Mechanics and course structure

• web page, assignments and references in postscript
• schedule precept
• goal of course: learn numerical computing through applications, sometimes called scientific computing
• 5 assignments (biology, economics, chemistry, physics, computer science), basic parts + extra credit; will assign discussants, count on participating
• term project: report at midterm and reading period
• grading: assignments, class discussion, term project, 5-minute quizzes
• text: Numerical Recipes in C [PTVF92], really a reference, useful later in life, available in postscript on web -- but I want you to write relatively short C programs from scratch
• reference list, reserve books:
  • numerical methods: [Act90], [Act96], [Atk85], [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 make programs bullet-proof; we're after the algorithmic and numerical issues; we'll review in week 2 precept
• math prerequisites: MAT 104 is entirely adequate, if you learn some topics we'll cover along the way; just remember what a derivative is, we'll motivate any more advanced math intuitively

Modeling in general

• philosophy of modeling: painting vs. photography
• quantitative vs. qualitative
• reasons: prediction, sufficiency, suggestivity
• 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], [SS97]
  • 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