| Week |
Topics |
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1
MWF
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Singular Value Decomposition
See Brunton & Kutz chapter 1, Strang (1993), Strang's "... 4 Lines" notes, Moler (2016), Martin & Porter (2012), Kolda & Bader (2009)
- Monday 9/16: Introductions, "On the Nature of Applied Mathematics" (see Lin & Segel section 1.1), and start SVD
- Wednesday 9/18: Strang's "4 lines" example of the 4 subspaces,
- Friday 9/20: Image Compression, PCA, "eigendigits" example
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2
MWF
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Fourier Transforms
See Lin & Segel chapters 5 and 6, Logan chapter 5, Brunton & Kutz chapter 2, Trefethen chapters 1–4
- Monday 9/23: Definitions of the 4 Fourier variants, emphasizing the relationships between the discrete/continuous and bounded/unbounded properties of the 2 spaces
- Wednesday 9/25: Derivatives, convolutions, Green's function of the heat equation, and FFT
- Friday 9/27: Smoothness and Spectral Accuracy
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3
MWF
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- Monday 9/30: Simple FFT examples (fftexamples.mlx)
- Wednesday 10/2: Image Compression examples with FFT and Wavelets
"Optimization is the Cornerstone"
- Friday 10/4: Over- and Under-determined systems, Sparsity and Compressed Sensing (B&K chapters 3–4)
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4
MWF
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- Monday 10/7: CVX
- Wednesday 10/9: CVX examples with matrices
- Friday 10/11: Robust PCA
I meant for us to also survey some key ideas about clustering and classification from Brunton & Kutz chapter 5, but I can give you some notebooks for that if you want to look at it yourself (just let me know and I can send you the files).
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5
WF
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No class on Monday 10/14
Essentials of Complex Analysis
See Part D of Kreyszig.
- Wednesday 10/16: Review of complex numbers and functions, limits, derivatives, and analytic functions
- Friday 10/18: Cauchy-Riemann conditions, complex contour integration, and examples of path independence
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6
MW
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- Monday 10/21: Integral around a pole and Cauchy's Integral Theorem
- Wednesday 10/23: Cauchy's Integral Formula and Taylor Series
No class on Friday 10/25
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7
MWF
|
- Monday 10/28: Laurent Series
- Wednesday 10/30: Residue Theorem
Asymptotic Expansion of Integrals
See Bender & Orszag chapter 6, Hinch chapter 3
- Friday 11/1: Term-by-term integration and integration by parts
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8
MTWF
|
- Monday 11/4: Laplace's Method and Watson's Lemma
- Tuesday 11/5: Method of Steepest Descent
- Wednesday 11/6: Stirling Series and other examples
Course project presentations
- Friday 11/8: Hayley Coyle on Dynamic Mode Decomposition
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9
MTWF
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- Monday 11/11: Anna Vasenina on SINDy
- Tuesday 11/12: Xin Jin on Graph Embeddings Methods and Their Applications
- Wednesday 11/13: Chiyu Wei on Deep Learning
- Friday 11/15: Patrick Addona on Reduced Order Models
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10
MTW
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- Monday 11/18: Toby Harvey on Symplectic Runge-Kutta Schemes for Adjoint Equations and more
- Tuesday 11/19: Rohan Kapoor on Wavelets
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