by evaluating the perimeter of a regular poligon.
.
by evaluating the
perimeter of a regular poligon."
using MC method; evaluation of
integrals using MC method.
| Week | Lecture No. | Date | Chapter/Exam | Homework | |
|---|---|---|---|---|---|
| 1 | - | Mon, Aug 29 | in the aftermath of
hurricane Irene classes are canceled
|
||
| 1 | Wed, Aug 31 | Introduction to computational
physics; course logistics; Correct programs - wrong results I:
calculate by evaluating the perimeter of a regular poligon.
|
|||
| 2 | Fri, Sep 2 | Numerical integration; rectangle,
trapezoid, Simpson's rules; Newton-Cotes formulas
|
|||
| 2 | - | Mon, Sep 5 | Labor Day - No classes | ||
| 3 | Wed, Sep 7 | Programming languages; The choice of C as the
programming language for the course; Adaptive integration.
|
HW1 | ||
| 4 | Fri, Sep 9 | Correct programs - wrong results
II: use recurrence to compute a family of integrals.
|
|||
| 3 | 5 | Mon, Sep 12 | Boundary value problem for ODE;
Correct programs - wrong results III: Euler method; Kahan summation algorithm. |
||
| 6 | Wed, Sep 14 | Computer representation of floating-point numbers.
Machine .
|
|||
| - | Fri, Sep 16 | No class - to be
rescheduled. (Rescheduled for Oct 3)
|
|||
| 4 | 7 | Mon, Sep 19 | Analysis of "Correct programs - wrong results II:
use recurrence to compute a family of integrals."
|
HW2 | |
| 8 | Wed, Sep 21 | Analysis of "Correct programs - wrong results I: calculate by evaluating the
perimeter of a regular poligon."
|
|||
| 9 | Fri, Sep 23 | Analysis of "Correct programs - wrong results III:
Euler method'' and Kahan summation algorithm.
|
|||
| 5 | - | Mon, Sep 26 | No class - to be rescheduled
(Rescheduled for Oct 31)
|
||
| - | Wed, Sep 28 | No class - to be rescheduled
|
|||
| 10 | Fri, Sep 30 | Fibonacci numbers; recurrence
relations vs. analytical solution. |
|||
| 6 | 11 | Mon, Oct 3 | Midterm I take-home; Monte
Carlo method I; calculate using MC method; evaluation of
integrals using MC method.
|
HW3 | |
| 12 | Wed, Oct 5 | Monte Carlo method II; evaluation of
multidimensional integrals using MC method.
|
|||
| 13 | Fri, Oct 7 | Random number generators (RNG):
requirements; empirical tests; linear congruental
generators.
|
|||
| 7 | 14 | Mon, Oct 10 | Lagged Fibonacci
RNGs. Introduction to GNU scientific library (GSL).
|
HW4 | |
| 15 | Wed, Oct 12 | Generation of non-uniform
random numbers.
|
|||
| 16 | Fri, Oct 14 | Programming with GSL. Example: volume of
n-dimensional sphere using Monte Carlo integration.
|
|||
| 8 | 17 | Mon, Oct 17 | Solving ODE with GSL:
van der Pol oscillator.
|
HW5 | |
| 18 | Wed, Oct 19 | Solving ODE with GSL: 1D flame
propagation. Stiff differential equations.
|
|||
| 19 | Fri, Oct 21 | Restricted three body problem;
``Planet Dancing With a Pair of Stars''.
|
|||
| 9 | 20 | Mon, Oct 24 | Restricted three body
problem II.
|
||
| 21 | Wed, Oct 26 | Underwater sound propagation
and geometric accoustics; SOFAR channel.
|
|||
| 22 | Fri, Oct 28 | Boundary value problem for ODE.
Shooting method.
|
|||
| 10 | 23 | Mon, Oct 31 | Midterm II take-home.
1D root-finding; bisection; Newton method.
|
||
| 24 | Wed, Nov 2 | 1D minimization.
|
|||
| 25 | Fri, Nov 4 | Spinodal
decomposition
|
|||
| 11 | 26 | Mon, Nov 7 | Spinodal decomposition II:
Cahn-Hilliard equation.
|
HW6 | |
| 27 | Wed, Nov 9 | Numerical solution of partial differential
equations (PDEs).
|
|||
| 28 | Fri, Nov 11 | Fast Fourier Transform (FFT);
Using FFT for PDEs solution; Explicit and Implicit
discretization.
|
|||
| 12 | 29 | Mon, Nov 14 | Numerical solution of
Schrodinger equation I: Numerov algorithm. |
||
| 30 | Wed, Nov 16 | Numerical solution of
Schrodinger equation II. |
HW7 | ||
| 31 | Fri, Nov 18 | Converting differential
equations to dimensionless form.
|
|||
| 13 | Mon, Nov 21 | Thanksgiving recess | |||
| Wed, Nov 23 | Thanksgiving recess | ||||
| Fri, Nov 25 | Thanksgiving recess | ||||
| 14 | 32 | Mon, Nov 28 | Numerical solution of
Schrodinger equation III.
|
||
| 33 | Wed, Nov 30 | Algebraic eigenvalue problem. LAPACK -
Linear Algebra PACKage. Mixed language programming.
|
|||
| 34 | Fri, Dec 2 | Generalized
eigenvalue problem
|
|||
| 15 | 35 | Mon, Dec 4 | Parallel programming; MPI | ||
| 36 | Wed, Dec 7 | Parallel programming; OpenMP | |||
| 37 | Fri, Dec 9 | GPU programming; CUDA | |||
| 16 | Mon, Dec 12 | FINAL EXAM |