Hand in at lecture on Thursday 4th October, 2012
Mathematics 2C Assignment
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Tutorial TU
Total
(i) The ground state energy E (in J) of the single electron in a hydrogen atom is known to depend
on the
Extra tutorial questions (supplement to sheet 1)
Q 1. The escape velocity v of a spherical planet is the speed at which a projectile must be launched
from the planets surface in order to escape to innity. The escape velocity is conjectured to depend
on th
School of Mathematics and Statistics
Example Sheet 5
Class 2C
Q 45. For each of the following ODEs, nd the equilibrium point(s), the linearization about each of these
points and whether or not they are stable
(a)
dN
= a bN
dt
(b)
dN
= a(N b)N
dt
(c)
dN
=
School of Mathematics and Statistics
Example Sheet 2
Class 2C
In the following, the vectors e1 , e2 and e3 are unit, mutually perpendicular vectors that form a right-handed
triad.
Q 16.
If a = t2 e1 + (2t + 1)e2 + te3 and b = (t 1)e1 te2 + e3 determine
(i
School of Mathematics and Statistics
Example Sheet 1
Class 2C
Q 1. A spherical soap bubble is seen to undergo oscillations when slightly deformed. Assuming that the
frequency of these oscillations is a function of the surface tension S of the soap bubble,
School of Mathematics and Statistics
Example Sheet 4
Class 2C
Q 37. It is observed that a population of size N0 doubles in size after D units of time. Using the exponential
model
dN
= N,
dt
where N is the population at time t, show that
N = N0 2t/D .
The
School of Mathematics and Statistics
Example Sheet 3
Class 2C
In the following, the vectors e1 , e2 and e3 are unit, mutually perpendicular vectors that form a right-handed
triad.
Q 27. Two particles, A and B, move with constant velocities xA = 2e1 + e2 a
School of Mathematics and Statistics
Example Sheet 7
Class 2C
Q 58. A billiard ball A of mass 2m moving to the right with speed v collides with a second ball B of mass
m moving in the opposite direction with speed 2v. If the ball A rebounds with speed v t
School of Mathematics and Statistics
Example Sheet 9
Class 2C
Q 74. A y crawls along the spoke of a bicycle wheel of radius R, starting at the centre of the wheel. The
y lies at a distance r(t) from the centre of the wheel and r(t) satises
dr
= (R r)
dt
w
School of Mathematics and Statistics
Example Sheet 8
Class 2C
Q 65. Two springs with spring constants k1 and k2 are connected to a block of mass m which rests on a
smooth table as shown in Figure 1.
L
k1
k2
m
Figure 1: Conguration of mass m connected by s
School of Mathematics and Statistics
Example Sheet 6
Class 2C
Q 49. A colony of rabbits of initial size 20 with a growth rate of 10% per month is culled by the local
farmer at a rate of 20 per year. Use the exponential model to determine the number of rab
Ofce Hours: 13:30-14:30 Mon, Tues, Thurs, in maths 308 1
You must hand in your feedback exercise on the scannable paper
for 2E feedback exercise 1, which can be collected from a box on the
front counter of the school ofce during the opening hours of the
o
Ofce Hours: 13:30-14:30 Mon, Tues, Thurs, in maths 308 1
You must hand in your feedback exercise on the scannable paper
for 2E feedback exercise 1, which can be collected from a box on the
front counter of the school ofce during the opening hours of the
o
I 0835186130 I
Maths 2E Feedback Exercise Deadline: 3:00pm Friday 14th February 2014
Student Details:
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Write Answer Below (continue on back of form if necessary)
1
Ofce Hours: 13:30-14:30 Mon, Tues, Thurs, in maths 308 1
You must hand in your feedback exercise on the scannable paper
for 2E feedback exercise 4 which can be collected from a box on the
front counter of the school ofce during the opening hours of the
of
Ofce Hours: 13:30-14:30 Mon, Tues, Thurs, in maths 308 1
You must hand in your feedback exercise on the scannable paper
for 2E feedback exercise 3, which can be collected from a box on the
front counter of the school ofce during the opening hours of the
o
3/17/2014
WebAssign
2E Assignment 9
Velin Kerkov
2E Introduction to Real Analysis, Spring 2014
Instructor: Andrew Wilson
Due : Tuesday, March 18 2014 03:00 AM GMT
2E Assignment 9 (Homework)
Current Score : 15 / 20
1. 1/1 points | Previous Answers
2. 1/1 p
2/24/2014
WebAssign
2E Assignment 6
Yana Staneva
2E Introduction to Real Analysis, Spring 2014
Instructor: Andrew Wilson
Due : Tuesday, February 25 2014 03:00 AM GMT
2/3 submissions
2E Assignment 6 (Homework)
Current Score : 20 / 20
1. Question Details
2.
3/9/2014
WebAssign
2E Assignment 8
Yana Staneva
2E Introduction to Real Analysis, Spring 2014
Instructor: Andrew Wilson
Due : Tuesday, March 11 2014 03:00 AM GMT
1/3 submissions
2E Assignment 8 (Homework)
Current Score : 11 / 20
1. Question Details
2. Que
2E Assignment 7
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WebAssign
2E Assignment 7 (Homework)
Current Score : 9 / 20
Due : Tuesday, March 4 2014 03:00 AM GMT
Iva Babukova
2E Introduction to Real Analysis, Spring 2014
Instructor: Andrew Wilson
1/3 sub