HW11 are posted on Brightspace.
Apr 14	Weak solutions to scalar conservation laws in one dimension.
Apr 19	The Rankine-Hugoniot conditions. Strictly hyperbolic systems of conservation laws in one dimension.	HW13 is posted on Brightspace. Due: 4/26, 12pm. Solutions to HW12 are posted on Brightspace.
Apr 21	Simple and rarefaction waves. The Riemann problem.
Apr 26	Breakdown of solutions to 2x2 systems of conservation laws. Entropy solutoins.	Solutions to HW13 are posted on Brightspace.
Apr 28	Guest lecturer, Xinyue Zhao: applications of PDEs in biology.

Anonymous feedback
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