Problem 1: Fourier Series:
Problem 1: Fourier Series: (cont)
Problem 1: Fourier Series (cont)
Subproblem (c)
Problem 2: Steady Solutions
Problem 3: Heat conduction with inhomogeneous boundary conditions
Math 257/316 Assignment 5
Due Monday October 26th in class
SOLUTIONS
Problem 1: Sketch the odd, even, and full periodic extensions on [3L; 3L] of
(a) ex , with L = 1
(b) 4 x2 , with L = 2
(c) g(x) =
1 + x, x < 0
, with L = 1.
x/2,
x0
SOLUTION:
Figure 1: P
Math 257/316 PDE
Assignment 4
[Separation of variables]
1. Determine whether the method of separation of variables can be used to replace the
following PDEs by a pair of ODEs. If so, nd the equations.
(a) xuxx + tut = 0.
(b) uxx + uyy = x.
(c) ux + uxt +
Mathematics 100-105
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Student-No.:
Midterm 1
Duration: 45 minutes
This test has 5 questions on 6 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer i
Mathematics 100-107
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Student-No.:
Midterm 1
Duration: 45 minutes
This test has 5 questions on 9 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer i
Mathematics 100-105
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Student-No.:
Midterm 1
Duration: 45 minutes
This test has 5 questions on 8 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer i
MATH 100, Section 110
Midterm 1 September 30, 2014
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Midterm 1
Duration: 45 minutes
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Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions;
Mathematics 100-107
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Midterm 1
Duration: 45 minutes
This test has 5 questions on 9 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answer i
Mathematics 100-109
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Midterm 1
Duration: 45 minutes
This test has 5 questions on 8 pages, for a total of 40 points.
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Q1 and Q2 are short-answer questions; put your answer i
Mathematics 100-109
Page 1 of 6
Student-No.:
Midterm 1 template
Duration: 45 minutes
This test has 5 questions on 6 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your
MATH 100, Section 110
Midterm 1 September 30, 2014
Page 1 of 7
Midterm 1
Duration: 45 minutes
This test has 5 questions on 7 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions;
Mathematics 100-103 xed
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Midterm 1 template
Duration: 45 minutes
This test has 5 questions on 8 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put
Mathematics 100-103 xed
Page 1 of 7
Student-No.:
Midterm 1 template
Duration: 45 minutes
This test has 5 questions on 7 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put
MATH 100-102, Midterm 1
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Student-No.:
Midterm 1
Duration: 45 minutes
This test has 5 questions on 7 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answ
MATH 100-102, Midterm 1
Page 1 of 9
Student-No.:
Midterm 1
Duration: 45 minutes
This test has 5 questions on 9 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are short-answer questions; put your answ
Part 1. Multiple choice questions must be answered on the Scantron form by completely
shading in the appropriate circle with blue or black pen or pencil. Responses on your Scantron
sheet will be used to calculate your midterm grade, however, you should al
!
!
Part 1. Multiple choice questions must be answered on the Scantron form by completely
shading in the appropriate circle with blue or black pen or pencil. Responses on your Scantron
sheet will be used to calculate your midterm grade, however, you shoul
April 2007
Mathematics 103
Name
Page 2 of 10 pages
Marks
[20]
1.
Multiple Choice Questions: Select ONE correct answer (a, b, c, d, or e) for each question and
write it in the table at the bottom of the page. You will not be graded for any work or answers
Math 100, Section 105 Solutions to Problem Set 1
September 27, 2010
1. (Calculation of limits) (a) For x = 1 we have (b) lim
x 2 x x1
=
x(x1) x 1
= x, and we know lim x = a so lim
xa
x2 x x 1 x 1
= 1.
x2 +x does not exist, since x 1 0 while the numerator
Math 100, Section 105 Problem Set 1
Due: September 17th, 2010
Student number: LAST name: First name: Mark:
Instructions
Please print this sheet out and write your student number, last name (all capitals) and rst name. Please use your ocial name as it appe