Spring 2021 - MATH 314 D100

Introduction to Fourier Methods and Partial Differential Equations (3)

Class Number: 3529

Delivery Method: Remote

Overview

  • Course Times + Location:

    Mo, We, Fr 11:30 AM – 12:20 PM
    REMOTE LEARNING, Burnaby

  • Exam Times + Location:

    Apr 24, 2021
    8:30 AM – 11:30 AM
    REMOTE LEARNING, Burnaby

  • Prerequisites:

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

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:



This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Course Outline

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 contains the core of the traditional boundary value problems curriculum, but will also introduce the computer graphics and numerical computational tools associated with the analysis of PDEs and their solutions.

Central 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.

COURSE DELIVERY

  •  Lecture: synchronous- lectures will be held at fixed times, on-line
  •  Midterm(s): synchronous; date: TBA
  •  Final exam: synchronous; date: TBA

Grading

  • Assignments (6)(5% each) 30%
  • Midterm 20%
  • Final Exam 50%

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.

Grading is subject to change

Materials

MATERIALS + SUPPLIES:


Required: 

  • Access to strong and reliable internet.
  • Ability to scan documents (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)

REQUIRED READING:

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


ISBN: 9780898719352

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site 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

TEACHING AT SFU IN SPRING 2021

Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).