MAS192 Differential and Difference Equations (NJTech)
|Semester 1, 2016/17||10 Credits|
|Lecturer:||Dr Istvan Ballai||Reading List|
This unit introduces students to differential and difference equations, which are fundamental to many areas of applied mathematics. The course is based around techniques for solving elementary first and second order differential and difference equations, using both analytic and simple numerical methods. The use of the computer algebra package Maple to solve problems is an important part of the course. The course also explores one area in which the techniques learned can be applied, namely population dynamics.
There are no prerequisites for this module.
No other modules have this module as a prerequisite.
- Introduce elementary techniques for solving first and second order differential and difference equations;
- Introduce some simple applications of differential and difference equations in population dynamics.
- Be able to solve simple first and second order differential and difference equations;
- Understand simple applications of differential and difference equations in population dynamics and real life applications, e.g. interest calculation, simple harmonic oscillator, etc.
32 lectures, 32 tutorials
One formal 2 hour written examination. All questions compulsory.
- Integration: Revision of indefinite integrals and integration methods
- First order differential equations: definition, variable separation, integrating factor, homogeneous differential equations, Ricatti-type differential equations, applications
- Second order differential equations: homogeneous/non-homogeneous, the method of undetermined coefficients, Euler-Cauchy differential equation, the problem of forced oscillators (resonance, damping).
- Population dynamics: one species models (the Malthusian model, the logistic model, the problem of constant harvesting, equilibrium levels), two-species models (the prey-predator model, the Lotka-Volterra equations)
- Discrete mathematics and difference equations: First order linear difference equations, second order homogeneous and non-homogeneous difference equations and application to finance.
|B||Boyce and DiPrima||Elementary Differential Equations and Boundary Value Problems||Blackwells||Amazon|
|B||Fulford, Forrester and Jones||Modelling with differential and difference equations||Blackwells||Amazon|
|B||Jones, Plank and Sleeman||Differential equations and Mathematical Biology||Blackwells||Amazon|
|B||Jordan and Smith||Mathematical Techniques||Blackwells||Amazon|
|B||Kelley and Peterson||Difference equations: an introduction with applications||Blackwells||Amazon|
|B||Kreyszig||Advanced Engineering Mathematics||Blackwells||Amazon|
|B||Swokowski||Calculus with analytic geometry||Blackwells||Amazon|
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop on Mappin Street.