ECE411

Numeric Modeling of Physics & Biological Systems
Fall 2012
Designation: 
Technical Elective for ECE
Catalog Data: 

3 units.  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. As a result, students will be prepared to formulate problems or model systems in physics, biology, and related disciplines, and to solve them numerically or in simulation.

 

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

Offered: Fall Semester

Prerequisite(s): 
ECE 330A
Textbook(s): 

Numeric Modeling of Physics & Biological Systems, W Fink, Class Notes

Numerical Recipes in C: The Art of Scientific Computing, WH Press, BP Flannery, SA Teukolsky, et al., Cambridge University Press, Cambridge, NY

MATLAB for Engineers, H Moore, 3rd Edition, Pearson 

Theoretical Physics on the Personal Computer, EW Schmid, G Spitz, W Loesch, 2nd Edition, Springer, ISBN-10: 3540522433, ISBN-13: 978-3540522430

Neural Networks: An Introduction, B Mueller, J Reinhardt, Berlin: Springer

Introduction to the Theory of Neural Computation (Lecture Notes vol. 1), J Hertz, A Krogh, RG Palmer, Reading, MA: Addison-Wesley

Genetic Algorithms in Search, Optimization and Machine Learning, DE Goldberg, Addison-Wesley, 1989

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 (411: basic; 511: advanced).
    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.
  2. Solve systems of linear equations efficiently.
  3. 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.
  4. Formulate problems or model systems in physics, biology, and related disciplines, and solve them numerically or in simulation.
  5. Know and assess the validity, limits, and pitfalls of numerical simulations.
Course Topics: 
  • Basic (411)/advanced (511) working knowledge of MATLAB.
  • Numerical differentiation: Two-Point formula and 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, and Runge-Kutta Method.
  • Artificial Neural Networks: multi-layer feedforward networks, Hopfield attractor networks, and associated training algorithms (simple perceptron learning rule, Error-Backpropagation, Hebb learning, Projection Rule, etc.).
  • Method of Successive Over-Relaxation for solving systems of linear equations: discretization of second order differential equations and Liebmann Method.
  • Fourier Heat Conduction equation and Fourier method for solving partial differential equations.
  • Using the above techniques, modeling and numeric simulation of: (1) harmonic, anharmonic, and coupled oscillators; (2) artificial neural networks; (3) electric lenses; (4) geo-thermal power station.
Class/Laboratory Schedule: 

Class Schedule: Two 75-minute lectures.

Approximately ten homework sets, including MATLAB exercises (411: basic; 511: advanced), during semester. Two midterm and one final written examinations.

Relationship to Student Outcomes: 

(a) an ability to apply knowledge of mathematics, science, and engineering (H)
(b) an ability to design and conduct experiments, as well as to analyze and interpret data (M)
(d) an ability to function on multidisciplinary teams (L)
(e) an ability to identify, formulate, and solve engineering problems (H)
(f) an understanding of professional and ethical responsibility (M)
(i) a recognition of the need for, and an ability to engage in life-long learning (L)
(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice (H).

Prepared by: 
Dr. Wolfgang Fink
Prepared Date: 
1/01/13

University of Arizona College of Engineering