1051 Assignment 2
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Due Monday 29th August 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late
MATH1051
Assignment 4
All questions must be submitted by 3 pm on Thursday 20 October. Assignments can be submitted at your
tutorial or to the assignment submission machine (3rd floor, Priestley Building #67). You do need a cover
sheet which will be emaile
1051 Assignment 3
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Due 19th September 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late assi
1051 Assignment 3
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?
?
?
?
?
Due 19th September 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late assi
1051 Assignment 2
?
?
?
?
?
?
Due Monday 29th August 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late
`Solvable Graphs and Existence Methods
J. Tinton
Abstract
Let P = r. It is well known that A 
s. We show that there exists an independent smooth,
BrahmaguptaBrahmagupta subring. On the other hand, S. Bhabhas characterization of curves
was a milestone i
Some Convergence Results for CoIsometric Fields
J. Tinton
Abstract
Let KY > 2 be arbitrary. In [11], the authors address the uniqueness of countable, pairwise
Selberg scalars under the additional assumption that every conditionally rightWeyl category is
Semester One Final Examinations, 2015
Math 1051 Calculus & Linear Algebra 1
Formula Sheet
tan = sin / cos ,
cot = cos / sin ,
sec = 1/ cos ,
csc = 1/ sin
sin2 + cos2 = 1,
tan2 + 1 = sec2 ,
cot2 + 1 = csc2
cos 2 = cos2 sin2 = 2 cos2 1 = 1 2 sin2 .
sin 2
Summary of integrals in vector calculus
by Michelle Jones (a student in MATH2000) and Tony Roberts
Note: Many details  such as orientation, and outward normals  are not covered below. You
should consult the course notes for a precise statement of the re
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 2
Semester 1, 2016
SOLUTIONS
(1) Show that
cosh(ln x) + sinh(ln x) = x,
x > 0.
Solution: We have
cosh y + sinh y = ey
so, for y = ln x (where x > 0 and for which eln x = x), we have
cosh(ln x) + sinh(ln x) = x
UQ MATHEMATICS
MATH2000/MATH2001
Revision questions
Z
1
Z
1
3
exp x 2 dxdy.
1. Evaluate the integral
0
y2
2. Find the mass of the portion of the sphere of radius a centred at the origin which lies in
the positive octant (x 0, y 0 and z 0). The density of
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 1
Semester 1, 2016
SOLUTIONS
(1) Consider the initialvalue problem
sin(x y)
dy
sin(x y) = x2 ,
dx
y(1) = 1.
(a) Show that the differential equation is exact.
(b) Find a solution to the initialvalue problem,
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 5  Solutions
(1)
0
A. Choose r(t) = a cos ti + a sin tj +
ti + a cos tj + 0k and by
0k so r (t) = a sin
2
(0 a sin t)(a sin t) +
Stokes theorem the integral is
F(r(t)r0 (t)dt =
0
2a sin t0a cos t + (a cost
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 1
Semester 1, 2016
Submit your answers  along with this sheet and your cover sheet  by 2:00pm on Tuesday, 22
March, to the designated assignment box in the Priestley Building (67).
You may find some of these
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 4
Semester 1, 2016
Submit your answers  along with this sheet and your cover sheet  by 2:00pm on Tuesday, 3
May, to the designated assignment box in the Priestley Building (67).
You may find some of these pr
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 3
Semester 1, 2016
Submit your answers  along with this sheet and your cover sheet  by 2:00pm on Tuesday, 3
May, to the designated assignment box in the Priestley Building (67).
You may find some of these pr
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 5
Semester 1, 2016
Submit your answers  along with this sheet and your cover sheet  by 2:00pm on Tuesday, 31
May, to the designated assignment box in the Priestley Building (67).
You may find some of these p
DEPARTMENT OF MATHEMATICS
MATH2000
Assignment 3
Semester 1, 2016
SOLUTIONS
(1) Evaluate the integral
1
Z
1
Z
x max(x, y) dy dx,
0
0
where max(x, y) is the maximum value of x and y.
Solution: We have
so
Z 1Z
(
x,
max(x, y) =
y,
1
1
Z
x max(x, y) dy dx =
0
11
MATH2000 Calculus & Linear Algebra Ii
Second Semester Examination, November, 2008 (continued)
Q4 Use 'Stokes theorem to compute the integral ff curlF dS where F(;z:,y,z) =
xzi + yzj + myk and S is the part of the sphere x2 + y2 + z 5 With 2 > 0 that l
Semester One Final Examination, 2016 MATH2000 Calculus and Linear Algebra II
Formula sheet
0 Variation of parameters
W = 31in yiyg
u= dx 1): da:
W W
o Gauss Divergence Theorem
5ij F  11 d8 = I div(F) dV
3 V
o Stokes Theorem
f(curlF)  11 d8 = for  T as
DEPARTMENT OF MATHEMATICS
MATH2000
Revision questions, semester 2, 2007
Z
1
Z
1
3
exp x 2 dxdy.
1. Evaluate the integral
0
y2
2. Find the mass of the portion of the sphere of radius a centred at the origin which lies in
the positive octant (x 0, y 0 and z
'1.
3
MATH2000 Calculus and linear algebra II
Second Semester Examination, 2009 (continued)
(a) Let y1, y2 be solutions to the ODE
y + p(6)y + q(w)y = 0
Show that y(:c) = clyll+ ngg is also a solution to the ODE, Where c1,02 are
constants. (3 marks)
1 0
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #7 Solutions
Semester 2, 2016
1. Find and classify the critical points of the functions f given by:
a) f (x, y) = xy ex
2 y 2
,
1
b) f (x, y) = 8xy (x + y)4 ,
4
c) f (x, y) = sin x sin y,
d) f (x, y) = ex (1 cos y).
a)
f = (1 2x2 )y
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #6 Solutions
1. Find
Semester 2, 2016
dw
a) by using the appropriate chain rule and b) by first converting w to a function
dt
of t:
i) w = xy,
x = 2 sin t,
ii) w = xy tan z,
iii) w = xyz,
y = cos t,
x = t,
x = t2 ,
y = t2 ,
y = 2t,
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052
Extra Questions: Limits & Continuity
Semester 2 2016
1. Let D = R2 \cfw_(0, 0) and let f : D R be given by
f (x, y) =
1 exp(x2 y 2 )
.
x2 + y 2
Show that the lim(x,y)(0,0) f (x, y) does not exist.
SOLUTION:Let y = x (with x 6= 0). Then f (x, x) =