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Office:  521 Snow Hall
Email:  jvhart@ku.edu
Phone:  785-864-5186
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Math 596: Math in Biomedical Research, Fall 2016

Math 596 students should go to the Blackboard page for this course.  You can download course materials and submit assignments there.

Fall 2017, Math 596 Syllabus

Fall 2017, Math 596 Schedule

Math 596 Course Summary

1
. Time-frequency analysis of music using short-time Fourier analysis

Supplementary files:    Two piano notes                                                                   Spectrogram, .wav

Happy Birthday Song                                                           Spectrogram, .wav
Für Elise, Ludwig van Beethoven:                                        Spectrogram, .wav
The Entertainer, Scott Joplin:                                               Spectrogram, .wav

Moonlight Sonata, Ludwig van Beethoven:                          Spectrogram, .wav
Flight of the Valkyries, Wilhelm Richard Wagner:                 Spectrogram, .wav

2. Stochastic SIR models for inhomogeneous populations

Supplementary files:    SIR demonstration models
beta=gamma=1, r=.1, uniform Lambda:                            Lambda 1, SIR plot 1
beta=gamma=1, r=.1, .75 random Lambda:                      Lambda 2, SIR plot 2
beta=gamma=1, r=.1, .2 random Lambda:                        Lambda 3, SIR plot 3
beta=gamma=1, r=.1, .01 random Lambda:                      Lambda 4, SIR plot 4

Three neighbor graph demonstration
beta=gamma=1, r=.1, 1 initially infected:                           Lambda 1, SIR plot 1, SIR video 1
beta=gamma=1, r=.1, 1 initially infected:                           Lambda 2, SIR plot 2, SIR video 2
beta=gamma=1, r=.1, 4 initially infected:                           Lambda 3, SIR plot 3, SIR video 3

Continental United States map and Lambda selection
N=500: Map selection,
Lambda

Continental United States SIR model
beta=gamma=1, r=.1, NE initially infected:
SIR plot 1, SIR video 1
beta=2, gamma=3, r=.25, NE initially infected:                  SIR plot 2
, SIR video 2
beta=gamma=1, r=.1, 1 region initially infected:
SIR plot 3
, SIR video 3
beta=1, gamma=5, r=.2, 3 regions initially infected:          SIR plot 4, SIR video 4

Continental United States SIS model

beta=1, gamma=10, r=.3, 1 initially infected:                     SIS plot 1, SIS video 1

World map and Lambda selection
N=750: Map selection, Lambda

World SIR model
beta=gamma=1, r=.2, mainland US initially infected:        SIR plot 1, SIR video 1
beta=2, gamma=1, r=.3, mainland US initially infected:    SIR plot 2, SIR video 2

World SIS model
beta=1, gamma=2, r=.25, mainland US initially infected:  SIS plot 1, SIS video 1

3. Artificial Neural Networks

Supplementary files:   Multi-Layer ANN Binary Classification Examples:

Example 1: Decision Contour, Decision Shaded, 3D Plot, Squared Error
Example 2: Decision Contour, Decision Shaded, 3D Plot, Squared Error
Example 3: Decision Contour, Decision Shaded, 3D Plot, Squared Error

Multi-Layer ANN Four Group Classification via Binary Classifiers Example:
Example: Decision Contour, Binary Decisions Shaded, 3D Plot, Squared Error

Multi-Layer ANN Function Approximation Example:
Example: Approximation of f(x,y)=(sin(x)cos(xy)+sin(2y))/2 on [-3,3]x[-3,3], Function Plot, Samples, ANN Approximation, Squared Error

4.  ODE Models of Pendulums

Supplementary files:   Single Pendulums:

Example 1: Video, Angle Plot, Angular Velocity Plot
Example 2: Video, Angle Plot, Angular Velocity Plot

Double Pendulums:

Example 1: Video, Video with Plots
Example 2: Video, Video with Plots
Example 3: Video, Video with Plots

Last Updated: 3/21/2017