- ECE/Chemical Engineerring/Math 777 --- Nonlinear Dynamics, Bifurcations and Chaos
- Mathematics 415 --- Mathematics for Dynamical Modeling
- Physics 505 --- Chaos and Time-Series Analysis
- Statistics 840 --- Multivariate Function Estimation for Observational Data, with Emphasis on Splines

**Electrical and Computer Engineering, Chemical Engineering and Mathematics 777 --- Nonlinear Dynamics, Bifurcations and Chaos, Prof. Ian Dobson**- Prereq: Consent of instructor; a solid background in ordinary
differential equations and linear algebra is a minimum.
*4:00-5:15 TR*in*3444 Engineering Hall*, 3 creditsAdvances in the theory of dynamical systems are penetrating many areas of science, engineering and mathematics. The qualitative aspects of this theory give a powerful way to grasp and visualise how dynamical systems work. Chaotic and bifurcation phenomena are observed in many applications and 777 should be of interest to students in

**engineering, physical sciences and mathematics.**777 aims to introduce graduate students to

- The powerful geometric view of the qualitative theory of dynamical systems.
- The parts of bifurcation theory most useful in applications.
- The mind-boggling chaos to be found in apparently simple systems.

For more details, including a syllabus and reading list, see the 777 home page.

**Math 415 --- Mathematics for Dynamical Modeling, Prof. Robert Turner**- Prereq: Calculus and some knowledge of matrix theory
*1:20pm, MWF*in*b105 Van Vleck*The course will develop mathematical techniques including difference equations, ordinary differential equations, and partial differential equations, to study models arising in the life and social sciences, with emphasis on biological applications.

Topics: linear difference equations and population growth, nonlinear difference equations, stability, bifurcation, host-parisitoid systems, scaling and dimensional analysis.

Review of ordinary differential equations, phase plane analysis, local and global behavior, drug delivery, predator-prey systems, disease propagation, Michaelis-Menton kinetics, sigmoidal kinetics and other models of molecular events, nerve conduction, action potentials, Fitzhugh-Nagumo approximation of Hodgkin- Huxley equations, oscillators in chemical systems.

As time permits and depending on class background: introduction to partial differential equations, diffusion, and convection, traveling waves, the spread of genes, substance transport in axons.

The course will introduce the setting for each type of model, so there is no prerequisite beyond the mathematical one.

**Physics 505 --- Chaos and Time-Series Analysis, Prof. Clint Sprott**- Prereq: Consent of instructor (calculus and programming
experience useful)
*3:30-5:10 Tuesdays*in*1313 Sterling Hall*, 2 creditsThis course is an introduction to the exciting new developments in chaos and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data. Emphasis will be on physical concepts rather than mathematical proofs and derivations. Fifteen, 100-minute lectures as listed below will include demonstrations, computer animations, slides, and videos. Homework will consist of weekly programming assignments, and so access to a computer (any type) and some programming experience (any language) is assumed. The course will be taught at a level accessible to graduate and advanced undergraduate students in all fields of science and engineering. Lecture notes and other material will be posted on the World Wide Web.

For more details, see the Physics 505 homepage.

*Text:*Robert C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Oxford University Press, 1994)*Course Outline:*- Introduction and Overview
- One-Dimensional Maps
- Dynamical Systems Theory
- Chaotic Dissipative Flows
- Iterated Maps
- Strange Attractors
- Stability and Bifurcations
- Hamiltonian Chaos
- Lyapunov Exponents and Entropy
- Nonlinear Prediction and Noise Reduction
- Fractals
- Calculation of Fractal Dimension
- Multifractals
- Non-Attracting Chaotic Sets
- Spatiotemporal Chaos and Complexity

**Statistics 840 --- Multivariate Function Estimation for Observational Data, with Emphasis on Splines, Prof. Grace Wahba**-
*TR 2:30-3:45*in*Computer Sciences and Statistics 1289,*3 credits``This course is about various aspects of curve fitting, surface fitting, and more generally modern multivariate function estimation, given scattered, noisy, direct, and indirect data, with particular emphasis on smoothing spline and related methods. The course is designed to appeal to advanced graduate students in CS, AOS and other physical sciences, engineering, and economics who might find the methods useful in analyzing data as part of their research, as well as graduate students in Statistics and Biostatistics who are interested in the developmental aspects of the methods. Specific mathematical prerequisites beyond advanced calculus are not required, but some mathematical maturity is desireable, since students will be asked to read about Hilbert spaces at the start of the course. A more detailed description of the course, prereqisites and projects (no sit-down exams) can be found here.'' --- Prof. Wahba.