MTH 371 Homework 5
Yu Guan
May 7, 2016
1
Problem 1
We know that p(x) = x4 x3 + x2 x + 1 so q(x) = p(x) + (x + 2)(x + 1)x(x
1)(x 2) + c. The only difference between p(x) and q(x) is when x = 3. There
for we plug x = 3 and let q(x) = 30, we get c = 89.
2
P

MTH 371 Homework 6
Yu Guan
March 1, 2016
1
Problem 1
The code for linear spline
Guan/Desktop/Machine Learning/QQ20160301061034.png
Figure 1: code
2
Problem 2
The code for natural cubic spline
1
Guan/Desktop/Machine Learning/QQ20160301061404.png
Figure 2:

MTH 371 Homework 4
Yu Guan
May 5, 2016
1
Problem 1
f (x) = 21 cos(x) is contitnous function from [0, 0.5] to [0, 0.5], by Brouwers fixed
point theorem, that is x = f (x) for some x in [0, 1].
xn+1 = 12 cos(xn ) By operation, we can get solution is x 0.451

MTH 371 Numerical Methods Homework 3
Phuc Pham
Yu Guan
February 16, 2016
1
Problem 1
x3 2x 5 = 0
x0 = 3, tol = 0.1
x0 = 3 + 2 0.1 = 3.2
x = 3.2 f (3.2)/f 0 (3.2)
x 2.45598
2
Problem 2
a. f (1) = 1, f (2) = 6. By the Intermediate Value Theorem, there is a

MTH 371 - Assignment 01
Phuc Pham
Yu Guan
May 7, 2016
1
a.
Problem 1
4
f (x + 2h) = f (x) + 2hf 0 (x) + 2h2 h2 f 00 (x) + h3 f (3) ()
3
4 3 (3)
0
2 2 00
f (x 2h) = f (x) 2hf (x) + 2h h f (x) h f ()
3
4 3 (
0
f (x + 2h) f (x 2h) = 4hf (x) + h [f 3)() + f (

MTH 371 - Project 03: TicTacToe Magic
Phuc Pham
Yu Guan
March 29, 2016
The project of mine is going to win a game which is TicTacToe or Pick15.
The rules of the game is really simple.The game involves two players. You start
by listing the single digit num

MTH 371 - Assignment 08
Phuc Pham
Yu Guan
April 5, 2016
1
a.
Problem 1
R
0
sin(x)dx
n
Trapezoid
Simpson
2
1.5707963268
2.094395102393195
4
1.8961188979
2.004559754984421
8
1.9742316019
2.000269169948388
Table 1: example of table
b.
R2
1
x log(x)dx
n
Trape

MTH 353 Project 1
Yu Guan
February 22, 2016
In this project, I will focus on discussing about the the Whilson-Cowan
Nerual Population Model, which is a typical nerual network algrothim in many
mathematics modeling studys. First of all, let we state the th

MTH 371 - Assignment 01
Kirsten Heikkinen
Phuc Pham
Yu Guan
February 2, 2016
1
Problem 1
1. Make a 1 21 matrix, and the value increses 1 from -10 to 10.
2. Make a 1 101 matrix, and the value increses 0.01 from 0 to 1.
3. Make a 1 21 matrix, and the value