Functions
WHAT IS A FUNCTION?
A function is a rule that assigns to each element in a set , a unique
element, called (), in a set .
The set is called the domain of the function.
The set is called the co-domain.
For each in , () is called the image of .
The
MTH1020 Analysis of Change
Problem Set 6
Limits, continuity, differentiability
(1) Given the function
x 1 if x < 3
x2 + 1 if 3 x 7
f (x) =
2 x if x > 7
calculate
(i)
x3
lim f (x)
(iii) lim f (x)
(ii) lim + f (x)
(iv) lim+ f (x)
x7
x7
x3
(2) (a) Draw the
MTH1020 Analysis of Change
Problem Set 5
Logarithms and exponentials
(1) Which of the following statements are true, and which are false? Explain your answers.
(a) For any positive a and x, loga x3 = 3 loga x.
(b) log2 10 = log2 (5) + log2 (2).
(c) For an
MTH1020 Analysis of Change
Problem Set 7
Differentiability, differentiation techniques
d
1
2
(1) Use the definition of derivative to prove that
= 3.
2
dx x
x
(2) Find the derivatives of the following functions.
1
(i) y = 7 x
2 x
(vii) f (x) = (3 x2 ) co
MTH1020 Analysis of Change
Problem Set 4
1. Vectors cross products
(1) Some determinants. Useful practice for the determinant for cross products. Calculate
the following 2 2 determinants.
2 4
0 1
1 35
3 0
(g)
(e)
(c)
(a)
3
1
1
1
0
1
0
7
a b
3 2
1
MTH1020 Analysis of Change
Problem Set 3
(1) Let p = 5j and q = 3i + 3j.
(i) Find |p| and |q|.
(ii) Plot position vectors for p and q. From the diagram, find the angle between p and
q.
(iii) Using your answer to the previous two parts, calculate p q geome
Differentiation
WHAT IS THE DERIVATIVE OF A FUNCTION?
An example: average and instantaneous velocity
Suppose a particle is moving in a straight line so that, at time seconds, it is () = 2 metres
from the origin.
What is the particles average velocity over
MTH1020 Analysis of Change
Problem Set 2
Complex numbers
(1) Express the following in Cartesian form.
(a) exi
(b) 4ei
(c) 3e 2 i
5
(d) 2e 6 i
(e) e2+4i
2
(f) iexi
(g) (2 3i)e 2 i
(h) e4+3xi
(i) e3 3 i
(j) (2 i)e(3+4i)x
(2) Find:
(a) Im [e2xi ]
(b) Re e(2
Vectors
WHAT IS A VECTOR?
For the purposes of this course, a vector is a quantity that has length and direction.
(Sometimes we say magnitude rather than length.)
We can represent a vector geometrically by an arrow; its length represents the vector's
magni
MTH1020 Analysis of Change
Problem Set 1
Complex numbers
(1) Practice your complex number arithmetic! Evaluate the following in standard Cartesian
form x + yi and then locate each answer on a separate Argand diagram.
2 3i
4i
3 i
(h)
8 + 6i
i4 + i9 + i16
(
MTH3251/ ETC3510
Tutorial 2.
1. Consider simple random walk Xn = 5 + ni=1 Yi , where Yi are i.i.d. random
variables taking values 1 or -1 each with probability 1/2. Denote by the
minimum between time 1000 and the first time Random Walk Xn hits 0. In
other
MTH3251/ ETC3510
Tutorial 3.
1. Q2 Set 3. Let Xn , n = 0, 1, 2, . . . denote an unbiased Normal Random Walk.
X0 = 10, and Xn+1 = Xn + Yn+1 , with cfw_Yn are i.i.d. N (0, 1).
(a) Show that Xn is a martingale. Give EX20 .
(b) Show that Mn = Xn2 n is a mart
Promise
In 1989 an 8.2 earthquake almost flattened America, killing over 30,000
people in less than four minutes. In the midst of utter devastation and chaos,
a father left his wife safely at home and rushed to the school where his son
was supposed to be,
Promise
In 1989 an 8.2 earthquake almost flattened America, killing over 30,000
people in less than four minutes. In the midst of utter devastation and chaos,
a father left his wife safely at home and rushed to the school where his son
was supposed to be,
CONDITIONS OF USE
These slides are restricted for use in Introduction
to Management at RMIT University.
Any other use or application will be considered a
breach of copyright.
RMIT University 2017
1
Topic 7: approaches to
Academic
HUMAN TNE:
developing
com
CONDITIONS OF USE
These slides are restricted for use in Introduction
to Management at RMIT University.
Any other use or application will be considered a
breach of copyright.
RMIT2017
1
Academic approaches to
Topic 6: TNE:
developing
competencies,
ORGANIS
Topic 5: Managing Socially Responsible and Ethical Behaviour
Tutorial activity prepared by Dr. M Heffernan, O.A.M. 2016
Pre-reading: 7-Eleven wage abuse scandal has lessons for all directors
http:/www.afr.com/business/retail/7eleven-wage-abuse-scandal-has
2016: Introduction to Management Topic 6: Leadership
Developed by Prof. Martin Wood
Focus
Tutorial Questions
1.
2.
3.
4.
Why do we have such a fascination with leaders?
Is it the leaders in organisations who make things happen?
What does it mean to lead?
N
Student News
Students lack the skills and discipline
essential in a workplace, warns boss
School leavers and graduates need to show more human skills to enter
the world of work
Richard Jinman | Sunday 16 August 2015 01:45 BST | P 0 comments
A good degre
MTH3251/ ETC3510
Tutorial 3.
1. Q2 Set 3. Let Xn , n = 0, 1, 2, . . . denote an unbiased Normal Random Walk.
X0 = 10, and Xn+1 = Xn + Yn+1 , with cfw_Yn are i.i.d. N (0, 1).
(a) Show that Xn is a martingale. Give EX20 .
(b) Show that Mn = Xn2 n is a mart
MTH3251/ ETC3510
Tutorial 1 with Solutions.
1. Let Z have standard Normal distribution N (0, 1).
(a) Show that E(Z) = 0 and V ar(Z) = 1.
(b) Use Excel to generate 20 observations of Z. Use commands:
RAND() returns an observation from U(0,1) distribution (
MTH3251/ ETC3510
Tutorial 2.
1. Consider simple random walk Xn = 5 + ni=1 Yi , where Yi are i.i.d. random
variables taking values 1 or -1 each with probability 1/2. Denote by the
minimum between time 1000 and the first time Random Walk Xn hits 0. In
other
School of Mathematical
Sciences
MTH3251
Financial Mathematics
ETC3510
Modelling in Finance and
Insurance
Exercise Book
Semester 1, 2017
1
Random variables and distributions: Review
1. Show that the mean of N (, 2 ) distribution is .
2. Show that the varia
MTH3020
Assignment 1
2015
MTH3020 COMPLEX ANALYSIS AND INTEGRAL
TRANSFORMS
Assignment 1
Complete the following questions. They are due on Friday of Week 5 at
3 pm and should be submitted in the appropriate box located on the ground
floor of building 28.