By David D. Nolte
Example Syllabus:
First Semester:
(Week of …)
Aug. 19
IMD Chap. 1 Physics & Geometry
Section 1: State space and flows
Section 2: Coordinate representations
Aug. 26
IMD Chap. 1 Physics & Geometry
Section 3: Coordinate transformations
Section 4: Uniformly rotating frames
Sept. 2 (Labor Day Week)
IMD Chap. 1 Physics & Geometry
Section 5: Rigid-body motion
Sept. 9
IMD Chap. 1 Physics & Geometry
Section 5: Rigid-body motion
Wrap up Chap. 1
Sept. 16
IMD Chap. 2 Lagrangian Mechanics
Section 1: Calculus of variations
Section 2: Lagrangian applications
Sept. 23
IMD Chap. 2 Lagrangian Mechanics
Section 3: Dissipation
Section 4: Lagrange multipliers
Section 5: More applications
Section 6: Conservation laws
Sept. 30
IMD Chap. 2 Lagrangian Mechanics
Section 7: Central force motion[1]
Section 8: Virial Theorem
Midterm #1 (Oct. 2) Covers Chap. 1 and Chap. 2.1-2.6
Oct. 7 (Oct. Break Week)
IMD Chap. 3 Hamiltonian Dynamics
Section 1: Hamiltonian function
Section 2: Phase space
Oct. 14
IMD Chap. 3 Hamiltonian Dynamics
Section 3: Integrable systems and action-angle variables
Section 4: Adiabatic invariants
Oct. 21
IMD Chap. 4 Nonlinear Dynamics and Chaos
Section 1: One-variable dynamical systems
Section 2: Two-variable dynamical systems[2]
Section 3: Limit cycles[3]
Section 4: Discrete iterative maps
Oct. 28
IMD Chap. 4 Nonlinear Dynamics and Chaos
Section 5: Three-dimensional state space and chaos
Section 6: Driven flows[4]
Nov. 4
IMD Chap. 5 Hamiltonian Chaos
Section 1: Hamiltonian systems[5]
Section 2: Nonintegrable systems[6]
Section 3: Chirikov Standard Map
Midterm #2 (Nov. 6) Covers Chaps. 2.3-2.8, 3 and 4.1-4.4 (and implicitly earlier topics)
Nov. 11
IMD Chap. 5 Hamiltonian Chaos
Section 4: KAM theory[7]
Section 5: Web map[8]
Nov. 18
Special Section: Stochastic Dynamics
Section 1: Flipping coins and Probability
Nov. 25 (Thanksgiving week)
Special Section: Stochastic Dynamics
Section 2: Stochastic Motion
Random Walk and Diffusion
Dec. 2
Special Section: Stochastic Dynamics
Section 2: Stochastic Motion
Dynamics with Noise
Review
Final Exam Covers all topics comprehensively
[1] https://galileo-unbound.blog/2019/07/05/the-three-body-problem-longitude-at-sea-and-lagranges-points/ ; https://galileo-unbound.blog/2019/07/19/getting-armstrong-aldrin-and-collins-home-from-the-moon-apollo-11-and-the-three-body-problem/
[2] https://galileo-unbound.blog/2019/04/24/biased-double-well-potential-bistability-bifurcation-and-hysteresis/
[3] https://galileo-unbound.blog/2019/08/26/the-fast-and-the-slow-of-grandfather-clocks/
[4] https://galileo-unbound.blog/2019/03/20/georg-duffing-and-his-equation/
[5] https://galileo-unbound.blog/2019/06/16/vladimir-arnolds-cat-map/
[6] https://galileo-unbound.blog/2018/12/10/the-wonderful-world-of-hamiltonian-maps/
[7] https://galileo-unbound.blog/2019/10/14/how-number-theory-protects-you-from-the-chaos-of-the-cosmos/
[8] https://galileo-unbound.blog/2018/10/27/how-to-weave-a-tapestry-from-hamiltonian-chaos/
Second Semester
(Week of …)
Jan. 13
Chap. 6 Coupled Oscillators and Synchronization
Section 2: Simple synch
Section 3: Rational resonance
Jan. 20 (MLK week)
Chap. 6 Coupled Oscillators and Synchronization
Section 4: External Synch
Section 5: Synch of Chaos
Jan. 27
Chap. 7 Network Dynamics
Section 1: Network Structures
Section 2: Random Network Topologies
Feb. 3
Chap. 7 Network Dynamics
Section 3: Synchronization on networks
Section 4: Diffusion on networks
Feb. 10
Chap. 8 Evolutionary Dynamics
Section 1: Population dynamics
Section 2: Virus infection
Feb. 17
Chap. 8 Evolutionary Dynamics
Section 3: Replicator equation
Section 4: Quasi-species
Feb. 24
Chap. 9 Neurodynamics
Section 1: Neuron function
Section 2: Neurodynamics
March 3
Special Notes on Artificial Neural Nets (ANN)
March 10
Chap. 11 Metric Spaces and Geodesic Motion
Section 1: Manifolds and metric tensors
Section 2: Tensor derivatives
Section 3: Geodesic curves
Section 4: Geodesic motion
Midterm 1 (Evening, March 12) (Chaps 6, 7, 8, 9.1 and 9.2)
March 24
Chap. 12 Relativistic Dynamics
Section 1: Special Relativity
Section 2: Lorentz transformations
Section 3: Minkowski space
March 31
Chap. 12 Relativistic Dynamics
Section 4: Relativistic trajectories
Section 5: Relativistic dynamics
Section 6: Linear acceleration
