Spring 2021
MAP 4401: Advanced Differential Equations
MAP 5317: Advanced Differential Equations for Engineers

Office: DM 432
Phone: Number: 305 348 2957
Email: meziani at fiu.edu
Office hours via zoom TBD:


Objective: This is an introductory course in Partial Differential Equations with applications. It focuses on the use of the separation of variables and Fourier series to solve boundary value problems encountered in Physics and Engineering (such as heat transfer, wave propagation, and potential theory). The settings of the boundary value problems include rectangular coordinates, cylindrical coordinates, and spherical coordinates. Series expansions in Bessel functions and Legendre polynomials will be used to solve the boundary value problems.


Prerequisites: Differential Equations (MAP 2302) and Multivariable Calculus (MAC 2313).

Cross-Listing: This Course is cross-listed as MAP 4401 and as MAP 5317.  Please note the following restrictions

  • Students majoring in Mathematics: You can register in the course only as MAP 4401 (it will not earn you graduate credits).
  • Graduate students majoring in other disciplines such as Engineering or Physics: You can register in the course as either MAP 4401 or MAP 5317. If you register in the course as MAP 5317, you will have to turn in more projects. The projects for MAP 5317 might include problems dealing with numerical analysis, Green's function, and Fourier transforms.

Textbook: No formal textbook will be used. I will be posting my own notes (including exercises) that you can access HERE
Here is a list of texts that you can consult (these texts were used in the past for this course)

  • Fourier Series and Boundary Value problems, by R.V. Churchill and J.W. Ward, McGraw-Hill
  • Fourier Series and Integrals of Boundary Value Problems, by J. Ray Hanna, Wiley-Interscience
  • Partial Differential Equations with Fourier Series and Boundary Value Problems, by Nakhle Asmar, Prentice Hall


Examinations:

  • For MAP 4401: There will be three tests and a comprehensive final. The three tests will be worth 69% of the grade and the final exam will be worth 31% of the grade.
  • For MAP 5317: In addition to the examinations listed above, there will be two projects. The three tests will be worth 59%, the projects 10% , and the final 31%


The grade will be assigned according to the following scale.

  • A : 90 to 100,  A- : 90 to 92
  • B+: 85 to 89,  B: 80 to 84; B-: 77 to 79
  • C+: 70 to 76, C: 65 to 69
  • D+: 60 to 64, D: 55 to 59, D-: 50 to 54.
  • F: less than 50

Tests: TBA

Make-up policy: The final test is mandatory. A failure to take the final will result in an F. Make-up for hourly tests will be considered only in special and justifiable circumstances and at most one make-up test will be allowed. If for some reason you have a legitimate reason to miss an hourly test, you must make arrangements to take the test before the test date. A legitimate cause of absence such as personal or family illness or conditions over which the student has no control must be documented with a written verification by the proper authorities and a phone number that can verify the excuse.

Incomplete grades: It is difficult to qualify for an incomplete grade. An incomplete grade is not a substitute for a failing grade. In order to be considered for an incomplete grade, the student must have completed at least three fourth (3/4) of the course and must be passing the grade of C or better.

Drop date: The last day to drop the course with a DR/WI can be found in the official FIU  academic calendar

Notes:
The links to the following notes will be updated regularly as the course progresses