Spring 2024 - MATH 314 D100
Introduction to Fourier Methods and Partial Differential Equations (3)
Class Number: 3819
Delivery Method: In Person
Course Times + Location:
Jan 8 – Apr 12, 2024: Mon, Wed, Fri, 10:30–11:20 a.m.
Exam Times + Location:
Apr 20, 2024
Sat, 8:30–11:30 a.m.
1 778 782-4792
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-.
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.
Final Exam 50%
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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).
Partial Differential Equations : Analytical and Numerical Methods
Mark S. Gockenbach
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