Lectures

• Chapter 8: The Dynamics of Many Particle Systems
  • Applet: MDSimulation

• Chapter 10: Electrodynamics
  • Applet: FieldLine
  • Applet: Laplace

• Chapter 18: Quantum Systems
  • Applet: Eigen
  • Applet: Eigen2
  • Applet: TDSE

• Chapter 11: Numerical Integration and Monte Carlo Methods
  • Applet: HitOrMiss
  • Applet: Gaussian

• Chapter 17: Monte Carlo Simulation of the Canonical Ensemble
  • Applet: Ising
  • Applet: IsingExact

• Chapter 13: Percolation
  • Applet: Percolation
  • Applet: Renormalization Group

• Chapter 14: Fractals
  • Fractal Geometry of Rocks A recent article from Physical Review Letters.
  • Applet: Regular Fractals
  • Applet: Surface Growth

• Chapter 15: Complexity
  • Applet: Game of Life Cellular Automaton

• Chapter 2: The Coffee Cooling Problem
  • Lecture 1, August 31
    • Newton's Law (§2.1) and the Euler Algorithm (§2.2,3)
    • Translations into C++ of the True Basic programs from §2.4 and §2.5.
  • Lecture 2, September 2
  • Lecture 3, September 4
• Chapter 3: The Motion of Falling Objects
  • Lecture 4, September 9
  • Lecture 5, September 11
  • Lecture 6, September 14
  • Lecture 7, September 16
  • Lecture 8, September 18
• Chapter 4: The Two-Body Problem
  • Lecture 9, September 23
    • The Two-Body Kepler Problem
    • Simulation of a Planetary Orbit
  • Lecture 10, September 28
    • Integrable Hamiltonian Systems
    • The Three-Body Problem is Not Integrable
  • Lecture 11, October 2
    • Simulating the Three-Body Problem
  • Lecture 12, October 5
    • Helium Atom as a Classical Three-Body Problem
    • C++ Program with Adaptive Step-Size Algorithm
  • Lecture 13, October 7
    • Two-Body Scattering
    • The Lennard-Jones Potential
  • Lecture 14, October 9
    • Two-Body Scattering (continued)
  • Lecture 15, October 12
    • More on the Asteroid Project
• Chapter 5: Simple Linear and Nonlinear Systems
  • Lecture 16, October 14
    • Simple X Window program xHello.cpp
  • Lecture 17, October 16
    • Motif animation of simple pendulum
  • Lecture 18, October 19
    • Microsoft Windows graphics programming
  • Lecture 19, October 23
    • Midterm problems
    • Simplified Motif programming
  • Lecture 20, October 26
    • Using xSimple.h
• Chapter 6: The Chaotic Motion of Dynamical Systems
  • Lecture 21, October 28
    • Population dynamics and logistic map
  • Lecture 22, October 30
    • Logistic map: fixed points and period doubling
    • Analogs in pendulum motion
  • Lecture 23, November 2
    • Bifurcation diagram
    • Feigenbaum's universal constants
    • Chaotic region
  • Lecture 24, November 4
    • Lyapunov exponent
    • Controlling chaos
  • Lecture 25, November 6
    • Bisection search root-finding algorithm
    • Recursive function for f^(p) (x, r)
  • Lecture 26, November 9
    • The 2-dimensional Hénon Map and Strange Attractor
    • The Lorenz Model of Deterministic Nonperiodic Flow, and the Lorenz Attractor
  • Lecture 27, November 11
    • Forced Damped Nonlinear Pendulum
  • Lecture 28, November 13
    • Hamiltonian Chaos in the Kicked Rotor
    • The Standard Map, Kolmogorov-Arnold-Moser Theorem
  • Lecture 29, November 16
    • Hamiltonian chaos in the double pendulum
  • Lecture 30, November 18
    • Chaos in Stadium Billiard Systems
    • Period doubling and chaos in Rayleigh-Bénard convection
  • Lecture 31, November 20
    • Rayleigh-Bénard convection in liquid ⁴He: experimental evidence for period-doubling and chaos in the power spectrum
• Chapter 9: Normal Modes and Waves
  • Lecture 32, November 23
    • Fourier Transform and Power Spectrum
    • O(N²) algorithm vs. O(N log₂(N)) FFT algorithm
  • Lecture 33, November 24
    • Cooley-Tuckey FFT algorithm using bit-reversal and the Danielson-Lanczos lemma
    • Cases N = 4 and N = 8
  • Lecture 35, November 30
    • More on the Cooley-Tuckey FFT algorithm:
      Numerical Recipes Section 12.2 Fast Fourier Transform
    • Application to damped oscillator and chaos
  • Lecture 36, December 2
    • FFT continued
    • Nonlinear damped driven pendulum
  • Lecture 37, December 4
    • More on pendulum power spectra
    • Aliasing and other FFT problems
• Chapter 12: Section 12.6 Random Number Sequences
  • Lecture 38, December 7
    • Applications of random numbers
    • Generating true random numbers
    • Pseudo-random number sequences
    • Linear congruential generators
  • Lecture 39, December 9
    • Standard C/C++ generator: int rand()
    • A better generator: double drand48()
    • Chi-square test: chi_square.cpp
  • Lecture 40, December 11
    • Numerical Recipes Section 7.1 Uniform Deviates
    • FFT test of randomness: rand_power.cpp
    • Auto-correlations: Program auto_corr.cpp
  • Lecture 41, December 14
    • More on auto_corr.cpp
    • Program box.cpp: Order to disorder (Chapter 7 Section 1)

Maintained by: Dr. R.J. Gonsalves
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