BME 301: Numerical Methods in BME
Fall 2015 Syllabus
When:
Where:
Instructor:
Instructor Office:
Office Hours:
E-mail:
Phone:
Texts:
M, W 10:30 11:20 pm
PSY102
Dr. Xiao Wang
ISTB4 265
Mondays 4 -5pm, or by appointments
[email protected]
(480) 727 - 8696
Nu
Nonlinear Dynamics
BME 301
Xiao Wang
Oct 28, 2015
Simplified Model
Method of Nullcline
Switching Response
Experiment
Default low LacI/GFP
ATc induction high LacI/GFP
Model
Model Insights: Bistability and Hysteresis
Same dose, different steady state
va
Nonlinear Dynamics
BME 301
Xiao Wang
Oct 28, 2015
Simplified Model
Method of Nullcline
Switching Response
Experiment
Default low LacI/GFP
ATc induction high LacI/GFP
Model
Model Insights: Bistability and Hysteresis
Same dose, different steady state
va
Numerical methods for ODE
BME 301
Oct 14, 2015
Announcements
Oct 19 review for midterm
All previous homework
Oct 21 midterm
Open book, open notes
No computer
All paper pencil problems
Oct 19 ABET vi
Dynamic systems
BME 301
Todays objec8ve
Get the full picture of why we study nite
dierence
Review of calculus for introduc8on of nite
dierence methods
Deriva8ve
df (x)
f (x) f (x0 )
= f '(x) = lim
xx 0
dx x0
x x0
h = x
Integra(on
BME 301
Oct 07, 2015
Todays objec(ve
Numerical Integra(on
Problem
xn
I=
xn
f (x)dx = y dx
x0
x0
Taylor series again
(x x0 )2
(x x0 )k (k )
f (x) = f (x0 ) + (x x0 ) f '(x0 ) +
f "(x0 ) +. +
f (x0 )
2
(k)!
(x x0 )k+1 (k+1)
Nonlinear Equations
Todays Objective
Understand nonlinear systems
Understand the general form nonlinear
systems
Examples of nonlinear systems
methods
Nonlinear Equations
Any equation that include:
log(x)
Square root(x)
Sin(x)
Et
Linear Systems
Todays objective
Understand what is linear system
Understand Gaussian Elimination
Types of problems
Steady state
Linear
nonlinear
Dynamic behavior
Example
Biomechanic
Image processing
Metabolic engineering
C2H5OH +
Todays objective
Get more comfortable with Matlab
Understand source and consequence of
numerical error
Matlab
for
while
if
Use function
Debug
Matrix Multiplication
Numerical Analysis and Error
Numerical analysis mathematical th
Partial Differential Equation
BME 301 : Numerical
Methods in BME (Fall 2015)
Ordinary Differential Equation
A differential equation with one independent variable
Example : f(x) derivatives with respect to x
Partial Differential Equation
A differen