Chapter 1:  Introduction to Progamming and Numerical Solutions  (Jan 20+22)

• 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  (Jan 25, 27, 29)

• 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  (Feb 01, 03, 05, 08)

• 2.Order DEQ: Simple Harmonic Motion, Euler-Cromer method 
• Driven Harmonic Motion, transition to chaos, Lyapunov exponent
• Bifurcation, Logistic Map
• Billard problem
  

 Chapter 4:  Planetary Motion  (Feb 10, 12, 15, 17) 

• Kepler's laws in cartesian coordinates
• Elliptic orbits and stability of the inverse-square force law
  
• Correction to 1/r²-orbits: general relativity, 3-body; least-square fit
• 3-Body problem, Kirkwood Gaps
  

 Chapter 5:  Potentials and Fields   (Feb 19, 22, 24)

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

 Chapter 6:  Waves    (Feb 26,  Mar 01, 03, 05)

• Ideal wave equation (in space-time, DEQ), stability
• Frequency spectra, (fast) Fourier analysis, power spectrum
• Realistic string: stiffness and friction
• Spectral methods   

 
Chapter 7:  Random Systems    (Mar 08, 10, 12, 22, 24, 26, 29)

• Random Number Generators
• Random Walk, Self-Avoiding Walk, Flory Exponent
• Diffusion equation, entropy
• Cluster growth
• Fractal dimensions
• Percolation and 2. order phase transition
  

Chapter 8:  Statistical Mechanics, Ising Model and Phase Transitions    (Mar 31, Apr 05, 07, 09, 12, 14)

• Ising Model, Mean-Field Theory
• Monte-Carlo method
• Ising model and 2.order phase transition, critical exponents, correlation function
• External magnetic field, 1.order phase tranition
   

 Chapter 9:  Molecular Dynamics    (Apr 16, 19, 21, 23)

• Dilute gas, equations of motion, Verlet method
• Boundary conditions and initialization
• Equilibrium and equipartition theorem
  
• Solidification and Melting Transition   

 
Chapter 10:  Quantum Mechanics    (Apr 26, 28, 30, May 03+04)

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