Weekly Meetings: Thursdays, 5pm EST, on Zoom
Recordings are posted here.
Topic: Fourier Analysis, Reference: Stein & Shakarchi "Fourier Analysis"[S&S]
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| Date | Speaker | Title | Reading | Abstract |
| July 17 |
UMS Officers
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Introduction | NIL |
We will first introduce Summer UMS and then decide on the logistics, topic, speakers, and general plan for this year's seminar. We will also be taking volunteers to give talks during the meeting. If you would like to give a talk or participate in the seminar in general but cannot attend this week, please email Joseph Rowland McGill.
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| July 24 |
Yiming Song
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Waves and Fourier analysis | [S&S] ch 1 (pg 1-22) | We will motivate Fourier analysis with some fun, classical examples by thinking about waves. Then we will give a preview of some cool results and applications of Fourier analysis. |
| July 31 |
Jon Kwong
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On the hows and whys of the Fourier series | [S&S] ch 2 (pg 29-58) |
On the hows and whys of the Fourier series Abstract: With the knowledge that functions can be decomposed into sums of sinusoids, the next most natural question would be how exactly we should take this sum. We tackle this question for periodic functions by defining the Fourier series and outline an important theorem which ensures the uniqueness of this series. We will also preface the next chapter by intuiting why the Fourier series properly approximates the given function, and in doing so, introduce the notions of convolution and the Dirichlet Kernel.
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| August 7 |
Sabrina Yu
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Convergence of Fourier Series | [S&S] ch 3 (pg 69-87) |
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| August 14 |
TBD
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Some Applications of Fourier Series | [S&S] ch 4 (pg 100-120) |
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| August 21 |
TBD
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The Fourier Transform on R | [S&S] ch 1 (pg 129-161) |
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| August 28 |
TBD
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The Fourier Transform on R^d | [S&S] ch 1 (pg 175-207) |
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