CPS 111
Computational Modeling for the Sciences
Spring 2007

CPS 111 Home

 Syllabus

It is hard to commit to a specific syllabus for a course that is being taught for the first time. Because of this, the outline below is to be viewed as a plan rather than a contract. In particular, the number of lectures devoted to each topic is very much tentative. References to the textbook (see the readings and software page) are given when appropriate, and additional notes will be handed out as needed.

  • Introduction and motivation (1 lecture; Chapter 0)

    • Mathematical versus computational modeling

    • Examples: differences and commonalities

    • The modeling process

    • Expectations from this course

  • A selection of modeling formalisms

    • A first set of examples: scalar, discrete recurrences (3 lectures; Chapter 1)

      • Stationary, first-order scalar recurrences

      • Fixed points and stability

      • Nonstationary, first-order scalar recurrences

      • Systems of scalar recurrences

    • Linear, Discrete Dynamic Systems (LDDS; 3 lectures; Sections 3.1-3.7)

      • Linearity

      • Matrix algebra

      • Definition of LDDS

      • Eigenvalues and eigenvectors

      • Asymptotic analysis

      • The 2x2 LDDS

    • Randomness (4 lectures; Sections 2.1-2.3 and 3.8-3-10)

      • Motivation: modeling uncertainties

      • Basics of probability

      • Brownian motion

      • Markov chains

    • Continuous-time models (1 lecture)

    • Models and systems in general (1 lecture)

      • Functions and maps

      • General definition of a system

      • Dynamic systems

[Midterm Exam About Here]

  • Developing and implementing models

    • Incorporating data (2 lectures; parts of Chapter 4)

    • Validating the model (1 lecture; Section 2.4)

    • Computational considerations (3 lectures)

      • Modeling versus algorithmic errors

      • Conditioning and sensitivity

      • Time scales, discretization, and stiffness

      • Mathematical versus algorithmic stability

  • Using models

    • Analysis of the modeling results (2 lectures)

    • Presenting results (1 lecture)

  • Case studies [Interleaved with previous 2 items] (5 lectures)

    • [Tentative] I. M. Howat, S. Tulaczyk, P. Rhodes, K. Israel, and M. Snyder. A precipitation-dominated, mid-latitude glacier system: Mount Shasta, California. Climate Dynamics. 28:85-98, 2007.

    • [Tentative] R. M. May, R. M. Anderson, and M. E. Irwin. The Transmission Dynamics of Human Immunodeficiency Virus (HIV). Philosophical Transactions of the Royal Society of London. Series B, 321(1207):565-607, 1988.

    • Other papers can be discussed in alternative to these, depending on student interest. Discussion will focus on the questions listed on the course concept page.