Means and Variances for some commonly used
distributions
Distribution
Mean
Variance
Bernoulli-
(1 )
Binomial B (n, )
n
n(1 )
Poisson Po()
Uniform U (a, b)
a +b
2
Normal N (, 2 )
(ba)2
12
2
Standard Normal N (0, 1)
0
1
Exponential Exp()
1
1
2
G Glonek (Uni
MATHS 2201 Engineering Mathematics IIA
Assignment 1, 2013
Due: 5:00pm, Tuesday 19 March (week 3) 2013.
1. A recent study found that 17.8% of passenger vehicles had defective tyres and 13.0%
had defective brakes. Assume further that 25% of vehicles with de
Practice Questions
Digital Systems (ELEC ENG 2100)
Last revised: February 21, 2017
These exercises are intended to reinforce the learning outcomes from ELEC ENG 2100 Digital Systems.
Many of the exercises are drawn directly from the course textbook, Digit
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 10, Week 11
1. Consider the function f (x) = | sin x| for < x < and f (x + 2) = f (x) for all x.
Sketch the function and find its Fourier series.
2. Consider the function
f (x) =
x
`
0<x`
L x
L`
`<x<L
(a
MATHS 2201 Engineering Mathematics I Tutorial Exercise 4
Week of 26 March 2012
1. For each of ten streets with bicycle lanes, investigators measured the distance between the centre
line and a cyclist in the bicycle lane. They used photography to determine
MATHS 2201 Engineering Mathematics I Tutorial Exercise 1
Week of 5 March 2012
1. A pair of fair dice are rolled and the total of the two faces is calculated.
(a) Write down the sample space for this experiment.
(b) Find the probability that the total is a
MATHS 2201 Engineering Mathematics I Tutorial Exercise 1
Week of 5 March 2012
1. A pair of fair dice are rolled and the total of the two faces is calculated.
(a) Write down the sample space for this experiment.
Solution:
Note: In these solutions, the dots
MATHS 2201 Engineering Mathematics I Tutorial Exercise 4
Week of 26 March 2012
1. For each of ten streets with bicycle lanes, investigators measured the distance between the centre
line and a cyclist in the bicycle lane. They used photography to determine
MATHS 2201 Engineering Mathematics I Tutorial Exercise 3
Week of 19 March 2012
1. The paper Ultimate Load Capacities of Expansion Anchor Bolts (J. Engr. Energy, 1993, pp.
139-158) reports the following summary data on shear strength for a sample of 3/8 in
MATHS 2201/7201, Engineering Mathematics IIA
Tutorial 10, Week 11
1. Consider the function f (x) = | sin x| for < x < and f (x + 2) = f (x) for all x.
Sketch the function and find its Fourier series.
2. Consider the function
f (x) =
x
`
0<x`
L x
L`
`<x<L
MATHS 2201/7201, Engineering Mathematics IIA
Tutorial 6, Week 7
1. The functions y1 (x) = 1, y2 (x) = sin x and y3 (x) = cos x are all solutions of the third-order
ODE
y (3) + y 0 = 0
(1)
for < x < . Calculate the Wronskian of y1 , y2 and y3 . Are these f
MATHS 2201 Engineering Mathematics IIA Tutorial 2
1. Suppose the diameters of pistons produced by a certain manufacturer are normally distributed
with mean 120mm and standard deviation 0.2mm. The diameters of the corresponding cylinders
are normally distr
MATHEMATICS IB - SEMESTER 1, 2012
Tutorial 3 Algebra Solutions
ALGEBRA
Problem: A vector u is said to be orthogonal to a subspace V Rn if u is orthogonal to every v V . Prove that u
is orthogonal to V if it is orthogonal to each vector in any basis for V
MATHEMATICS IB - SEMESTER 2, 2012
Tutorial 4 Solutions
ALGEBRA
Question:Let V be a subspace of Rn and u a vector in Rn . We showed in lectures that we can
write u = w1 + w2 , where w1 V and w2 is orthogonal to V. Show that this decomposition of u is
uniqu
MATHS 2201 Engineering Mathematics I Tutorial Exercise 2
Week of 12 March 2012
1. Suppose the diameters of pistons produced by a certain manufacturer are normally distributed
with mean 120mm and standard deviation 0.2mm. The diameters of the corresponding
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 8, Week 9
1. A simple model for torsional oscillation of a suspension bridge (such as the Tacoma Narrows
bridge) consists of a rigid rod of mass m and length 2l supported at either end by elastic
cables
MATHS 2201 Engineering Mathematics I Tutorial Exercise 2
Week of 12 March 2012
1. Suppose the diameters of pistons produced by a certain manufacturer are normally distributed
with mean 120mm and standard deviation 0.2mm. The diameters of the corresponding
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 9, Week 10
1. Consider the initial value problem
y 00 + xy 0 + (2x2 + 1)y = 0,
y(0) = 1,
y 0 (0) = 1.
