Lecture 0.1: Mechanics, course structure, introduction to modeling
Mechanics and course structure
- course web page: assignments and references in postscript,
outlines of lectures, master schedule, useful links, etc.
- precept: in MECA lab
-
goal of course: learn numerical computing through applications
-
5 assignments: biology, economics, chemistry, physics, computer
science; basic parts + extra credit; may assign discussants, count on
participating!
- term project: proposal (oral and written) at midterm and
report (oral and written) during reading period
-
grading: assignments, class discussion, term project, 5-minute quizzes
-
optional text:
Numerical Recipes in C [PTVF92]. This is really a reference,
and may be useful later in life. It's available in postscript on
web -- but I want you to write relatively short C programs
from scratch. I will also suggest other readings as we go.
-
reference list, reserve books:
- numerical methods: [Act90], [Act96], [Atk85], [Ham89], [Smi85]
- biological applications: [EK88], [Smi89]
(these reserved in biology library)
- physics applications: [GT96], [Tay86]
- digital signal processing, FFT: [Ste96], [Rus92]
- programming prerequisites:
COS 126 is entirely adequate, don't get fancy,
don't try to make programs bullet-proof; we're after the algorithmic
and numerical issues; we'll review in an early precept
- math prerequisites:
MAT 104 is entirely adequate, if you learn some topics
we'll cover along the way; just remember what a derivative and an integral
are, we'll motivate any more advanced math intuitively
Modeling in general
- philosophy of modeling: painting vs. photography
- quantitative vs. qualitative
- reasons: quantitative prediction, qualititative prediction,
development of intuition, theory formation, theory testing
- independent and dependent variables, space, time
-
discrete vs. continuous choices for time, space, dependent variables
Examples
-
discrete-time/discrete-space:
-
spatial epidemic models [Dur95];
-
Sugarscape: growing artificial societies [EA96];
-
cellular automata in general [Wol86], seashells [Mei95], [Hay95]
-
lattice gasses [GT96]
-
difference equations:
-
population growth (linear) [EK88, chapter 1]
-
population genetics (nonlinear) [EK88, chapter 3]
-
digital signal processing, digital filters [Ste96]
-
event-driven simulation:
-
market dynamics [SHC96], [SS98]
-
population genetics
-
network traffic
-
ordinary differential equations:
-
market dynamics
-
epidemics [EK88, Sect. 6.6], [KS92, Chapt. 24];
-
seashells [Mei95], [Hay95]
-
insulin-glucose regulation [EK88, p. 147ff];
-
predator-prey systems [EK88, p. 218ff]
-
partial differential equations:
-
heat diffusion; population dispersal [EK88, p. 437ff];
-
wave motion [Tay86]
-
spread of genes in a population [EK88, p. 452ff], [Fis37]
-
combinatorial: (and hence not ``numerical'')
-
scheduling problems
-
traveling salesman problem
master reference list