SYLLABUS for course PHYD38 (in-person), Spring 2025
Title: Intro to Nonlinear Physics and Chaos
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Lectures  (L) on Mo. in HL B110 (Highland Hall)  10:00-12:00  (12*2 hr lect)
Tutorials (T) on Mo. in AC 332, (Acad. Res. Ctr) 13:00-14:00
A1-A4 four sets of assignments, submit to Quercus > Assignments by 10am
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 6 Jan	 L1  L2 
13 Jan   L3, T1
20 Jan 	 L4, T2
27 Jan	 L5, T3, A1   
 3 Feb   L6, T4  
10 Feb   L7, T5       midterm exam 13:00-14:00  
17 Feb   --  --       reading week
24 Feb   L8, T6, A2        
 3 Mar   L9, T7
10 Mar   L10 T8, A3   
17 Mar   L11 T9
24 Mar   L12 T10       drop date w/o acad. penalty       
31 Mar   --  --  A4
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(TBA) in Apr, 	       final exam in person
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 This syllabus will change slighty during the course, please download
 updates every week. Numbers in square brackets are chapters in Strogatz book

	0. Introduction to the course structure, requirements, and  
    main textbook: S. Strogatz "Nonlinear Dynamics and Chaos" 2nd ed. 2018 

	1. Chaos, Fractals and Dynamics and the 
		Importance of being nonlinear [1]   day 1

	2. 1-D Flows
		Flows on a line [2]    day 2
		Bifurcations [3]
		Catastrophes [3]
		Flows on a circle [4]
	
	3. 2-D Flows
		Linear systems [5]
		Physics of flight. Stability (cf. miniblog). Required material.
		Phase plane portraits [6]
		Limit cycles [7]
		Bifurcations again [8]
	
	4. Chaos
		Lorenz Equations [9]
		1-d maps [10]
		Fractals [11]
		The exponential fractal 
		Strange attactors [12]

	5. Nonlinear data analysis
		Machine Learning, Machine Intelligence 
	        Neural Networks
	
 NONLINEAR WORLD 
 (Additional topics one or more of which may be presented, time allowing):
 Topics preliminarily selected for 2025 are denoted by *
		
*  More bifurcation diagrams of discrete mappings
   Stability and bifurcations in Engineering
		Euler beam buckling as bifurcation
		Nonlinear behavior of materials
 	Nonlinearity, chaos and complexity in Physics and Astrophysics
* 		The three body and N-body systems
			Orbits, Lagrange points, Lyapunov timescales in 
			planetary and galactic systems
	Nonlinear continuum mechanics
			Incompressible and compressible fluids
			Vortices and turbulence in air and water
* 			Turbulent jets: Chaos out of order and order in the chaos 
	Dynamics of galacic and protoplanetary disks
			Linear and nonlinear stability and evolution
			Nonlinear waves, Fluid resonances, Particle resonances  
	Nonlinear optics
	Quantum chaos
	Noise and corruption of signals in physical systems 
		Noise: white, pink, black, non-power law 
		Convolution, PSF.  Deconvolution. Wiener & Kalman filters
	Chaotic stock market
	Modeling and forecasting of nonlinear time-dependent processes