(1)
(a) Find the first six terms of the power series solution of (1)
(b) Calculate successive approxi
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 6, Week 7
1. The functions y1 (x) = 1, y2 (x) = sin x and y3 (x) = cos x are all solutions of the third-order
ODE
y (3) + y 0 = 0
(1)
for < x < . Calculate the Wronskian of y1 , y2 and y3 . Are these fun
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 11, Week 12
1. By solving for each of the three cases > 0, = 0, and < 0, show that the eigenvalues
of the boundary value problem
X 00 X = 0,
X 0 (0) = 0,
X 0 () = 0
are n = n2 for n = 0, 1, 2, . . . , an
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 7, Week 8
1. Consider the nonhomogeneous ODE
y 00 + 4y 0 + 4y = r(x).
(1)
(a) Find the general solution of the associated homogeneous ODE of (1).
(b) Use the method of undetermined coefficients to find a
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 10, Week 11
1. Consider the function f (x) = | sin x| for < x < and f (x + 2) = f (x) for all x.
Sketch the function and find its Fourier series.
2. Consider the function
f (x) =
x
`
0<x`
L x
L`
`<x<L
(a
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 11, Week 12
1. By solving for each of the three cases > 0, = 0, and < 0, show that the eigenvalues
of the boundary value problem
X 00 X = 0,
X 0 (0) = 0,
X 0 () = 0
are n = n2 for n = 0, 1, 2, . . . , an
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 6, Week 7
1. The functions y1 (x) = 1, y2 (x) = sin x and y3 (x) = cos x are all solutions of the third-order
ODE
y (3) + y 0 = 0
(1)
for < x < . Calculate the Wronskian of y1 , y2 and y3 . Are these fun
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 5, Week 6
1. Flow out of Torrens Lake is controlled by a sluice gate, which can be raised to create
an opening at the bottom through which water can flow. Suppose that at time t = 0, an
electrical malfun
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 5, Week 6
1. Flow out of Torrens Lake is controlled by a sluice gate, which can be raised to create
an opening at the bottom through which water can flow. Suppose that at time t = 0, an
electrical malfun
MATHS 2201 Engineering Mathematics I Tutorial Exercise 3
Week of 19 March 2012
1. The paper Ultimate Load Capacities of Expansion Anchor Bolts (J. Engr. Energy, 1993, pp.
139-158) reports the following summary data on shear strength for a sample of 3/8 in
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 9, Week 10
1. Consider the initial value problem
y 00 + xy 0 + (2x2 + 1)y = 0,
y(0) = 1,
y 0 (0) = 1.
(a) Find the first six terms of the power series solution of (1)
(b) Calculate successive approximati
MATHS 2201 Engineering Mathematics IIA Tutorial Exercise 1
1. In cars with ABS brakes, faults occasionally occur with the wheel sensors and a warning light is
illuminated. It can also happen that the warning light comes on even when no fault is present.
I
MATHS 2201/7201, Engineering Mathematics IIA
Tutorial 8, Week 9
1. A simple model for torsional oscillation of a suspension bridge (such as the Tacoma Narrows
bridge) consists of a rigid rod of mass m and length 2l supported at either end by elastic
cable
MATHS 2201 Engineering Mathematics IIA
Assignment 3, 2017
Due: 12:00 noon on Tuesday 28th March (Week 5) 2017.
Note that for full marks, please show all working, give your matlab code and include
any matlab output or plots that are needed for your answers
C&ENVENG 2025
Strength of Materials II
Semester 1, 2017
Assignment 4:
Transverse shear (Chapter 6)
Transformation of stress and thin-walled pressure vessels (Chapter 7)
Due: 5pm Friday, 26 May 2017
The assignment should be done by students individually. S
C&ENVENG 2025
Strength of Materials II
Semester 1, 2017
Assignment 3: Bending and Beam
Due: 5pm Monday, 1 May 2017
The assignment should be done by students individually. Solution should start with a clear statement
of the problem, a summary of the given
School of Mathematical Sciences
Engineering Mathematics IIA, MATHS 2201
Assignment 8 question sheet
Due: Tuesday, 16/05/2017 (Week 10), by 12.00pm
When presenting your solutions to the assignment, please include some explanation in words
to accompany your
School of Mathematical Sciences
Engineering Mathematics IIA, MATHS 2201
Assignment 10 question sheet
Due: Tuesday, 30/05/2017 (Week 12), by 12.00pm
When presenting your solutions to the assignment, please include some explanation in words to
accompany you