Numeric Modeling of Physics & Biological Systems
Fall 2015
Catalog Data: 

ECE 411 -- Numeric Modeling of Physics & Biological Systems (3 units) 

Description: This course 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; geo-thermal 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.

Grading: Regular grades are awarded for this course: A B C D E

ECE 330A

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 and Gerhard Spitz, Wolfgang Loesch, and A.H. Armstrong. Theoretical Physics on the Personal Computer. 2nd ed. Springer. 1990.

Course Learning Outcomes: 

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

  1. Use MATLAB for data manipulation, data plotting, and programming.
  2. Numerically differentiate and integrate functions with several techniques of different accuracy and efficiency.
  3. Transform systems of differential equations and solve them numerically with several techniques of increasing numerical accuracy.
  4. Solve systems of linear equations efficiently.
  5. 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.
  6. Formulate problems or model systems in physics, biology and related disciplines, and solve them numerically or in simulation.
  7. Know and assess the validity, limits, and pitfalls of numerical simulations.
Course Topics: 


  • 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

  • Multi-layer feedforward networks
  • Hopfield attractor networks
  • Associated training algorithms: 
    • simple perceptron learning rule
    • Error-Backpropagation
    • Hebb learning
    • Projection Rule

Method of Successive Over-Relaxation

  • 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
    • geo-thermal power station
Class/Laboratory Schedule: 

Two, 75-minute lectures per week

Relationship to Student Outcomes: 

ECE 411 contributes directly to the following specific Electrical and Computer Engineering Student Outcomes of the ECE department:

  • an ability to apply knowledge of mathematics, science and engineering (High)
  • an ability to design and conduct experiments, as well as to analyze and interpret data (High)
  • an 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)
  • an ability to function on multidisciplinary teams (Low)
  • an ability to identify, formulate and solve engineering problems (Medium)
  • an understanding of professional and ethical responsibility (Medium)
  • a recognition of the need for, and an ability to engage in life-long learning (Low)
  • an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice (High)
Prepared by: 
Dr. Wolfgang Fink
Prepared Date: 

University of Arizona College of Engineering