Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu

office: Stevenson Center 1515

phone: (615) 322 7147 fax: (615) 343 0215

mail to: 1326 Stevenson Center Ln, Vanderbilt University, Nashville TN 37240

MATH
4110 - 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 7110 syllabus.

Textbook: No textbook will be adopted. Support references are given in the syllabus.

Classes meet on TR, 11:00am–12:15pm, at Stevenson Center 1313 (3rd floor of the Mathematics Building).

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 7110 syllabus.

Textbook: No textbook will be adopted. Support references are given in the syllabus.

Classes meet on TR, 11:00am–12:15pm, at Stevenson Center 1313 (3rd floor of the Mathematics Building).

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: Thursdays, 4:00–7:00pm, or by appointment.

Instructor's office phone: (615) 322-7147.

Instructor's office: Stevenson Center 1515 (5th floor of the Mathematics Building).

Instructor's email: marcelo.disconzi@vanderbilt.edu.

Instructor's office hours: Thursdays, 4:00–7:00pm, or by appointment.

Instructor's office phone: (615) 322-7147.

Exams

Description |
Date |
Location and Time |
Remarks |

Test 1 | Sept 28 |
in class |
Study
guide. Solutions. |

Test 2 | Nov 2 |
in class |
Practice
problems. Solutions
to the practice problems. Solutions to the test. |

Final Exam | Saturday, Dec 16 |
3pm, at SC 1313 |
Study guide. |

Schedule

Below is an ongoing schedule for the course (for the academic calendar, click here). This will be updated regularly and, therefore, students should check this webpage frequently. The due date for each assignment will be posted as the course progresses.

Below is an ongoing schedule for the course (for the academic calendar, click here). This will be updated regularly and, therefore, students should check this webpage frequently. The due date for each assignment will be posted as the course progresses.

Date | Material covered | Homework | Remarks |

Aug 24 |
Introduction, motivations for PDEs. Class notes. Some notation and terminology. | ||

Aug 29 | Formal definition of PDEs, homogeneous vs. non-homogeneous, linear vs. non-linear PDEs. Class notes. | HW 1. | HW 1 is due on Sept 7. Solutions to HW 1. |

Aug 31 | Linear operators. First order PDEs. Class notes. | ||

Sept 5 | First order equations. Introduction to the method of characteristics. Class notes. | HW 2. |
HW 2 is due on Sept 14. Solutions to HW 2. |

Sept 7 | The method of characteristics. Burger's equation. Class notes. | ||

Sept 12 | Limitations of the method of characteristics. Shocks. Class notes. | ||

Sept 14 | Existence and uniqueness for first order quasi-linear equations. Class notes. | ||

Sept 19 | The wave equation. D'Alembert's formula. Class notes. | HW 3. | HW 3 is due on Sept 28. Solutions to HW 3. |

Sept 21 | Finite propagation speed for the wave equation. Generalized vs classical solutions. Class notes. | ||

Sept 26 | Review for the test. | ||

Sept 28 | Test 1. | ||

Oct 3 | Initial-boundary value problem for the wave equation. Separation of variables. Class notes. | HW 4. |
HW 4 is due on Oct 17. Solutions to HW 4. |

Oct 5 | Fourier series: basic ideas. Class notes. | ||

Oct 10 | Formal aspects of Fourier series. Class notes. Summary of theorems. | ||

Oct 17 | More on Fourier series: periodic functions and convergence of solutions to the wave equation. Class notes. | ||

Oct 19 | The Fourier transform. Class notes. | HW 5. | HW 5 is due on Oct 31. Solutions to HW 5. |

Oct 24 | The Laplace transform. Class notes. | ||

Oct 26 | A few tools from calculus in R^n. Class notes. | ||

Oct 31 | Review for the second test. | ||

Nov 1 | Test 2. | ||

Nov 7 | Laplace's and Poisson's equation. Class notes. | ||

Nov 9 | Fundamental solution to Laplace's equation. | ||

Nov 14 | Existence of solutions to Poisson's equation. | ||

Nov 16 | Existence of solutions to Poisson's equation. Class notes. | HW 6. | HW 6 is due on Nov 30. Here are a few extra practice problems that will not be collected. |

Nov 28 | Duhamel's principle. Solutions to the heat equation in R^n. Class notes. | ||

Nov 30 | Eigenvalues of the Laplacian. Class notes. | ||

Dec 5 | Review. | ||

Dec 7 | Review. |

Anonymous
feedback

Students are encouraged to bring suggestions and to discuss with the course instructor any concerns they may have, including something they think is not being properly handled in the course. But if you do not feel comfortable doing that, here you have the opportunity to send some anonymous feedback.

Students are encouraged to bring suggestions and to discuss with the course instructor any concerns they may have, including something they think is not being properly handled in the course. But if you do not feel comfortable doing that, here you have the opportunity to send some anonymous feedback.