University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
First Midterm Test Solutions Blue Version
31 January 2014
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 minu
-It might be easy to calculate a value f (a) of a function, but
difficult (or even impossible) to compute nearby values of f .
So we settle for the easily computed values of the linear function
L
whose graph is the tangent line of f at (a, f (a).
-If y =
-When log y is graphed as a function of log x, a straight line results
with slope -2 and vertical intercept 5. Determine the functional
relationship between x and y.
-In a related rates problem the idea is to compute the rate of
change of one quantity in
-Example
Poiseuilles Law expresses the flow of blood F as a function of the
radius r of the vessel according to
F = kr 4
where k is a constant. When the radius of a blood vessel is
restricted, such as by cholesterol deposits, drugs can be
administered tha
The derivative f0
(a) is the instantaneous rate of change of
y = f (x) with respect to x when x = a.
The tangent line to y = f (x) at (a, f (a) is the line through
(a, f (a) whose slope is equal to f0
(a), the derivative of f at a.
If we use the slope-int
University of Ottawa
Department of Mathematics and Statistics
MAT 1302D : Mathematical Methods II
Professor: Eric Hua
Second Midterm Exam Version A
Feb 28, 2012
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First Name
Student #
DGD # (1=VNR 5070; 2=LMX 124; 3=TBT 070; 4=DMS 1110)
Instructions
University of Ottawa
Department of Mathematics and Statistics
MAT 1302D : Mathematical Methods II
Professor: Eric Hua
First Midterm Exam Version A
Jan 31, 2012
Surname
First Name
Student #
DGD # (1=VNR 5070; 2=LMX 124; 3=TBT 070; 4=DMS 1110)
Instructions:
University of Ottawa
Department of Mathematics and Statistics
MAT 1302D : Mathematical Methods II
Professor: Eric Hua
Third Midterm Exam Version A
March 28, 2012
Surname
First Name
Student #
DGD # (1=VNR 5070; 2=LMX 124; 3=TBT 070; 4=DMS 1110)
Instruction
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341D: Introduction to Linear Algebra
Instructor: Catalin Rada
Test 1
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Please read these instructions carefully:
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Second Midterm Test Solutions Blue Version
28 February 2014
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 mi
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Third Midterm Test Solutions White Version
21 March 2014
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 minut
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Second Midterm Test Solutions White Version
28 February 2014
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 m
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Third Midterm Test Solutions Blue Version
21 March 2014
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 minute
MAT 1302A Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2014 Lecture 1
Course webpage:
http:/mysite.science.uottawa.ca/asavag2/mat1302
Alistair Savage (uOttawa)
MAT 1302A Mathematical Methods II
Winter 2014
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
First Midterm Test Solutions White Version
31 January 2014
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 min
MAT 1302A Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2014 Lecture 2
Alistair Savage (uOttawa)
MAT 1302A Mathematical Methods II
Winter 2014 Lecture 2
1 / 28
Overiew
Announcements
DGDS start next week.
La
MAT 1302A Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2014 Lecture 4
Alistair Savage (uOttawa)
MAT 1302A Mathematical Methods II
Winter 2014 Lecture 4
1 / 30
Review
We have developed an algorithm for solv
MAT 1302A Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2014 Lecture 5
Alistair Savage (uOttawa)
MAT 1302A Mathematical Methods II
Winter 2014 Lecture 5
1 / 30
Announcements
First midterm: In class on Frida
MAT 1302A Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2014 Lecture 3
Alistair Savage (uOttawa)
MAT 1302A Mathematical Methods II
Winter 2014 Lecture 3
1 / 28
Review
Goal: Develop an algorithm for solving
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Final Exam Solutions
April 2014
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Instructions:
(a) You have 3 hours to complete this exam.
(b)
1.1
SOLUTIONS
Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for
row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section.
1.
x1 + 5 x2 = 7
2 x1 7 x2 = 5
1