SYLLABUS for course PHYD38 (in-person), Spring 2025
Title: 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 HL B110, 12:00-13:00  (orig. sched. as AC 332 13-14)  
A1-A4 four sets of assignments, submit to Quercus > Assignments, due 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 12:00-13:00  
17 Feb   --  --       reading week
24 Feb   L8, T6, A2        
 3 Mar   L9, T7
10 Mar   L10 T8   
17 Mar   L11 T9, A3
24 Mar   L12 T10     Research talks on 24th; drop date w/o acad. penalty 24.03.       
   *** lectures have ended, thank you guys! it was fun. 
 4 Apr   --  --  A4  due on Fri 10pm
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22 Apr, 19:00-22:00  BV264 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  
	textbook: S. Strogatz "Nonlinear Dynamics and Chaos" 3rd ed. 2024

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

	2. 1-D Flows                      
		Flows on a line [2]  				  
		Bifurcations [3]
		Catastrophes [3] 			 
		Flows on a circle [4]
	
	3. 2-D Flows
		Linear systems [5]         
		Physics of flight. Stability (etudes; required material)
		Phase plane portraits [6]
		Limit cycles [7]         
		Bifurcations again [8] 
		[Dog and duck in a pond - not req! Read Etudes & Variations]	
	4. Chaos
		Lorenz Equations [9]  
		1-d maps [10]         
		Fractals [11]         
		The exponential fractal         
		Strange attactors [12]

	5. Nonlinear world. Additional topics in Nonlinear Science
        (several will be presented, perhaps from among those marked with *): 
	*	The three body and N-body systems 
	*	More bifurcation diagrams of discrete mappings
	*	Incompressible and compressible fluid disks (galacic, protoplanetary):
		Lin. & nonlin. stability & evolution. Waves, resonances  
	*	Turbulent jets: order our of chaos 
    *   Nonlinear acceleration of slowly converging series
		Noise and signals in physical systems: white, pink, black noise 
		Chaotic stock market
		Modeling and forecasting of nonlinear time-dependent processes