This is the one of five required core courses
in the MS
in Space Sciences degree.
We will cover
Numerical
methods for the solution of engineering physics problems; systems of linear
equations, ordinary differential equations including one-dimensional initial
value problems and boundary value problems; partial differential equations (PDEs)
including elliptic, parabolic and hyperbolic PDEs; finite difference method.
Application to problems such as diffusion, transport, remote sensing,
inversion, and plasma waves.
Prerequisites: MA 345 (Differential Equations),
as much mathematics as possible
For undergraduates, it is recommended
that you have taken at least PS 215, 208, 219 (Physics I, II, III), ES
201, 202, 204, 206 (Statics, Dynamics, Solids, Fluids).
Text: Numerical Methods for Engineers, 4th
edition, by Chapra and Canale
See the syllabus for more detailed information.
HISTORY
What
is a Computer?
MATHEMATICAL TRICKS AND TRIVIA
Solving
the quadratic equation and some history
about this equation.
Mean
Value Theorem and Taylor's
Theorem
Joseph
Raphson
The
Golden Ratio
|
|
Tentative
Schedule |
|
|
Week |
Topics |
Parts
in Chapra |
|
1 |
Basics and simple routines |
1 |
|
2-3 |
Root-finding and optimization |
2, 4 |
|
4-6 |
Differentiation and integration |
6 |
|
7-8 |
Solving ODEs |
7 |
|
9-10 |
Linear algebra |
3 |
|
11-12 |
Solving PDEs |
8 |
|
|
Exam schedule |
|
Exam |
Date |
|
1 |
Monday, Sep 29 |
|
2 |
Monday, Oct 27 |
|
3 |
Monday, Nov 24 |
|
Final Presentation |
Mon/Wed , Dec 1/3 |