THE UN IVERSITY OF NE\t\1 SOUTH \t\!ALES
SCHOOL OF l\IIATHEJVIATICS AND STATISTICS
November 2014
MATH2121
Theory and Applications of
Differential Equations
(1) TIME ALLOWED- 2 HOURS
(2) TOTAL NUMBER OF QUESTIONS - 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTI
Topic 1. Introduction Page 1
MATH2521 COMPLEX ANALYSIS
S2 2016
TUTORIAL PROBLEMS
PART A: TOPICS 1 TO 11 (OF 15 TOPICS)
The more
Reference
Spiegel
Church5
Church6
Church7
Church8
Church9
The
(1)
(2)
(3)
difficult questions are marked with the symbol * in t
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
NOVEMBER, 2014
MATH2521
COMPLEX ANALYSIS
(1 TIME ALLOWED 2 hours
(2 TOTAL NUMBER OF QUESTIONS 4
3 ANSWER ALL QUESTIONS
5
)
)
( )
(4) THE QUESTIONS ARE OF EQUAL VALUE
( ) THIS PAPER MAY
PHYS1110
Investigation 2:
Archimedes Principle
Wen-Hsuan Schoen
TSENG
Z3419615
Aim
The purpose of this investigation is to measure the mass and volume of
the objects. This can be also used to calculate the density of different
fluids, and make further obs
PHYS1110
Investigation 3:
Coefficient of static friction
Wen-Hsuan Schoen
TSENG
Z3419615
Aim
The purpose of this investigation is to measure the coefficient of static
friction between the angle of the slope and the surface. This is to help to
understand t
PHYS1110
Investigation 1:
Using a kettle to calculate the specific
heat of water
Wen-Hsuan Schoen
TSENG
Z3419615
Aim
The aim of this investigation is to determine the specific heat of water, C w , by timing
the time takes for a kettle to boil water. This
Chapter 4
Systems of Ordinary
Differential Equations
The Dynamical Systems
Point of View
continued
MATH2121
Theory and Applications of
Differential Equations
Dr Anna Cai
School of Mathematics and Statistics,
Red Centre, RC-2083
[email protected]
S2, 201
Topic 12. Real improper integrals Page 1
MATH2521 COMPLEX ANALYSIS
S2 2016
TUTORIAL PROBLEMS
PART B: TOPICS 12 TO 15 (OF 15 TOPICS)
The more
Reference
Spiegel
Church5
Church6
Church7
Church8
Church9
The
(1)
(2)
(3)
difficult questions are marked with the
math2521 November 2014
1
MATH2521 Complex Analysis November 2014
1.
a) For the following three regions in the complex plane
I) |z 2| 2,
II)
0 < Arg(z i) < /4,
III)
Re(z 2 ) > 1
i) Sketch each region in a separate diagram;
ii) State with reasons, whether o
2013
1. i) in lectures
ii)
y = Aex + Be2x +
iii) Recurrence relation
x 2x
e
3
an
(n + 2)(n + 1)
an+2 =
y = Aex + Bex
X
a0 2m X
a1
y=
x +
x2m+1
(2m)!
(2m
+ 1)!
m=0
m=0
The answers are consistent, with y(0) = a0 = A + B, y 0 (0) = a1 = A + B.
iv) a0 = 1, a1
Please note that the Library does not automatically
receive copies of all past exam papers from the
Examinations Team.
The Library did not receive the Session One 2015 paper
for this course code.
You will need to contact your course convenor.
