Chapter 1:  Introduction to Progamming and Numerical Solutions  (Aug. 28+30)

• 1.Order differential equations (DEQs) and Euler method for numerical solution
  
• Code design and construction
• Code debugging, checking results, independence of numerical parameters
• plotting
  

 Chapter 2:  Projectile Motion with Drag  (Sep. 01, 04, 06)

• 1-D: car/bicycle with velocity-dependent force
• 2-D: smooth cannon shell
  
• Turbulence and wind effects
  
• Effects of spinnng
  

  Chapter 3:  Oscillatory Motion and Chaos  (Sep. 08, 11, 13, 15)

• 2.Order DEQ: Simple Harmonic Motion, Euler-Cromer method 
• Driven Harmonic Motion, transition to chaos, Lyapunov exponent
• Bifurcation
• Navier Stokes equation and Lorentz model
  
• Billard problem
  

 Chapter 4:  Planetary Motion  (Sep. 18, 20, 22, 25) 

• Kepler's laws in cartesian coordinates
• Stability of the inverse-square force law
  
• Correction to 1/r²-orbits: general relativity, 3-body; least-square fit

 Chapter 5:  Potentials and Fields   (Sep. 27, 29, Oct. 02)

• Partial differential equations (PDEs): Laplace equation and relaxation algorithm
  
• Inclusion of charges: Poisson equation
  
• Magnetic field (wire, solenoid), numerical integration
  

 Chapter 6:  Waves    (Oct. 04, 06, 09)

• Wave equation (in space-time, DEQ), stability
• Frequency spectra, (fast) Fourier analysis
• Stiffness and friction
• Spectral methods   

 
Chapter 7:  Random Systems    (Oct. 11, 13, 16, 18, 20, 23, 25)

• Random Number Generators
• Monte Carlo integration
• Random Walk
• Diffusion, entropy
• Cluster growth
• Fractal dimensions
• Percolation
  

Chapter 8:  Statistical Mechanics, Phase Transitions and Ising Model    (Oct. 27, 30, Nov. 01, 03, 06)

• Ising Model, Mean-Field Theory
• Monte-Carlo time method
• Ising model and 2.order phase transition, critical exponents
• 1.order phase tranition
   

 Chapter 9:  Molecular Dynamics    (Nov. 08, 10, 13)

• Dilute gas, Verlet method
• Melting Transition   

 
Chapter 10:  Quantum Mechanics    (Nov. 15, 17, 20, 22, 27, 29, Dec. 01)

• Time-independent Schroedinger equation (SEQ)
• Numerical solutions (trial+matching method)
• Energy minimization and variational approach
• Time-dependent SEQ: higher-order DEQs
• Spectral methods
  

Chapter 11:  Interdisciplinary Topics    (Dec. 04)

• Neural Networks