Chapter 1:  Introduction to Progamming and Numerical Solutions  (Jan 19,21,24)

• 1.Order differential equations (DEQs) and Euler method; nuclear decay
  
• Code design and construction
• Code debugging+checking; numerical parameters and accuracy
• Runge-Kutta Method
  

 Chapter 2:  Drag Forces in 1- and 2-D Motion  (Jan 26,28,31)

• 1-D: car/bicycle with velocity-dependent force
• 2-D: smooth cannon shell
  
• Effects of turbulence, wind spinning 

  Chapter 3:  Oscillatory Motion and Chaos  (Feb 02,04,07,09)

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

 Chapter 4:  The Solar System  (Feb 11,14,16,18) 

• 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 21,23,25,28)

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

 Chapter 6:  Waves and Spectral Analysis    (Mar 02,04,07,09)

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

----     Midterm Exam: Mar 11 in class     ---- 

Chapter 7:  Random Systems    (Mar 21,23,25,28,30, Apr 01,04,06)

• 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    (Apr 08,11,13,18)

• 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 20,22,25,27)

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

 
Chapter 10:  Quantum Mechanics    (Apr 29, May 02,03)

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