2012
1. i)
ln 1 + y 2 = tan(x) + ln(5)
ii) y = A cos(x/2) + B sin(x/2) + sin(x)/5
iii) the o.d.e should be
6x2 y 00 + 7xy 0 + (2x
1)y = 0
The indicial equation is 6r(r 1) + 7r 1 = 0 and r1 = 1/2, r2 = 1/3. Consider the solution
with r2 only as the solutio
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS,
NOVEMBER 2015
IVIATH2521
COMPLEX ANALYSIS
(1) TIME ALLOWED 2 hours
(2 rITOTAL NUMBER OF QUESTIONS 4
(3 ANSWER ALL QUESTIONS
THIS PAPER MAY BE RETAINED BY THE CANDIDATE
)
)
4) THE QUES
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
NOVEMBER, 2012
MATH2120
MATHEMATICAL METHODS FOR
DIFFERENTIAL EQUATIONS
(1) TIME ALLOWED 2 hours
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE OF EQUAL
math2521 November 2015
1
MATH2521 Complex Analysis November 2015
1.
a) Let S be the region in the complex plane satisfying
z
Re
0
z1
Identify S in terms of an inequality in x and y where z = x + iy for x, y R and sketch S.
Is S a domain? - give brief reas
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
November 2014
MATH2121
Theory and Applications of
Differential Equations
(1) TIME ALLOWED 2 HOURS
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE NOT OF
9
THE ROLE OF INCREASING RETURNS, TECHl\ICAL
PROGRESS A:-;n CUMULATIVE CAUSATION I:-.J THE
THEORY OF IYl'ER:-JATIONAL TRADE AND
ECO:'-JOMIC GROWTH"
Traditional theory, both classical and neo-classical, asserts that
free trade In ~(l()ds between dim-rent r
Big Mac Index
I
Big Mac Index: The Economist attempt to assess overvaluation or
undervaluation of currencies by comparing a globally-uniform good:
McDonalds Big Mac.
http:/www.economist.com/content/big-mac-index
Example: Big Mac Index for China
In China,
University of New South Wales
School of Economics
Economics 3104/5304: International Macroeconomics
Tutorial Question Set 3
(To be solved after the short presentation on the Big Mac Index.)
Exercise 1
Consider the following information for a sample of cou
University of New South Wales
School of Economics
Economics 3104/5304: International Macroeconomics
Tutorial Question Set 4
NOTE: Please submit Exercise 1 at the start of Week 6 tutorial. Your assignment must be typed,
not hand-written with exception for
KALECKI/KALDOR/LEWIS ON DEVELOPMENT AND
THE IMPORTANCE OF DUALITY
1. THE ROLE OF THE SURPLUS
2. AN IMPORTANT DIFFERENCE BETWEEN
DEVELOPED AND DEVELOPING
ECONOMIES
3. THE LEWIS MODEL OF DUAL
DEVELOPMENT
4. THE IMPORTANCE OF THE
AGRICULTURAL SECTOR
5. THE R
ECON 3104/5304: International Macro Lecture 4
Sang-Wook (Stanley) Cho
UNSW Australia
S1 2017
ECON 3104/5304: International Macro Lecture 4
1
Exchange Rates, Money, and Prices (Long-Run)
We want to understand the long-run relationships between money,
pric
PHYS1110
Investigation 1:
Using a kettle to calculate the specific
heat of water
Wen-Hsuan Schoen
TSENG
Z3419615
1
Aim
The aim of this investigation is to determine the specific heat of water, , by timing
the time takes for a kettle to boil water. This ex
1A
This lecture is full. Please sit in
all seats, with no empty seats inbetween. Thank you.
ARTS1630
Introductory Japanese A
School of Humanities and Languages
Week 1, 2017
1
Todays lecture
Introduction of the course
Introduction of the staff members
Stu
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
NOVEMBER, 2011
MATH2120
MATHEMATICAL METHODS FOR
DIFFERENTIAL EQUATIONS
(1) TIME ALLOWED 2 hours
(2) TOTAL NUMBER OF QUESTIONS ?
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE NOT OF E
PHYS1110
Investigation 3:
Coefficient of static friction
Wen-Hsuan Schoen
TSENG
Z3419615
Aim
The purpose of this investigation is to measure the coefficient of static friction between
the angle of the slope and the surface. This is to help to understand t