There's no sense in being precise when you don't even know what you're talking about
- John von Neumann
The purpose of computing
is insight, not numbers.
- R. W. Hamming
Bit patterns have no inherent
meaning. They my represent instructions, signed integers, unsigned integers,
floating-points numbers, and so on. What is represented depends on the
instruction that operates on the bits in the word. The major difference between
computer numbers and numbers in the real world is that computer numbers have
limited size, hence limited precision.
- John L Hennessey & David A
Patterson
There are right ways and
wrong ways to show data; there are displays that reveal the truth and displays
that do not.
- Edward Tufte
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 and
Scientists, 2nd edition, by Hoffman
See the syllabus for more detailed information.
HISTORY
What
is a Computer?
Old
calculating machines
Algorithm
Horner's Rule
Floating
point arithmetic
Comedy - Tom Lehrer (download wma files)
New Math
Wernher von Braun
The Boehm-Jacopini
theorem
The CORDIC algorithm
MATHEMATICAL TRICKS AND TRIVIA
Solving
the quadratic equation and some history
about this equation.
Mean
Value Theorem
Joseph
Raphson
The
Golden Ratio
Lambert
's W
function
Laplace
Successive Overrelaxation
The
Data Analysis Briefbook
Numerical Recipes