Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MATH 314 D100

Introduction to Fourier Methods and Partial Differential Equations (3)

Class Number: 3216

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Prerequisites:

    MATH 260 or MATH 310, with a minimum grade of C-; and one of MATH 251 with a grade of B+, or one of MATH 252 or 254, with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

Fourier series, ODE boundary and eigenvalue problems. Separation of variables for the diffusion wave and Laplace/Poisson equations. Polar and spherical co-ordinate systems. Symbolic and numerical computing, and graphics for PDEs. Quantitative.

COURSE DETAILS:

What we perceive of the world around us are variations of physical effects (like heat, sound & light) over space and time. Partial differential equations (PDEs) are the mathematical language for describing this sensory landscape in terms of continuous functions. This course is a broad introduction to linear PDE theory, along with
computer graphics and numerical computational tools associated with the analysis of PDEs and their solutions.

One central approach to the theory of linear PDEs are the Fourier series and Fourier transform. The numerical implementation of the Fourier series, the fast Fourier transform (FFT), is one of the most important numerical algorithms in scientific computing. The trio of elementary PDEs: the potential, heat and wave equations will be introduced through their Fourier solutions. The generalization of these to higher dimensions will naturally lead to the “special” functions, such as the Bessel function and spherical harmonics.

The computational tools will be developed from numerical routines based upon the linear algebra of matrices and vectors. The numerical computing and graphics will be performed through the modification of downloaded Matlab/Python scripts and Maple worksheets.

Grading

  • Assignments 35%
  • Midterm 25%
  • Final Exam 40%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient). 

Materials

REQUIRED READING:

Partial Differential Equations : Analytical and Numerical Methods
2/E
Mark S. Gockenbach
SIAM


ISBN: 9780898719352

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.