Q 0 air New _ DO @193wa m
Ci Ma cK WWW 0% AM 0: n K, Qifff'i [1, L112
5 >
1: ,
m
CWWAK Su )3? w/zw CiC/wbwg 7, K Q5,
fA/Qm @Lm Cy KKK MEAN/M (we CLLLJCij S 2 O
, Q Kc
X 2 9" 2 CW9
Ck 37C 3 Lk r if. I [Vt t1 h" 1 71 f '52 ,7" f f E 5; 1 g ; s,
3 u)
The University of Sydney
School of Mathematics and Statistics
Solutions to Assignment
MATH2962: Real and Complex Analysis (Advanced)
Semester 1, 2016
Web Page: http:/www.maths.usyd.edu.au/u/UG/IM/MATH2962/
Lecturer: Florica Crstea
1. Find the region of co
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
2017
Week 7 Exercises
Starred questions are suitable for students aiming for a credit or higher.
1. Verify that all fields are integral domains and that a nontrivial commutative
ring R with id
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
2017
Week 6 Exercises
Starred questions are suitable for students aiming for a credit or higher.
1. Today is Monday. What day will it be after 100100 days have elapsed?
*2. It has been predict
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
Week 5 Exercises
2017
Starred questions are suitable for students aiming for a credit or higher.
1. Is the following argument clear (and valid)?
All clear explanations are satisfactory. Some e
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
Week 4 Exercises
2017
Starred questions are suitable for students aiming for a credit or higher.
1. According to an ancient Sicilian legend, there lived a barber in a remote village
who shaved
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
Week 4 Solutions
2017
1. There are two possibilities assuming the barber existed: the barber shaved himself
or the barber did not shave himself. If the barber did shave himself, then the
descr
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
1. We calculate
2017
Week 6 Solutions
100100 = 2100
(mod 7)
= (23 )33 2
= 133 2
= 2,
(mod 7)
so that, after 100100 days have elapsed, it will be 2 days after a Monday, which is
a Wednesday.
*2
THE UNIVERSITY OF SYDNEY
MATH3066 ALGEBRA AND LOGIC
Semester 1
Week 5 Solutions
2017
1. It is not entirely clear whether the author implicitly assumes that all excuses are
explanations. If an excuse need not be an explanation, then best to let the univers
7
RESEARCH METHODS
An introduction to mathematical models in sexually
transmitted disease epidemiology
G P Garnett
.
Sex Transm Inf 2002;78:712
Mathematical models serve a number of roles in
understanding sexually transmitted infection
epidemiology and co
8063
Semester 1, 2011
THE UNIVERSITY OF SYDNEY
Faculties of Arts, Economics, Education,
Engineering and Science
MATH3063
Differential Equations & Biomaths (N)
Semester 1
Time Allowed: Two Hours
June 2011
Lecturer: M.R. Myerscough
This exam consists of 6 p
8063
Semester 1, 2010
THE UNIVERSITY OF SYDNEY
Faculties of Arts, Economics, Education,
Engineering and Science
MATH3063
Differential Equations & Biomaths (N)
Semester 1
Time Allowed: Two Hours
June 2010
Lecturer: M.R. Myerscough
This exam consists of 6 p
8063 SEMESTER 1, 2007
THE UNIVERSITY OF SYDNEY
FACULTIES OF ARTS, ECONOMICS, EDUCATION,
ENGINEERING AND SCIENCE
MATH3063
DIFFERENTIAL EQUATIONS 85 BIOMATHS (N)
Semester 1 Time Allowed: Two Hours
June 2007 Lecturer: A. Nelson
THIS EXAM CONSIS
THE UNIVERSITY OF SYDNEY
Differential Equations & Biomathematics
Semester 1
Assignment 1
2013
This assignment is due at 5pm on Wednesday 10 April at Carslaw room 626.
