BME 6705: Nonlinear Systems in Life Sciences
Fall 2005
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INSTRUCTOR: Nikolaos
Tsoukias
OFFICE: EAS
2674 PHONE: 305 348-7291
Office
Hours
EMAIL:
Textbooks: Required
Nonlinear Dynamics and Chaos, by Steven H. Strogatz
Recommended
Engineer's
Guide to MATLAB, by Edward B. Magrab
Introduction to ODEs by Sherley Ross
Partial
Differential Equations for Scientists and Engineers- Stanley J. Farlow
Class Description:
Concepts and applications of nonlinear
dynamics to life sciences.
Numerical methods and computer modeling for biomedical
applications. The objective of this course is to provide the
mathematical and computational foundation for model development and analysis.
Course Objectives:
By the end of
this course, students should:
1.
Learn
to develop code and apply computational algorithms.
2.
Learn
to use software packages such as Matlab, Femlab, LSODE.
3.
Learn
to research pertinent scientific literature
POINTS
DISTRIBUTION: HW Assignments 25%
Project 25%
Mid
Term Exam 25%
Final
Exam 25%
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Week Topic Reference
1-2 Differential Equations
2-6 Numerical
Methods
-Interpolation
-Integration
-Differentiation
-Optimization/Nonlinear Programming
7-8 Matrix Algebra and solution
of systems of ODEs
9 Mid
Term Exam
9 Stability in one dimension Ch.2
Strogatz
10 Bifurcations in one
dimension Ch.3 Strogatz
11 Two dimensional linear
systems Ch.5 Strogatz
12 Two dimensional non-linear
systems Ch.6 Strogatz
13 Limit Cycle
14 Bifurcations in two
dimensions Ch.8 Strogatz
15 Final Exam
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Grading Scale
95-100 A
90-94.9 A-
86-89.9 B+
82-85.9 B
78-81.9 B-
74-77.9 C+
70-73.9 C
66-69.9 C-
60-65.9 D