BME MATH METHODS
PROJECT 1
Salvatore DAcunto
Creating Data
The first step was to generate some arbitrary data.
A sine wave was chosen
Amplitude = 3
Frequency = 2 Hz
Total Time = 1 s
Sine Wave
Adding Noise
The next step was to add random noise to the

5.1.13
They are called saddle points because according to Wikipedia: The name derives
from the fact that the prototypical example in two dimensions is a surface that
curves up in one direction, and curves down in a different direction, resembling a

HW 1.6
Salvatore DAcunto
Vector field in opposite direction as image in handout for some reason.
Sorry I was traveling for work this week and did not have
scanner or computer paper. If it is unclear I can resend
Saturday morning or whenever you review. T

HW 5: HIGHER ORDER
LINEAR ODES
Salvatore Dcunto
Models
Two models were created.
One model was created plotting the equation against a
vector of w/w1.
At the suggestion of a classmate (Nicole) the plot was
also made symbolically.
Strangely these graphs

1) Velocity vs Position for falling chain. Sliders added to vary g and yi. See code
in Attachment 1.
2) Used Matlab dsolve to solve differential equation for the change in height in
equation 1. This needed to be subtracted from the initial height i

5/6
Module 1.3
Problem 2.6.11
% y' = 2*cos(x)*y, y(0)=1
clear all
clc
close all
h1=0.25;
x=0:h1:10;
y=zeros(1,length(x);
y(1)=1;
% Euler h=0.25
for i = 1:length(x)-1
y(i+1)=y(i)+h1*(2*cos(x(i)*y(i);
end
figure(1)
plot(x,y)
hold on
% RK4 h=0.25
for i

5.5/8
X -1
#25? -1
What time T? -0.5
close all
clc
% Varying M
t=0:0.01:15;
k1=1;
k2=1;
M = 1:1:10;
figure(1)
for p=1:length(M)
A=(k1./(k1+k2).*M(p).*(1-exp(-(k1+k2).*t);
plot(t,A)
hold on
end
title('Varying M')
xlabel('t')
ylabel('A(t)')
% Varying k1
t=0