Math 4426: Fourier Series and PDEs II

CRN 15416
TTh 12:30PM - 1:45PM, HOLDEN HALL 110

Instructor: Professor Yuriko Renardy (
Office: Femoyer 406 (Phone (cell and text message): 540-320-1573)
Office Hours: TTh after class ends, 1.45PM-2.30PM, Other times by appointment.

Course Content:
This is the second semester of a two-semester sequence. The first semester (Math 4425) included the derivation of the heat and wave equations; the solution of initial boundary-value problems using separation of variables and Fourier series; the Sturm-Liouville eigenvalue-eigenvector problem, and the solution of systems of ordinary differential equations. Math 4426 requires proofs; the topics include function spaces, completeness, linear operators, uniform convergence, generalized functions, and Fourier transforms.

Software: Students are required to use Mathematica for computation and visualization. Mathematica is available free to all Virginia Tech students through the Virginia Tech Computing Center. You may download it here. For those who do not wish to install Mathematica on their computeres, it is available on all computers in the Math Emporium where it can be used without charge. Tutorials on Mathematica are available here.

Text A recommended reference is "Introduction to Partial Differential Equations" by Peter J. Olver, Undergraduate Texts in Mathematics, Springer Publishing 2014, available through the VT Libraries as an e-book. This is not a required textbook. Further references will be placed in the Resources section of You will need to take notes in class. Because of this, attendance will be taken and class participation will be a part of the grade.

MATH 2214 (Introduction to Differential Equations) and MATH 2224 (Multivariable Calculus), MATH 2204, a strong background in Advanced Calculus MATH 3224, MATH 4425.

Final Exam Schedule: May 7, 2016, 7:45AM - 9:45AM.


Student Responsibility

Special needs:Students who need accommodation for a disability (learning mode, psychological, physical, etc.), or have emergency medical information to share with me, or would need special arrangements in case the building must be evacuated, please feel free to meet with me to discuss what can be done to help fulfill the requirements of the class. Also, they may contact the Dean of Students who will see that their special needs are considered and appropriately addressed. Students requiring testing accomodations must work through the appropriate university offices. Any paperwork must be completed and validated prior to the first test.