UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH1251 MATHEMATICS FOR ACTUARIAL STUDIES
AND FINANCE 1B Algebra S2 2007
TEST 2 VERSION 1A
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Students Family Name
Initial
UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH1251 CALCULUS S2 2007
TEST 1 VERSION 2a
This sheet must be lled in and stapled to the front of your answers
Students Family Name
Initials
Tutorial Code
Tutors Name
Note: The use of a c
MATH1251 Sample Solutions
2009 Test 2 ver. 1b
These solutions were written and typed by Ryan Xie. Thanks to Richard Chen and Allan Chen
for their help. Please ask for permission if you are using this for commercial purposes.
Steps have most likely been om
MATH1251 Sample Solutions
Appendix for Calculus Test 2
In this Ill show something I think is pretty neat, and I think its more rigorous than the
other proofs to nd L for a sequence. Obviously, use this at your own peril and I accept no
responsibility for
Week 10 Version 3
Time allowed: 25 minutes.
1. (0 marks if correct, -1 mark if incorrect)
Dene the statement, The set of vectors cfw_v1 , v2 , . vn is linearly dependent.
2. (3 marks)
Prove that S = cfw_x R3 | x1 + x2 = x3 is a subspace of R3 .
3. (1
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
SEMESTER 2 2015
MATH1251
Mathematics for Actuarial Studies
and Finance 1B
(1) TIME ALLOWED Two (2) hours
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE
Refer to Q1, examine the graph which of the airlines is the best long term performer in terms
of share price?
Virgin Austraiia
China Suuti'lem Airlines
Singapnre Airiines
El Refer to .04, which of the following areas has. choice largely been made by a sta
ANUx Introduction to Actuarial Science
Lesson 3
Analysis of State Transitions
Introduction to Analysis of State Transitions
The cash flow calculations and models you have seen so far in the course have all assumed that the
cash flows are guaranteed to occ
lOMoARcPSD
Summary - Notes for final exam covering all course material
Macroeconomics 1 (University of New South Wales)
Distributing prohibited | Downloaded by Alex Wu ([email protected])
lOMoARcPSD
ECON 1102 ~ 2013 Notes
Measuring Macroeconomic Perf
ANUx Introduction to Actuarial Science
Lesson 7
Modelling a Life Insurance Company 2
In Lesson 6, we looked at the investigation of the financial condition of a life insurance company
through the use of simulations. In this Lesson we will continue to do t
ANUx Introduction to Actuarial Science
Lesson 4
The Life Table
History of the Actuarial Profession
Were almost half way through the course and its time for a (very) short history lesson. Were going
to briefly have a look at the history of the actuarial pr
1
2010 V1A
Q1 (i) The polynomial q belongs in spancfw_p1 , p2 , p3 if we can express it as some linear
combination of the three. We may thus equate q to a linear combination as follows.
For some t1 , t2 , t3 F
t1 p1 (x) + t2 p2 (x) + t3 p(3)x q( x)
(t1
MATH1251 Solutions
2009 Test 1 ver. 2a
These solutions were written and typed by Ryan Xie, and checked and edited by Richard Chen.
Thanks to Allan Chen for his help. Please ask for permission if you are using this for commercial
purposes.
Steps have most
Math1251 Solutions
2007 Test 3 ver. 2a
These solutions were written and typed by Ryan Xie. Thanks to Richard Chen and Allan Chen
for their help. Please ask for permission if you are using this for commercial purposes.
Steps have most likely been omitted a
Week 3 Version 1
Time allowed: 25 minutes.
1. (3 marks)
1
(1 + x2 )n dx.
Let In =
0
(a) Show that In =
2n
2n
+
In1 for n 1.
1 + 2n 2n + 1
1
(1 + x2 )2 dx.
(b) Use the reduction formula to evaluate
0
2. (2 marks)
Find
1
dx.
x+ 4x
3. (2 marks)
Solve the di
Week 3 Version 2
Time allowed: 25 minutes.
1. (3 marks)
e
(ln x)n dx.
Let In =
1
(a) Show that In = e nIn1 for n 1.
e
(ln x)4 dx.
(b) Use your result to nd
1
2. (2 marks)
cos4 x dx.
