Fourier Analysis and Partial Differential Equations (MAT4212.01)

Andrew McIntyre

Fourier analysis may be seen as decomposing an arbitrary function, or wave form, into sine and cosine functions. In this sense, it is clearly of interest in analyzing audio signals. However, it goes much further than this. In computer science, it extends to processing of images and data compression. In physics, it is central to quantum mechanics. More broadly, it is the main solution method for partial differential equations, the other subject of this course, which are ubiquitous in physics. Almost any situation in physics involving a field will be modeled by partial differential equations, including heat conduction, wave motion, Schrödinger’s equation, and the Laplace equation of electrostatics. Moreover, mathematically, Fourier analysis is where linear algebra and analysis merge, and it is at the center of many other concepts and open questions. The course will be grounded in computational techniques. Students may choose a more applied or more theoretical emphasis.

Note that in our non-standard calculus sequence, we do not cover some standard computational techniques of calculus in the introductory course MAT 4288 Calculus: A Classical Approach. Some of those techniques can be covered in this class instead. Therefore, this class is a possible choice for students who took Calculus: A Classical Approach and want to go further with calculus.

Learning Outcomes:
- Develop and practice computational techniques of calculus, particularly integration rules
- Compute Fourier series
- Solve linear partial differential equations by separation of variables, including wave and heat equation
- Connect linear algebra and analysis; understand key ideas in Hilbert spaces
- Continue to develop higher-order conceptual thinking in mathematics ("mathematical maturity")

Delivery Method: Remotely accessible
Prerequisites: MAT 4288 Calculus: A Classical Approach, or any other college-level calculus (by permission of instructor). Contact Andrew McIntyre by email or Slack, before 4000 registration opens, to be added to the class.
Course Level: 4000-level
Credits: 4
M/Th 1:40PM - 3:30PM (Full-term)
Maximum Enrollment: 20
Course Frequency: Every 2-3 years

Categories: All courses , Mathematics , Remotely Accessible