# zombie apocalypse modeling
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy.integrate import odeint
#plt.ion()
P
d
B
G
A
=
=
=
=
=
0
0.0001
0.0095
0.0001
0.0001
#
#
#
#
#
birth rate
natural death perc
# zombie apocalypse modeling
# First we are importing a bunch of libraries such as sys, numpy, matplotlib,
scipy
# Note: different ways of importing
import sys
import numpy as np # Note: since we'll be using this a lot, we import it with a
standard alias
# zombie apocalypse modeling
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy.integrate import odeint
#plt.ion()
P
d
B
G
A
=
=
=
=
=
0
0.0001
0.0095
0.0001
0.0001
#
#
#
#
#
birth rate
natural death perc
# zombie apocalypse modeling
import sys
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
plt.ion()
#
P
d
B
G
A
These are
= 0
= 0.0001
= 0.0095
= 0.0001
= 0.0001
a
#
#
#
#
#
bunch of rates that are part of our model (no
import sys
import matplotlib
matplotlib.use('Agg')
from pylab import savefig
from scipy import linspace, polyval, polyfit, sqrt, stats, randn
from pylab import plot, title, show , legend
#Linear regression example
# This is a very simple example of using
Lectures 3 & 4 & 5 & 6 & 7 & 8 & 9
and beyond
Ordinary Differential Equations
Acknowledgement: Paul Dawkins @ Lamar University
http:/tutorial.math.lamar.edu
Prof. Michel Dupuis CBE Dept. CE 531
1
ODEs
One ODE: First-order linear differential equation
One
Lecture 3 & 4 & 5 & 6
and beyond
Ordinary Differential Equations
Acknowledgement: Paul Dawkins @ Lamar University
http:/tutorial.math.lamar.edu
Prof. Michel Dupuis CBE Dept. CE 531
1
ODEs
One ODE: First-order linear differential equation
One ODE: First-o
Lecture 3 & 4
and beyond
Ordinary Differential Equations
Acknowledgement: Paul Dawkins @ Lamar University
http:/tutorial.math.lamar.edu
Prof. Michel Dupuis CBE Dept. CE 531
1
ODEs
One ODE: First-order linear differential equation
One ODE: First-order non
Lecture 3 & 4
and beyond
Ordinary Differential Equations
Acknowledgement: Paul Dawkins @ Lamar University
http:/tutorial.math.lamar.edu
Prof. Michel Dupuis CBE Dept. CE 531
1
ODEs
One ODE: First-order linear differential equation
One ODE: First-order non
CE 531: Chemical Engineering Mathematics and Computation
Fall 2016
Credits: 3
Registration #:
Time and place for lectures:
21438 (lectures)
NSC 222, Tuesday & Thursday, 5:006:20pm,
8/29/2016 to 12/09/2016.
Instructor:
Prof. Michel Dupuis,
614 Furnas Hall,
Lecture 3 CE531 Fall 2016
Prof. Michel Dupuis CBE Dept. CE 531
Legendre Transforms - 1
Definition
If
Y = Y ( x)
Y is a function of x , i.e.
the Legendre transformation provides a means
to create a new function which is a function of the
Y
=
x
derivative o
Lecture 1
Vector, Calculus, etc
Presentation adapted from Paul Dawkins notes:
Paul Dawkins @ Lamar University - http:/tutorial.lamar.edu
Prof. Michel Dupuis CBE Dept. CE 531
Calculus
Vector arithmetic
Algebra
Trigonometry
Derivatives
Integrals
Vector arit
CE 531 Mathematics and Computation
HOMEWORK #02
assigned Tuesday 9/27, due Tuesday 10/4
1. Determine in terms of an explicit formula y ( x) the solution of the initial value problem
dy
y
+= x
dx 1 + 3 x
=
y (0) 1
Write equation in the standard format:
1
)
CE 531 Mathematics and Computation
HOMEWORK #02
assigned Tuesday 9/27, due Tuesday 10/4
General approach; derivative of a product; integrating factor; integration by parts;
Special equation; substitution;
1. Determine in terms of an explicit formula y ( x
CE 531 Chemical Engineering Mathematics and Computation
Homework #06
Posted Thursday, 10/20; due Thursday, 10/27
For all problems that ask you to write Matlab code, you MUST supply a printout
ON PAPER of your code, including all functions and/or scripts i
CE 531 Mathematics and Computation
HOMEWORK #01
assigned Thursday 9/8, due Thursday 9/15
Example of a good student: turns in homework written neatly in pencil or ink, on clean sheets
of white paper that have been stapled together at the beginning of class
CE 531 Mathematics and Computation
HOMEWORK #03
assigned Tuesday 10/11, due Tuesday 10/18
system of eqs.; eigenvalues & eigenvectors; change of variables for general solution; change of
variables for initial conditions; back-transform to original variable
CE 531 Mathematics and Computation
Example of a good student: turns in homework written neatly in pencil or ink, on clean sheets of white paper
that have been stapled together at the beginning of class. Example of not-so-good student: walks in halfway
thr
CE 531 Mathematics and Computation
HOMEWORK #03
assigned Tuesday 9/20, due Tuesday 9/27
Write MatLab code to integrate the first order differential equation below using
Eulers method over the range : 0 t 1
y + 2y =2 e 4t
y (0) =1
1/ Plot the exact solutio
