Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Mechanical Engineers
AM 3413

Fall 2017
The University of Western Ontario
October Examination 25 October 2017 12:30 30 minutes
Name:
Student Number:
Instructions: Closed book; Justify Answers; No Electronics permitted; Fill in Name and St
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Mechanical Engineers
AM 3413

Fall 2017
The Unlverelty of Western Ontario
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November Examination 24 November 2017 12:30 30 minutes
Name: _._._ Student Number:
Instructions:
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2010
The University of Western Ontario
Applied Mathematics 1411b
First Tutorial Test: 29 January 2013
Time: 45 minutes
Use this examination booklet to answer questions.
You are allowed to use calculators a
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2010
Western University
Applied Mathematics 1411A
Test 1 Friday February 5 2016
Time: 60 minutes
Version A
o This exam booklet has 3 problems on 7 pages, for a total of 50 points.
a Please answer all quest
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2010
Exercises for AM025
D.J. Jeffrey
Department of Applied Mathematics
U. Western Ontario
November 8, 2006
1
Determinants
1. For an n n matrix A,
(a) if A is singular then det(A) = 0.
(b) if A is singular
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2010
Exercises for AM1411
D.J. Jeffrey
Department of Applied Mathematics
U. Western Ontario
March 24, 2015
1
Row Echelon Form
1. If A is an n n matrix and x is an n 1 vector of unknowns, the equation Ax =
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2010
Solutions of equations  AM1411
D.J. Jeffrey
Department of Applied Mathematics
U. Western Ontario
March 23, 2015
1
Equations to solve
1. A system of 3 equations in 3 unknowns
(a) is never inconsistent
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2010
MultipleChoice Questions on Transformations
D.J. Jeffrey
Department of Applied Mathematics
U. Western Ontario
March 13, 2015
x2
y1
1
1. The matrix equation
=
y2
0
(1, 1)
0
x1
transforms the squar
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF APPLIED MATHEMATICS
Applied Mathematics 1411a
Second Tutorial Test, version 1, October 2223, 2013
Time: 60 min
The test is closed book! You are allowed
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF APPLIED MATHEMATICS
Applied Mathematics 1411a
First Tutorial Test, version 1, October 1 and 2, 2013
Time: 60 min
The test is closed book! You are allowe
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF APPLIED MATHEMATICS
Applied Mathematics 1411a
Third Tutorial Test, version 1, November 1213, 2013
Time: 60 min
The test is closed book! You are allowed
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF APPLIED MATHEMATICS
Applied Mathematics 1411a
First Tutorial Test, version 1, October 1 and 2, 2013
Time: 60 min
The test is closed book! You are allowe
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF APPLIED MATHEMATICS
Applied Mathematics 1411a
Second Tutorial Test, version 1, October 2223, 2013
Time: 60 min
The test is closed book! You are allowed
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
THE UNIVERSITY OF WESTERN ONTARIO
DEPARTMENT OF APPLIED MATHEMATICS
Applied Mathematics 1411a
Third Tutorial Test, version 1, November 1213, 2013
Time: 60 min
The test is closed book! You are allowed
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
1
AM 1411a, Fall 2014
Lectures 4, September 12
2
Gaussian and GaussJordan Elimination
2.1
Elementary row operations:
1. Scaling: cRi ! Ri (c is a nonzero number)
2. Interchange: Ri $ Rj
3. Eliminatio
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
Ex. Three systems of linear equations
1.
x y = 1
2x + y = 6
a) Working with equations: eq.2  2 eq.1 ) 3y = 4;
solve for y : y = 4 : Substitute y into eq.1: x = y + 1 =
3
4 = 7:
1+3
3
b) Working with
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Fall 2014
1
AM 1411a, Fall 2014
Lectures 3, September 10
2
Gaussian and GaussJordan Elimination
2.1
Elementary row operations:
1. Scaling: cRi ! Ri (c is a nonzero number)
2. Interchange: Ri $ Rj
3. Eliminatio
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Winter 2014
Section 1.1 23
I
Every elementary row operation is reversible. TRUE You can
reverse multiplying by a constant by multiplying by its inverse.
If you add row one to row two and replace row two, then you
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Winter 2014
Chapter 1:
Introduction to
linear equations
and functions
1.1
x1=x, x2=y, x3=z. etc
y=ax1+bx2+cx3+.mxn
Ex: y=3x14x2+7x3
number of solutions for
functions in:
R2
parallel lines, no solution
intercept
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Winter 2014
Chapter 3: Euclidean Vector Space
3.1: Vectors in R2, R3 and Rn
Parallelogram Rule for vector Addition:
when adding or subtracting vectors it doesn't matter which order the addition or subtraction occ
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Winter 2014
Chapter 5: Eigenvalues and eigenvectors
5.1: eigenvalues and eigenvectors
If A is a nxn matrix, then a nonzero vector x in Rn is
valid an eigenvector of A (or of the matrix operator TA)
if Ax is a sca
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Winter 2014
Chapter 2: Determinants
2.1: Determinants by cofactor
expansion
Determinant: abbc if
det(A) is cross product.
A1=1/det(A )[ ]
Minors and cofactors:
the minor entry of aij is denoted by Mij and is th
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics
AM 1411

Winter 2014
Chapter 6:
6.1: Inner Products
Unit circles and spheres in inner product space:
there are points in V, that satisfy u=1
Weights:
if wn represents the significance, in a real positive number of the v
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
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Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
MIDERM REVIEW
L`Hopital's Rule:
Suppose the functions f and g are differentiable on the open interval (a,b) and
g`(x)0 (but can be at a) there. suppose also that:
Must write down the lim of g(x) and f