Spring 2020 - MATH 314 D100
Introduction to Fourier Methods and Partial Differential Equations (3)
Class Number: 3701
Delivery Method: In Person
Course Times + Location:
Mo, We, Fr 11:30 AM – 12:20 PM
AQ 4140, Burnaby
Exam Times + Location:
Apr 16, 2020
8:30 AM – 11:30 AM
AQ 3154, Burnaby
1 778 782-3335
Prerequisites:MATH 310; and one of MATH 251 with a grade of B+, or one of MATH 252 or 254.
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.
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.
- Assignments (6)(5% each) 30%
- Midterm 20%
- Final Exam 50%
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
Partial Differential Equations : Analytical and Numerical Methods
Mark S. Gockenbach
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