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i
Arup Guha
12/28/2012
Written for UCF Domjudge Contest
Solution to Arab and North Africa Regional Contest Problem I: Blur
import java.util.*;
public class i cfw_
public static void main(String[] args) cfw_
Scanner stdin = new Scanner(System.in);
COT 4500
Homework 4 Solutions
Section 4.1 #1. Use the forward dierence and backward dierenec formulas to determine each
missing entry in the following tables.
a.
x
0.5
0.6
0.7
f (x)
0.4794
0.5646
0.6442
f (x)
0.852
0.852
0.796
I used the forward dierence
Numerical Calculus Homework #2 (Chapter 2) Solutions
Note: Each of the approximations was calculated by editing the posted code online. Namely, only the necessary functions, f, fprime, etc. were edited as necessary for the specific problem. Section 2.1 4
COT 4500 Section 3.5 Solutions
4. Construct the natural cubic spline for the following data: a. f (0) = 1, f (0.5) = 2.71828 Since we are constructing a natural cubic spline on a single interval, we are dealing with a degenerate case; The linear interpola
COT 4500
Homework 5 Solutions
Section 5.1 #2. Find the solution to each of the following initial value problems.
a. y = ety , 0 t 1, y (0) = 1.
This is a separable equation. We have
dy
et
=y
dt
e
Using what appears to be dodgy notation, but in fact can be
COT 4500
Homework 6 Solutions
Section 6.3 #6. Determine which of the following matrices are nonsingular, and compute the inverse
of these matrices:
a.
1 2 1
2
01
1 4
3
Augmenting this matrix yields
1 2 1 1 0 0
2 0 1 0
01
1 4
3001
We then perform Gaussia
COT 4500 Quiz #4 Solutions
Date: 3/2/2012
1) (25 pts) Use the Trapezoid Rule with n = 4 (4 trapezoids total), to approximate the following
integral:
.
Solution
The evaluation points are x = /2, x = 2/3, x = 5/6, x = and x = 7/6. The corresponding
value of
COT 4500 Quiz #5 Solutions
Date: 3/23/2012
1) (25 pts) Find the solution to the following differential equation with the initial condition
y()=32:
Solution
, multiply through by
, use integrating factor
Integrating factor =
.
, integrate both sides
Pluggi
Numerical Calculus (COT 4500) Final Exam
Date: 4/27/2012
Directions: Please answer each question on your own paper. Show your work. It will be
assumed that you used your calculator for basic calculations.
1) (10 pts) Chapter 1: Rounding Errors
(a) (5 pts)
Numerical Calculus Quiz #2 Grading Criteria
1) 10 points for p0, 10 points for p1, 5 points for explicitly stating the range.
2) p0 and p1 with a divergent calculation (correctly) 20 points
Correct 25 points
Incorrect algebra in changing equation to a fix
Numerical Calculus Quiz #3 Grading Criteria
1) 6 points per term, 1 pt bonus if all are correct, -1 for simplifying and not following directions
2) 2 points each for first row (8 pts total)
3 points each for second row (9 pts total)
4 points each for thir
Numerical Calculus Quiz #4 Grading Criteria
1) 2 pts for evaluating each x-value for plugging into the function (10 pts)
2 pts for each of the coefficients by which to multiply (10 pts, 1,2,2,2,1)
5 pts for the arithmetic of plugging this in, the right h,
COT 4500 Quiz #4 Solutions
Date: 3/2/2012
1) (25 pts) Use the Trapezoid Rule with n = 4 (4 trapezoids total), to approximate the following
integral:
.
Solution
The evaluation points are x = /2, x = 2/3, x = 5/6, x = and x = 7/6. The corresponding
value of
Numerical Calculus Quiz #5 Grading Criteria
1)
Rewriting in form y + f(x)y = g(x)
8 pts
Determining the Integrating Factor 3 pts
Integrating both sides 6 pts
Plugging in the initial conditions and solving for C 8 pts
Give a maximum of 10 points if the in
COT 4500 Quiz #5 Solutions
Date: 3/23/2012
1) (25 pts) Find the solution to the following differential equation with the initial condition
y()=32:
Solution
, multiply through by
, use integrating factor
Integrating factor =
.
, integrate both sides
Pluggi
Numerical Calculus Quiz #6 Grading Criteria
1)
10 pts Upper Triangular Form
5 pts Solving for z
5 pts Solving for y
5 pts Solving for x
2)
5 pts Putting a 0 in row 2, 3 column 1
5 pts Switching rows
5 pts Solving for z
5 pts Solving for y
5 pts Solving fo