X2 Applied Mathematics 1998/99

(Syllabus)

Look though these pages to find the exercises. Where you see the "Course Work" lables like these to the left and right do whatever it tells you. You should, of course, read all the material on these pages. You may be expected to know it!

Population models

These will be dealt with in two sections

• Single population models
  These models look at both continuous evolution and discrete evolution of a population of a single species.
• Two population models
  These models look at the continuous evolution of a population which consists of two species. There are two sorts that we examine:
1. Competing Species
   This is the rabbit-sheep model where both are competing for the same food supply.
2. Predator-Prey model
   This is the rabbit-fox model where one of the species preys on the other. There are two variants on this model that we examine:
• A simpler model
• A more elaborate model
3. Symbiosis
   This is the rabbit-sheep model modifed so that the the presence of both is mutually beneficial.

Optimisation: Linear Programming

• A two variable problem
  This problem was covered in the lectures.
• A two variable problem
  This is similar to the previous problem.
• A three variable problem
  One more degree of complexity that makes a graphical solution a bit more difficult.
  

Dynamics

• Motion of a particle
  This looks at the motion of a particle in a uniform gravitiational field with different models of drag.
  
• Motion of a planet
  This looks at the motion of a planet in a radial gravitational field for different initial conditions and power laws for the radial force.
  
• Forced damped simple harmonic motion
  Here we look at the motion of a force dampled oscillator such as a pendulum on the assumption the the amplitude of the oscillations are small.
  
• Forced damped simple pendulum
  The oscillations of a forced pendulum with damping is investigated. The swing of the pendulum is no longer considered to be small. This can lead to irregular motions...
  

Waves

• Waves in an unbounded domain
  We look at solutions of the initial value problem for wave equation in an unbounded domain.
  
• Waves in an bounded domain I
  Here we investigate solutions of the boundary value problem for wave equation in a domain restricted by one boundary.
• Waves in an bounded domain II
  Here we investigate solutions of the wave equation between two boundaries.
• Sound waves in a "box guitar"
  The difference in the sound waves depending on where the string is plucked.

Past Exam Papers

• Applied Mathematics and Numerical Analysis (1998) is located on the 1998 Exams page
• Applied Mathematics and Numerical Analysis Resit (1998) (in PDF format)