Assignment # 1

AMS 147

By Eric Yu

1) “Quadratic equation x^2+b*x+c = 0 has two roots. They are given by

r1 = (-b+sqrt(b^2-4*c))/2 and r2 = (-b-sqrt(b^2-4*c))/2.

Fix the value of c at c=1, plot r1 and r2 as functions of b for b in [2,3]. Plot two curves in

one figure. Use about 100 points to represent each curve.”

a. I simply set the value of c to 1. Set boundary for b and used about 100 points from

between 2, 3 for the curve. I then set r1 and r2 to its function and then plotted

them onto one figure.

b. c. The first curve (r1) slowly reached its peak value, while r2 quickly reached and

continued reaching the peak value. Since r2 is both –b and –square rooted, then it

was faster reaching its peak value than compared with r1.

2) “Plot the surface f(x,y)=sin(x^2+y^2)*exp(-sqrt(x^2+y^2)) for x in [-3,3] and y in [-3,3].

Use about 30 points in each dimension to represent the surface.”

a. I referred to the given codes we were to look at and studied them. On one of the

codes, it plotted a 3D plot similar to this problem. So I just modified the code and

inserted mine plotted it.

b. c. At first I didn’t know if this is the right graph because I had used it with wolfram

alpha to check it. Wolfram had a different graph, but I tried tweaking it but it still

came out with the same graph. The graph had 3 different axis: x,y, and f. The

various colors depict the depth of the graph and regions.

3) “Write a Matlab code to read in data from "data1.txt"

(in http://www.cse.ucsc.edu/~hongwang/Codes/Read_data) and plot the data. Plot the

fitting function f(x)=exp(-c*x)*cos(2*x) along with the data. Adjust the value of "c" to fit

the data. Use linear scales for both the X- and Y- axes.”

a. For this problem, I understood that we needed to load a file within the folder and

use that data to plot it. So I modified the other given code and used the write code

to load data1.txt. To graph and plot, it was as the same before, but this time, there

was also another function also implementing the data1.txt. I looked at the other

code and found out how to do it.

b. c. I wasn’t sure if I had done it right, but I managed to have 2 plotted data so I was

generally pleased with what I have. It was pretty difficult as I didn’t understand

the question at first.

Appendix – Codes

1) Problem 1 Codes

% Problem 1 % Quadratic equation x^2+b*x+c = 0 has two roots. They are given by %r1 = (-b+sqrt(b^2-4*c))/2 and r2 = (-b-sqrt(b^2-4*c))/2. %Fix the value of c at c=1, plot r1 and r2 as functions of b for b in %[2,3]. %Plot two curves in one figure. Use about 100 points to represent each %curve.

%by Eric Yu % clear all; clc; %

c = 1;

dx = .001;

b = [2 : dx : 3];

r1 = (-b + sqrt(b.^2-4*c))/2;

r2 = (-b - sqrt(b.^2-4*c))/2;

plot(b, r1, b, r2);

2) Problem 2 Codes

% Problem 2 %Plot the surface f(x,y)=sin(x^2+y^2)*exp(-sqrt(x^2+y^2)) for x in [-3,3] %and y in [-3,3]. Use about 30 points in each dimension to represent %the surface. % % %by Eric Yu %

clear all; clc; %

m=31; n=31; dx=6/(n-1); dy=6/(m-1); x1=[-3:dx:3]; y1=[-3:dy:3];

[x,y]=meshgrid(x1,y1);

f = sin(x.^2+y.^2)*exp(-sqrt(x.^2+y.^2));

h=surf(x,y,f);

3) Problem 3 Codes

%Problem 3 % %Write a Matlab code to read in data from "data1.txt" %and plot the data. Plot the fitting function f(x)=exp(-c*x)*cos(2*x) %along with the data. Adjust the value of "c" to fit the data. %Use linear scales for both the X- and Y- axes. % % %by Eric Yu %

clear figure(1) clf reset axes('position',[0.15,0.13,0.75,0.75])

load -ascii data1.txt x = data1(:,1); y = data1(:,2); x1 = [0:.2:10]; c = 0.03; f =exp(-c*x1).*cos(2*x1);

semilogy(x,y,'b-s','markerfacecolor','b') hold on semilogy (x,f, 'b-s','markerfacecolor','b') set(gca,'fontsize',10) axis([0,11,-1,2]) set(gca,'xtick',[0:.2:11]) set(gca,'ytick',[0:.5:2])