Find
0
3. (2 marks)
Solve the dierential equation (1 + x2 )
dy
= 12xy 2 ,
Week 4 Version 1
Time allowed: 25 minutes.
1. (3 marks)
Show that if z +
1
is a real number, then either Im(z) = 0, or |z| = 1.
z
2. (2 marks)
d2 x
dx
Are the solutions of the continuous time system 2 2 2 + x = 0 stable or unstable?
dt
dt
Give reasons.
3.
Week 4 Version 3
Time allowed: 25 minutes.
1. (4 marks)
Let w = 3 + 4i.
(a) Evaluate the following:
i. w
1
ii.
w
iii. The square roots of w.
(b) Hence, or otherwise, nd the solutions to
1 2
z +
2
25
w
z + 2w = 11 + 6i.
2. (3 marks)
By considering z 6 1 as
Week 4 Version 2
Time allowed: 25 minutes.
1. (3 marks)
Let the cube roots of unity be 1, , 2 .
Show that 1 + + 2 = 0, and hence or otherwise, fully simplify (1 )(1 2 )(1 4 )(1 8 ).
2. (2 marks)
Are the solutions of the discrete time system 2xn+1 2xn + xn
Week 7 Version 1
Time allowed: 25 minutes.
1. (3 marks)
Solve the dierential equation 2ydx + xdy = 0 by multiplying through by a function of the
form xa y b to make the equation exact.
2. (2 marks)
x
Solve the integral equation y(x) = 1 +
y(t) dt.
0
3. (2
Week 7 Version 2
Time allowed: 25 minutes.
1. (2 marks)
Find the general solution of the dierential equation
d2 y
dy
+ 4 + 4y = 8x.
2
dx
dx
2. (3 marks)
dy
Find all functions f (x) such that the dierential equation y 2 sin x + yf (x)
= 0 is exact.
dx
Henc
Week 7 Version 3
Time allowed: 25 minutes.
1. (4 marks)
(a) Find the general solution of the dierential equation
du
+ 2u = e2x .
dx
(b) Hence, use the substitution
dy
+ 2y
dx
to nd the general solution of the dierential equation
u=
d2 y
dy
+ 4 + 4y = e2x
MATH1251 Solutions
2007 Test 1 ver. 2a
These solutions were written and typed by Ryan Xie, and checked and edited by Richard Chen.
Thanks to Allan Chen for his help. Please ask for permission if you are using this for commercial
purposes.
Steps have most
MATH1251 Solutions
2007 Test 2 ver. 1a
These solutions were written and typed by Ryan Xie, and checked and edited by Richard Chen.
Thanks to Allan Chen for his help. Please ask for permission if you are using this for commercial
purposes.
Steps have most
MATH1251
Mathematics for Actuarial Studies
and Finance 1B
ALGEBRA PROBLEMS
Semester 2 2014
Copyright 2014 School of Mathematics and Statistics, UNSW
Contents
6 COMPLEX NUMBERS
6.1 A review of number systems . . . . . . . . . . . . . .
6.2 Introduction to
Outline
MATH1251 Calculus
Chapter 3: Taylor Series
1
Taylor polynomials
2
Sequences
3
Infinite series
4
Taylor series
5
Power series
A/Prof Thanh Tran
School of Mathematics and Statistics
The University of New South Wales
Sydney, Australia
Red Centre Room
Outline
MATH1251 Calculus
Chapter 2: Oridinary Differential Equations
1
ODEs and IVPs
2
First order ODEs
Separable ODEs
First order linear ODEs
Exact ODEs
Substitutions for ODEs
Modelling with first order ODEs
3
Second order ODEs
The homogeneous case
The
Brian Lam
10/11/2015
MATH1251: MATHEMATICS ASF 1B (CALCULUS)
1
INTEGRATION
x
m
n
cos x sin x dx
requires identities like cos2 x
1
1
1 cos 2x
, sin2 x 1 cos 2x
and
2
2
sin 2 x cos2 x 1 .
x
cos mx sin nx dx or cos mx cos nx dx or sin mx sin nx dx
Outline
MATH1251 Calculus
Chapter 4: Functions of Several Variables
1
Taylor series and tangent planes
School of Mathematics and Statistics
The University of New South Wales
Sydney, Australia
2
Classification of critical points
Red Centre Room 4061
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