WORKSHEET #4: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
Two computer labs ago you wrote computer code that implemented Eulers Method
yi+1 = yi + hf (xi , yi ),
i = 0, 1, 2, . . .
for appro
WORKSHEET #12: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
Solving Linear Systems Using MATLAB
During the past several labs, we have studied the predator-prey model for the interaction of
tw
WORKSHEET #13: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
Using MATLAB to solve various ODEs.
In this our nal lab, we are going to use, exclusively, MATLABs built in ODE solvers to
solve a
WORKSHEET #10: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
Solving Linear Systems Using MATLAB
Last time we computed the eigenvalues and eigenvectors of the 2 2 matrices below using
MATLAB.
WORKSHEET #10: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
Eigenvalues and Eigenvectors of a Matrix Using MATLAB
Computing eigenvalues and eigenvectors of a matrix using MATLAB is quite stra
Math 311-QUIZ 7
NAME:
Show all work to receive partial credit!
1. Find the solution of the initial value problem
y y y +y =0
y(0) = 0, y (0) = 1, y (0) = 0,
given that the characteristic equation ( 1)
Math 311-QUIZ 10
NAME:
Show all work to receive partial credit!
1. Find the eigenvalues and eigenvectors of the matrix
A=
4 13
2 6
(1)
2. Verify that
(t) =
e4t
1 4t
e
2
et
1 t
e
3
is a fundamental mat
WORKSHEET #1: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
Course Goal: To be introduced to and to gain a basic understanding of numerical ODEs.
Worksheet Goal: Today we will spend some time
Math 311-QUIZ 11
NAME:
Choose one of the two problems below as your quiz problem. The other
problem will then be viewed as extra credit.
1. Use the method of determinants to nd the solution of the lin
Math 311-QUIZ 9
NAME:
Show all work to receive partial credit!
1. Consider the matrix
1 1 1
A = 1 2 2
1 4 4
(a) Show that A is invertible by showing that det(A) = 0
(b) Use Gaussian elimination to nd
Math 311-QUIZ 8
NAME:
Show all work to receive partial credit!
1. Write y y 4y + 4y = 0 as a system of rst order equations.
2. Suppose that the current I of an RLC circuit is governed by the ODE
I + 4
Math 311-QUIZ 6
NAME:
Show all work to receive partial credit!
1. If y1 is a solution of
y + a(x)y + b(x)y = 0,
a second solution is given by
y2 (x) = y1 (x)
e a(x)dx
dx.
y1 (x)2
(1)
Given that y1 (x)
Math 311-QUIZ 3
NAME:
Show all work to receive partial credit!
1. Use separation of variables to nd the solution of the IVP
dy
= y(1 cos x),
dx
y(0) = 1.
2. Use the method of integration factors to so
Math 311-QUIZ 1
NAME:
Show all work to receive partial credit!
1. A ball is thrown upward with an initial velocity v0 = 7.7 meters per second from the
top of a building h0 = 56 meters high. Assume tha
Math 311-QUIZ 4
NAME:
Show all work to receive partial credit!
1. Consider the equation
y cos(xy)dx + x cos(xy)dy = 0
(a) Verify that (1) is an exact dierential equation.
(b) Solve (1).
(1)
2. Conside
Math 311-QUIZ 2
NAME:
Show all work to receive partial credit!
1. Consider the dierential equation
x2 y 5xy + 9y = 0.
(a) What is the order of (1)?
(b) Show that y(x) = 2x3 ln x is a solution of (1) f
WORKSHEET #6: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
PROBLEM 1: Use the taylor2.m from the web-page to solve the IVP
y = cos x sin y + x2 ,
y(1) = 3.
(1)
Use h = 0.1 and nd an approxima
WORKSHEET #5: MATH 317
ORDINARY DIFFERENTIAL EQUATIONS COMPUTER LAB
PROBLEM 1: Use the Eulers method code from the web-page to solve the IVP
y = cos x sin y + x2 ,
y(1) = 3.
(1)
Use h = 0.1 and nd an
Math 311 Fall 2012
Test 1 (100 points)
problem
1
2
3
4
5
total
points
30
15
15
20
20
100
Name:
score
1. (30 pts) Solution Techniques
a) One of the following is an exact ODE, the other is not. Determin
Math 311-EXAM 2 REVIEW
Place: The usual.
Time and Date: 9:10-10am, 11-09-05.
Sections That Will Be Covered:
1. The sections that we covered in Chapter 3 were 3.2-3.8. The main topics are reduction
of
Math 311-Final Exam
Place: The usual; Time and Date: 8:-10am, Thursday December 15, 2005.
Cheat Sheet: You can have one side of an 8 1 11 sheet of paper lled with formulas
2
for part I. If you are als
Math 311-EXAM 1 REVIEW
Place: The usual.
Time and Date: 9:10-10am, 9-28-05.
Sections That Will Be Covered:
1. The sections that we covered in Chapter 1 were 1.1, 1.2, 1.3, and 1.4. Note that no
proble
Math 311-EXAM 1, Fall 04
NAME:
Show all work to receive partial credit!
1. Consider the dierential equation
dy
= x y,
dx
(a) Find the function y that solves (1).
y(1) = 2.
(1)
(b) What is y(2) in deci