Resources
This is a partial listing of
resources you may find useful.
If you stumble upon something that you think would
be useful to others please email me!
Computational Physics
Resources/Texts:
Lecture
Notes on Computational Physics, M.
Hjorth-Jensen, University of Oslo (2010)
(available under Creative Commons License)
Numerical
Recipes, Press,
Teulkolsky,Vetterling,Flannery (1992)
(C version available online)
Computational
Physics with Python, M. Newman
(several introductory chapters available online +
Python resource links)
Computational Physics, 2nd ed., N.
Giordano and H. Nakanishi, (2006)
Computational Physics, 2nd ed., Landau, Paez and
Bordelanu (2008)
An Introduction to Computational Physics, T. Pang
(2006)
Computer
Language and Visualization Resources:
(These are examples, many other
resources available via a search)
Python Resources:
Canopy
(Package Manager for installation of
Python/NumPy/SciPy/Matplotlib)
(Free License for Students and Academics)
Python
Tutorial
NumPy
Tutorial
SciPy
Tutorial
Matplotlib
Tutorial
Syllabus/Notes
Below
you will find the topics/concepts we have covered
in the course and a link to any lecture notes.
Date
|
Topic
|
09/05
|
Introduction.
Logistics. Programing Language Options.
|
09/08
|
Equations
of Physics. Analytical
Solutions. Perturbative
Approaches. Computer Simulation as
Numerical Experiment.
|
09/10
|
Role of Computational
Physics in Science; Examples of Computer
Simulations; Binary Representation of
Numbers
|
09/12
|
Computer Representations of
Numbers: Unsigned Integers, Signed
Integers (Two's Complement); Floating
Point Representations: Sign, Exponent,
Mantissa/Fractional
|
09/15
|
Floating Point
Representations (IEEE-754): 32bit, 64bit,
128bit. Floating Point
Precision; Example: Round Off Error
During Subtraction
|
09/17
|
Types of Errors: Errors in
the Problem, Approximation Errors,
Round-off Errors; Errors in the Problem:
Modeling Approximations/Errors, Input Data
Errors; Approximation Errors:
Discretization Error, Convergence Error;
Example: Harmonic Number Sum Up vs. Sum
Down
|
09/19
|
Assignment Write-Up
Expectations;
Derivatives: Derivative Estimates Using
Taylor's Theorem;
Richardson Extrapolation of an O(h^n)
Algorithm
|
09/22
|
Derivatives: Forward
Difference, Backward Difference, 3-pt
Difference Formula, 5-pt Difference
Formula, 3-pt 2nd Derivative Formula,
(2n+1)-pt First Derivative Expansion,
(2n+1)-pt Second Derivative Expansion;
Integrals: Newton-Cotes Method
|
09/24
|
Trapezoidal Rule, Error
Term of Trapazoidal Rule, Rectangular
Rule, Error Term of Rectangular Rule
General Quadrature: Weighted Sum of
Function Values
|
09/26
|
Assignment
1 Discussion: Loss of Precision with
Floating Point Numbers, Series
Convergence Acceleration using
Richardson Extrapolation
Error Analysis and Stepsize Choice
|
09/29
|
Simpson's Rule, Change of
Variables to Improve Convergence,
Orthogonal Polynomials and Weight
Functions: Legendre, Laguerre, Hermite,
Chebyshev
|
10/01
|
Theory of Gauss-Legendre
Integration: Quadrature Points and
Weights.Supplementary
Notes on Romberg Integration
|
10/14
|
Supplementary
Notes on RK4 with Adaptive Stepsize
|
10/15
|
Example Code:
1D
Anharmonic Oscillator RK4 Fixed
(Python)
1D
Anharmonic Oscillator RK4 Adaptive
(Python)
|
10/20
|
Midterm Quiz! 11:00 - 11:50
AM
List of
Topics Covered in Quiz
|
10/30
|
Pendulum
with Leapfrog (Python)
|
11/16
|
Example Code:
Poisson
Equation by Jacobi (Python)
|
|