1. (i)
A simple model for the spread of a chronic infectious disease assumes that the ra
THE UNIVERSITY OF SYDNEY
Nonlinear Differential Equations & Applications
Semester 1
Tutorial Week 13
2016
Suggested Solutions
NOTE: When the eigenvalues are complex conjugates the TRACE is equal to TWICE the real
part of the eigenvalues, so you can use th
Mandal et al. Malaria Journal 2011, 10:202
http:/www.malariajournal.com/content/10/1/202
REVIEW
Open Access
Mathematical models of malaria  a review
Sandip Mandal, Ram Rup Sarkar and Somdatta Sinha*
Abstract
Mathematical models have been used to provide
THE UNIVERSITY OF SYDNEY
Nonlinear Differential Equations & Applications
Semester 1
Tutorial Week 9
2016
SELECTED SOLUTIONS
1. Simple epidemic model with partial immunity
(i) The compartmental model is
6
?
S

I
(ii )
R
Eliminating R gives
dS
= SI S I +
V 1 7 710%: V (215% Whh.h k 7 CmTX $3
CWJZK CW, \) 30g m U; WA LWWMMWQ cwk 4kg
\
MQKZQ a x cfw_5; (LR 4 gig; KW ka KW 23 :) 0 (5x.
1% * ~ 7 7
@w , 7 7 7 7 if f R 52% g; * if:TIf:
Jada 32M]? 2, 22:12.22 2 2:; 222 [2,3232 W
322,2 2:3 2272/29 & C 2:; My
v a @WW gm :2 WW
fmdmm%m&XmasmkiaQT:L
1 g A z
; i? W cfw_m ) v a; u ,
z : 3 t x
'4 V 15 2 i i
[w t .J .J .5 .13; i, .byjw
\
w w m cfw_7,
z" WW
ngwf;f]fiLfimwIgfif@:;:y&m%;f
S 1 L: r T ,; ;
33. L +3; .31; 43; "03030707037133 I b i! 13 6 I37; 03133329?
MATH3063
Nonlinear Differential Equations & Applications
Semester 1, 2016
Diagnostic Assignment 0
Due before midnight on MON 7th March
Explain each of the important concepts from Linear Algebra listed below in your own words.
Try to do this on your own an
THE UNIVERSITY OF SYDNEY
Differential Equations & Biomathematics
Semester 1
Assignment 1
2013
This assignment is due at 5pm on Wednesday 22 May at Carslaw room 626. Please include a coversheet
with your assignment. If you use a manilla folder, please writ
1. Consider the ordinary differential equation
1t: (:1:+,LL8)(:cu4)
Where :2: and u range over all real values.
(i) Draw the bifurcation diagram. Correctly label the axes. Indicate stable equilibria
with solid lines, unstable equilibria with dashed lines
1. Consider the ordinary differential equation
a3:(u+a?5)(M~fE3)
Where :L and a range over all real values.
(i) Draw the bifurcation diagram. Correctly label the axes. Indicate stable equilibria
with solid lines, unstable equilibria with dashed lines and
1. Consider the system of ODES
d3 _ 2 2 _ 7. + 3
dt 31(356 +7.74), (5X3 cfw_3
: :I;(z2+a:cy+y2) : x3+oLx13+ 731 A
Where 0:, and '7 are real parameters.
(2') Find all values of the parameters for which the system is a gradient system and
construct a suita
1. Consider the system of ODEs
d3; 2. '7 0:)
= y($2+amy+y2), =54 +0<X +p
d_y a a: a
= I 2 2 1:. g . 1"
dt was +721) x (FKVNEA
Where a, and 'y are real parameters.
(2') Find all values of the parameters for which the system is a gradient system and
constr
Quiz 1
Semester 1, 2016
The University of Sydney
Faculties of Arts, Economics, Education,
Engineering and Science
MATH2962: Real and Complex Analysis (Advanced)
Lecturer: Florica Crstea
Time allowed: 40 Minutes
This booklet contains 7 pages.
Last Name: .