April 7
Chap. 13 General Relativity
Section 1: Newtonian correspondence
Section 2: Riemann curvature
Section 3: Field equations
Section 4: Schwarzschild space time
April 14
Chap. 13 General Relativity
Section 5: Kinematics
Section 6: Deflection of light
April 21
Midterm 2 (In Class) (Chaps. 11 thru 13.6)
April 23
Class Presentations
April 28
Class Presentations
April 30
Class Presentations
Final Project Guidance:
The goal of the Final Project is to combine two or more “unrelated” topics from Phys 410-411 into a single simple study. These topics, individually and broadly, are: Lagrangians, Hamiltonians, Chaos, Synchronization, Networks, Neurodynamics, Evolutionary dynamics, Econophysics, Metric spaces, Special relativity, General relativity. The topics can draw from any of the subjects or chapters, even if not covered in class. Emphasis is placed on originality and possibly non-obvious connections. Work can be exclusively analytical or exclusively computational, but the best is a mix of both.
Class Presentation: Each student will give a 12 minute class presentation on their project. It will be 9-10 minutes of PowerPoint presentation followed by 2-3 minutes of questions from the class. Class participation asking questions of the presenter will be noted.
Write-up: The write-up consists of the Powerpoint slides plus up to 10 Appendix pages of supporting derivations, codes, bibliographic info, etc.
Two examples of “combined” ideas can be found at
– This was the project of a 2021 student who combined synchronization with gravitational time dilation. (Excellent example!)
– This combines the Lorenz butterfly with concepts of basins of attraction and limit cycles (plus a bit of sci-fi animé for fun).
The first step is to write up a single paragraph with a title proposing what you would like to do. The idea needs to be original – not something that can be found on the web. Tell me: What topics? What problem? What is your expected technical approach? What will you study as a function of what? What questions are you trying to answer? What do you think you might find? Why is this problem interesting?
Email this paragraph to me (make sure to use Phys 411 in the subject heading).
The final project grade is based mainly on your class presentation—your final written report is primarily to remind me of what I saw.
There are several points of advice for creating high-value content in your presentations:
1) All figures should have titles and numbered figure captions. The figure axes need to be labeled. Also, if there is more than one curve on a graph, the graph needs a legend or other annotation. Figure captions should explain in one or more sentences what the figure is meant to illustrate and what key parameters were set or changed.
2) There should be a single clear and concise introductory slide as your “elevator pitch” for what the project is, why it is interesting, and what was discovered. It should clearly state what two or more “concepts” you merged.
3) Make sure you show the dynamical equations and clearly explain all terms, especially if you have added new terms to an existing model.
4) It is always good to show “primary plots” that show good examples of different types of trajectories or other system behavior. But the main plots should be “secondary plots” which can show a family of curves as some parameter is changed. Then, if possible, there should be tertiary plots that show how some property of the system changed as a parameter was changed. As an example, a tertiary plot might be the average coupling needed for full synchronization as a function of standard deviation of the spread of initial frequencies. Plots that show average properties should also have error bars…these can be either standard deviations or standard errors, but which you chose should be stated in the figure caption.
5) In your conclusion, avoid saying that you did x1 and saw y1 and then did x2 and saw y2. The conclusion should be explanatory, saying why you saw y1 as you did x1 and why you changed to x2 and if y2 matched your expectation. In addition, if you did x2 and expected to see y2 but instead saw z2, you should suggest a possible explanation even if you don’t have time to test it.
Good Luck.
DN
Galileo Unbound 