# ECE 411

## Numeric Modeling of Physics & Biological Systems

### Course Level

### Units

### Prerequisite(s)

### Course Texts

- Fink, Wolfgang.
*Numeric Modeling of Physics & Biological Systems.*Class notes. - Goldberg, David E.
*Genetic Algorithms in Search, Optimization and Machine Learning*. Addison-Wesley Professional, 1989. - Hertz, John, Anders Krogh and Richard Palmer.
*Introduction to the Theory of Neural Computation (Lecture Notes vol. 1)*. Westview Press, 1991. - Moore, Holly.
*Matlab for Engineers*. 4th ed. Pearson, 2014. - Mueller, Berndt, Joachim Reinhardt and Michael Strickland.
*Neural Networks: An Introduction*. 2nd ed. Springer, 2002. - Press, William H., Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery.
*Numerical Recipes: The Art of Scientific Computing*. 3rd ed. Cambridge University Press, 2007. - Schmid, Erich, Gerhard Spitz, Wolfgang Loesch and A.H. Armstrong.
*Theoretical Physics on the Personal Computer*. 2nd ed. Springer, 1990.

### Schedule

### Course Description

Combines themes from mechanics, electromagnetics, thermal physics, and neural networks with an introduction to numerical methods as well as the use of Matlab. Students will become familiar with the underlying theory for a variety of systems in physics and biology (e.g., harmonic, anharmonic and coupled oscillators; electric fields of electric lenses; geothermal power station; and artificial neural networks), derive the necessary mathematical equations describing these systems, learn the necessary numerical methods to solve the underlying equations, and implement the system equations and numerical methods in Matlab to simulate these systems.

### Learning Outcomes

By the end of this course, the student will be able to:

- Use Matlab for data manipulation, data plotting, and programming
- Numerically differentiate and integrate functions with several techniques of different accuracy and efficiency
- Transform systems of differential equations and solve them numerically with several techniques of increasing numerical accuracy
- Solve systems of linear equations efficiently
- Understand the underlying theory for a variety of systems in physics and biology, model these systems by deriving the necessary mathematical equations describing these systems, understand and apply the necessary numerical methods to solve the underlying equations, and program the system equations and numerical methods in Matlab to simulate the systems
- Formulate problems or model systems in physics, biology and related disciplines, and solve them numerically or in simulation
- Know and assess the validity, limits and pitfalls of numerical simulations

### Course Topics

**Matlab**

- Basic working knowledge (411)
- Advanced working knowledge (511)

**Numerical differentiation**

- Two-point formula
- Three-point formula

**Numerical integration**

- Trapezoidal rule
- Simpson rule
- Newton-Cotes integration
- Gauss-Legendre integration

**Transformation of differential equations and solution methods**

- Euler method
- Improved Euler method
- Runge-Kutta method

**Artificial Neural Networks**

- Multilayer feedforward networks
- Hopfield attractor networks
- Associated training algorithms:
- Simple perceptron learning rule
- Error backpropagation
- Hebb learning
- Projection rule

**Method of successive overrelaxation**

- Discretization of second order differential equations
- Liebmann method

**Fourier heat conduction equation and Fourier method**

- Using the above techniques, model and numeric simulation of:
- Harmonic, anharmonic and coupled oscillators
- Artificial neural networks
- Electric lenses
- Geothermal power station

### Relationship to Student Outcomes

ECE 411 contributes directly to the following specific electrical and computer engineering student outcomes of the ECE department:

- Ability to apply knowledge of mathematics, science and engineering (high)
- Ability to design and conduct experiments, as well as to analyze and interpret data (high)
- Ability to design a system, component or process to meet desired needs within realistic constraints, such as economic, environmental, social, political, ethical, health and safety, manufacturability and sustainability (medium)
- Ability to function on multidisciplinary teams (low)
- Ability to identify, formulate and solve engineering problems (medium)
- Understanding of professional and ethical responsibility (medium)
- Recognition of the need for, and an ability to engage in, life-long learning (low)
- Ability to use the techniques, skills and modern engineering tools necessary for engineering practice (high)