38
2
First-Order Linear
Difference Equations
2.1
Aims
In this chapter we focus on solving
first-order difference equations of the
form
xn axn1 = b(n) ,
n 1.
(2.1)
In equation (2.1) a is a constant, b(n) is
a function of n and xn is the
state variable whos
Differential Equations: Introduction. . .
8
Differential Equations:
Introduction, Definitions
and Basic Concepts
8.1
Aims
After working through this chapter
you will be able to:
1. recognise DEs and have an appreciation of circumstances when
they arise in
179
Harvesting
6
6.1
Harvesting
Introduction
Consider an animal species that is
harvested or hunted, e.g. deer, fish or
rabbits. In this chapter, we study two
harvesting, or hunting, strategies for
this population.
Although the basic ideas are very
simple
Applications of First-Order DEs: Lake Pollution
10
Applications of
First-Order
Differential
Equations: Lake
Pollution
10.1
Aims
In this chapter we apply the techniques
that we learnt in chapter 9 to a variety
of problems that are based upon the
model deve
153
5
Linear Stability
Analysis of
Fixed-Points
5.1
Aims
After working through this chapter
you will
1. Be able to explain the importance of the concept of stability
when discussing fixed points.
2. Understand the ideas behind linear stability analysis.
1
First-Order Differential Equations
9
First-Order
Differential
Equations
9.1
Aims
In this chapter we focus on solving
first-order differential equations. We can
write a first-order differential equation
in the general form
dy
= f (y, x) .
dx
267
First-Orde
First Order Difference Equations: Concluding Thoughts
7
7.1
First Order Difference
Eqs : Concluding
Thoughts
Revision of key ideas
In chapters 16 we have encountered a
variety of ideas relating to the analysis of
first-order difference equations and
mathe
3.1
Applications of First-Order Difference
Equations: Finance
Aims
In this chapter we will derive first-order difference equations for
some common financial problems. We will do this by applying
the principles from chapter 1 that
change in reasons why
1
1
Introduction,
Definitions and
Basic Concepts
1.1
Aims
After working through this chapter you
will be able to:
1. recognise difference equations and
have an appreciation of circumstances when they arise in physical
problems;
2. undertake the process of
First-Order Non-Linear Difference Equations: An Introduction110
4
4.1
First-Order Non-Linear
Difference Equations
Introduction
First-order non-linear difference equations.
Motivation: population models for a single
species.
Population of the next gener