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 4:00-7:00 T R

EMAIL:                       tsoukias@fiu.edu

 

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%

 

 

 

 

 

 

 

 

 

 

 

 

 

TENTATIVE COURSE OUTLINE

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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                                                                                           Ch.7  Strogatz

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