# BME 233 Dynamic Systems in Biology and Medicine (2015-2016)

#### BME 233 Dynamic Systems in Biology and Medicine

**BME 233 Dynamic Systems in Biology and Medicine (Credit Units: 4)** Introduces principles of system theory to analyze biological, biochemical, physiological, and bioengineering systems. Analytical and computational tools are used to model and analyze dynamic systems such as population, neuronal and heart dynamics, biochemical and physiological systems, oxygen diffusion and similar. Graduate students only. (Design units: 0)

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1. Be able to describe the elements of system theory and apply these principles to analyze biomedical, chemical, social and engineering systems

2. Be able to use analytical and computational tools to model and analyze various dynamic systems

Basic understanding of differential equations, complex numbers, infinite sequences and series. Basic knowledge of linear algebra, such as systems of algebraic equations, vectors and matrices. MATLAB or programming language of choice necessary for computer exercises.

- Basic definitions of systems, system variables (inputs, outputs, states, parameters), and models
- Taxonomy of systems and model; Input-output and state-space models
- Linear time-invariant systems; impulse response; convolution; Laplace Transform
- Transfer function; Frequency response; Feedback and Control
- Nonlinear systems
- Equilibrium states, Phase portrait; Isoclines; Periodic orbits
- Stability; Attractors; Linearization
- Poincare-Bendixson Theorem
- Fast-slow systems and singular perturbation theory
- Elementary bifurcation theory

Meets for 3 hours of lecture each week for 10 weeks.

MATLAB or programming language of choice.

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- Homework: 30%
- Midterm(s): 30%
- Final: 40%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 0.0 credit units

Engineering Science: 0.0 credit units

Engineering Design: 0.0 credit units