MATH 215/255
Fall 2014
Assignment 1
1.1, 1.2, 1.3
Solutions to selected exercises can be found in [Lebl], starting from page 303.
1.1.3: Solve
dy
= sin(5x), for y(0) = 2.
dx
Answer.
y=
Z
Using y(0) = 2, we have 2 =
1
5
+ c and hence c =
Answer.
11
5 .
(1
MATH 215/255
Fall 2014
Assignment 8
due 11/19
3.4, 3.7, 3.5, 3.9
Solutions to selected exercises can be found in [Lebl], starting from page 303.
3.4.6: a) Find the general solution of x0 = 2x1 , x0 = 3x2 using the eigenvalue method
1
2
(rst write the sys
HOMEWORK N0.4 SOLUTIONS: MATH 215/255
1. Find the solution to the initial value problems:
(i) y + 4y + 5y = 0 with y (0) = 1, y (0) = 0.
(ii) y + 2y + 2y = 0 with y (/4) = 2, y (/4) = 2.
Solution:
(i) Let y = ert . The characteristic polynomial is r2 +
MATH 215/255
Fall 2014
Assignment 7
6.3, 6.4, 3.1, 3.3
Solutions to selected exercises can be found in [Lebl], starting from page 303.
6.3.3: Find the solution to
mx00 + cx0 + kx = f (t), x(0) = 0, x0 (0) = 0
for an arbitrary function f (t), where m > 0,
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215
Midterm Exam I February 2010
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This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Problem
1.
max score
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The University of British Columbia
MATH 215
Midterm Exam II March 2010
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This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Problem
1.
max score
10
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The University of British Columbia
MATH 215
Midterm Exam II March 2010
Name
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This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Problem
1.
max score
10
Be sure this exam has 8 pages including the cover
The University of British Columbia
MATH 215/255-103/104
Midterm Exam II November 2014
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Section Number
This exam consists of 4 questions worth 10 marks each. No notes nor calcul
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 215/255, Section 102
Midterm Exam II November 2009
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Pro
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 215/255, Section 102
Midterm Exam II November 2009
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Pro
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 215/255, Section 104
Midterm Exam I October 2014
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Probl
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215/255
Midterm Exam I October 2014
Name
Signature
Student Number
Section Number
This exam consists of 4 questions worth 40 marks. No notes nor calculators.
Problem
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 215/255
Midterm Exam II November 2014
Name
Signature
Student Number
Section Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Q
Given that y 36 y e t
d
m
dt
The homogenous equation:
y 36 y 0
Let
Auxiliary equation:
m 2 36 0
m 6i
So, the complementary function:
yc c1 cos 6t c2 sin 6t
Let y p Ae t
Differentiatinf with respect to t
d t
e e t
dt
Again differentiatinf with respect to
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215/255, Section 102
Midterm Exam I October 2009
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Probl
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 215/255
Midterm Exam II November 2014
Name
Signature
Student Number
Section Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Q
MATH 215/255
Fall 2014
Assignment 9
3.9, 8.1, 8.2
Solutions to selected exercises can be found at the end of the draft chapter of Lebls book
on nonlinear systems.
3.9.8: Consider the equation
!0 =
x
1/t
1
1 1/t
Check that a complementary solution is
t si
Be sure this exam has 12 pages including the cover
The University of British Columbia
MATH 215/255, Sections 101105
Final Exam December 2009
Name
Signature
Student Number
Circle Section:
101 Liu
102 Tsai
103 Seon
104 Dridi
105 Smith
No notes nor calculato
Be sure this exam has 10 pages including the cover
The University of British Columbia
Final Exam December 2007
Mathematics 215/255, Ordinary Dierential Equations
Name
Student Number
Circle Section: 101 Phan
Signature
102 Burghelea
103 Tsai
104 Flowers
105
Be sure this exam has 12 pages including the cover
The University of British Columbia
MATH 215/255, Sections 101105
Final Exam December 2009
Name
Signature
Student Number
Circle Section:
101 Liu
102 Tsai
103 Seon
104 Dridi
105 Smith
No notes nor calculato
Be sure this exam has 13 pages including the cover
The University of British Columbia
MATH 215, Section 201
Final Exam April 2010
Family Name
Given Name
Student Number
Signature
No notes nor calculators.
Rules Governing Formal Examinations:
1. Each candid
Be sure this exam has 13 pages including the cover
The University of British Columbia
MATH 215, Section 201
Final Exam April 2010
Family Name
Given Name
Student Number
Signature
No notes nor calculators.
Rules Governing Formal Examinations:
1. Each candid
Be sure this exam has 11 pages including the cover
The University of British Columbia
Final Exam December 2007
Mathematics 215/255, Ordinary Dierential Equations
Name
Student Number
Circle Section: 101 Phan
Signature
102 Burghelea
103 Tsai
104 Flowers
105
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215/255
Midterm Exam I October 2014
Name
Signature
Student Number
Section Number
This exam consists of 4 questions worth 40 marks. No notes nor calculators.
Problem
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215
Midterm Exam I February 2010
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Problem
1.
max score
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215/255, Section 104
Midterm Exam I October 2014
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Probl
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 215/255, Section 102
Midterm Exam I October 2009
Name
Signature
Student Number
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Probl
Nondimensionalization for dummies
Richard Hall CEESG presentation on 29 Feb 2012
Definition:
Nondimensionalization, or rescaling, refers to the process of transforming a series of
equations (usually ODEs or PDEs) to di
FINAL EXAM TOPICS: MATH 215/255 APRIL 2016
Note: The final exam is cumulative. Any topic from any part of the course could be tested either
individually or in combination with other course topics. Make sure you know and can do all webwork,
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