Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University
email: marcelo.disconzi at vanderbilt.edu
office: A1017, 17th & Horton (Sony bld)
phone: (615) 322 7147
mail to: 1326 Stevenson Center Ln, Vanderbilt University, Nashville, TN, 37240
Vanderbilt










Marcelo Mendes Disconzi
MATH 3120 - Introduction to Partial Differential Equations

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.

There is no textbook for this course, and we will follow the class notes posted below. Some additional references are suggested in the course syllabus.

Classes meet on TR, 2:45-4pm at Stevenson Center 1313.

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.

Class notes
Click here for the class notes, and here for the class notes in handwritten form. If you find some inconsistency or something that seems wrong in the class notes, it is likely a typo. In this case, double check the handwritten class notes and let the instructor know so that the notes can be corrected. Here are some complementary notes that cover some important background for the course.

Schedule
Below is schedule for the course which will be updated as the course progresses (for the academic calendar, click here). Sections refer to the class notes. HW will be collected on Brightspace.

 Date  Material covered  HW and remarks
 Jan 9  Introduction. Sections 1-3.  HW1 is posted on Brightspace.
 Jan 11  Separation of variables for the Schrodinger equation. Sections 4-4.4.  
 Jan 16  Canceled due to inclemental weather.  
 Jan 18  Spherical harmonics. The radial Schrodinger equation for the hydrogen atom. Sections 4.4-4.6.  HW2 is posted on Brightspace.
 Jan 23  Separation of variables for the 1d wave equation. Fourier series. Sections 5-6.1.  HW3 is posted on Brightspace.
 Jan 25  Some function spaces. Piecewise functions. Convergence of Fourier series. Sections 6.1-6.3.  
 Jan 30  Fourier series of periodic functions, sine and cosine Fourier series. Fourier series and the wave equation. Sections 6.4-6.5.  HW4 is posted on Brightspace.
 Fab 1  The wave equation in ℝ. D'Alembert's forumla. Existence and uniqueness. Domains of dependence and influence. Sections 7-7.1.  
 Feb 6  Generalized solutions to the 1d wave equation. Some tools for studying PDEs. Sections 7.2-8.4. See also the complementary notes.  HW5 is posted on Brightspace.
 Feb 8  Formal aspects of PDEs. Section 9.  
 Feb 13  Fundamental solution to the Laplacian in ℝn. Section 10.  HW6 is posted on Brightspace.
 Feb 15  Solutions to Poisson's equations. Harmonic functions. Sections 10-10.1.  
 Feb 20  The maximum principle. Brief overview of further results for Laplace's and Poisson's equations: Liouville's theorem, the Dirichlet problem, Green's function. Sections 10.1-10.2.  HW7 is posted on Brightspace.
 Feb 22  The wave equation in ℝn: finite speed of propagaion, Euler-Poisson-Darboux equation. The reflection method. Sections 11-11.1.  
 Feb 27  Kirchhoff's and Poisson's formulas. Existence and uniqueness of solutions to the Cauchy problem for the wave equation. Sections 11.2-11.4.  
 Feb 29  The inhomogeneous wave equation; Duhamel's principle. Vectorfields as differential operators. Sections 11.5-11.6.  HW8 is posted on Brightspace.
 Mar 5  The Minkowski metric and the Lorentz vectorfields. Some properties of differential operators. Section 11.7.  
 Mar 7  Decay estimates for the wave equation. Section 11.8.  
 Mar 9-17  Spring break.  
 Mar 19  Decay estimates for the wave equation. Classification of PDEs in elliptic, hyperbolic, parabolic. Sections 11.8-12.  
 Mar 21  The method of characteristics. The characteristic ODE system. Section 13.  HW9 is posted on Brightspace.
 Mar 26  The transversality condition in the method of characteristics. Section 13.  
 Mar 28  Local existence and uniquenes for quasi-linear equations via the method of characteristics. Section 13.  
 Apr 2  Burgers' equation. Shocks. Sections 13.2, 13.3.  
 Apr 4  Scalar conservation laws in one-dimension. Section 14.  HW10 is posted on Brightspace. This will be the last HW of the course.
 Apr 9  Review for the final exam.  A study guide for the exam is posted on Brightspace.
 Apr 11  Review for the final exam.  
 Apr 16  The Rankine-Hugoniot conditions. Section 14.1.  
 Apr 18  Systems of conservation laws in one dimension.  Not in the final exam.
 May 1st, 3pm  Final exam.  


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