DIFFERENTIAL EQUATIONS
EXAMPLE SHEET 2
You should make some attempt on all the questions on this sheet but only part of
the A questions and questions in section B will be marked for credit, and must be
handed in to your supervisor via the supervisors pige
Things to think about - Workbook 2
1
Playing with definitions
Recall that
Definition 1.1. The seqeuence (an ) if for all C > 0 there exists N N such that for all
n > N , an > C.
Definition 1.2. The seqeuence (an ) 0 if for all > 0 there exists N N such th
Things to think about - Workbook 2
1
Playing with definitions
Recall that
Definition 1.1. The seqeuence (an ) if for all C > 0 there exists N N such that for all
n > N , an > C.
Definition 1.2. The seqeuence (an ) 0 if for all > 0 there exists N N such th
Analysis I - Inequalities
Here are some practise questions to test your ability to solve inequalities.
The first ones are relatively straightforward, but the later ones are trickier.
You may wish to use case analysis on some of these.
1. Solve
x+1
<2
x
2.
Analysis I - Inequalities
Here are some practise questions to test your ability to solve inequalities.
The first ones are relatively straightforward, but the later ones are trickier.
You may wish to use case analysis on some of these.
1. Solve
x+1
<2
x
AN
Welcome to Analysis 1
Each week you will get one workbook with assignments to complete.
Typically you will be able to get most of it done in class and will
finish it off by yourselves. In week one there are no classes and so
you have no access to help wh
Analysis 1 - Why not just rearrange it?
Alex Wendland
November 27, 2015
Why define series as we do?
We all know what we mean by a finite sum and that we can rearrange it freely,
2+3+4=3+2+4=4+2+3=2+3+4=3+4+2=4+2+3=9
So when we deal with an infinite sum, c
DIFFERENTIAL EQUATIONS
EXAMPLE SHEET 3
You should attempt all the questions on this sheet but only part of a question in
section A and the questions in section B will be marked for credit, and must be
handed in to your supervisor via the supervisors pigeo
DIFFERENTIAL EQUATIONS
EXAMPLE SHEET 1
You should attempt all the questions on this sheet but a small amount of the A
questions and questions in section B will be marked for credit, and must be handed
in to your supervisor via the supervisors pigeon loft
Analysis I, Group C2, Mon 26th October 2015
Let (an ) be a sequence and a R. Let (ani ) and (ami ) be subsequences. What
type of sequences do each of the following definitions describe? Note that since
convergent sequences are bounded, it is sufficient to