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MT2003 APPLIED MATHEMATICS
AimsTo introduce students to applied mathematics through the construction, analysis and interpretation of mathematical models for problems arising in the natural sciences, and to introduce students to the techniques of analysis used in mathematical modelling, such as numerical methods, dimensional analysis, solution of ordinary and partial differential equations.
Mathematical models from population dynamics, Newtonian dynamics and wave motion that lead to ordinary and partial differential equations are developed in detail, and the basic elements of vector calculus in three dimensions are introduced.
ObjectivesBy the end of the course the students should be familiar with:
- Kinematics and the vector formulation of Newton's Laws
- Newtonian model of gravity, motion in constant gravity and particle motion under a variable force
- The energy equation as first integral of equation of motion, the concepts of kinetic and potential energy
- Motion of a particle under various forces
- P.D.E.'s, including wave equation, heat equation and Laplace equation
- Waves on a string, d'Alembert's solution, principle of superposition, application of boundary conditions, use of Fourier analysis
- Solution of algebraic equations by iterative methods
- Solution of ordinary differential equations by numerical methods
- Principles of mathematical modelling
- Basic vector calculus including the differential operators div, grad and curl
- Integration involving vector quantities, Green's Theorem, Stokes's Theorem and Divergence Theorem.
NEWTON D'ALEMBERT FOURIER STOKES LAPLACE
SyllabusAn outline of the syllabus is as follows:
Mathematical Modelling (10 lectures)
Newtonian Mechanics (7 lectures)
Numerical Methods (8 lectures)
Vector Calculus (17 lectures)
Partial Differential Equations (9 lectures)
TextbooksAdvanced Engineering Mathematics E Kreyszig; Wiley, 2001.
Vector Analysis M R Spiegel; McGraw-Hill; 1959.
Calculus R A Adams; Pearson Addison Wesley; 2006
Lectures, practicals and tutorialsThe average load, in hours per week, is as follows:
Maths lab: 2
These figures do not include the revision & exam period at the end of each semester.
Assessment30% of the assessment mark is from continuous assessment during the semester; 70% is from a 3 hour exam at the end of the semester.
Re-assessment is entirely by a 3 hour exam in August.
PrerequisitesMT1002 and MT2001
AvailabilityThis module is taught every year in Semester 2 at 12.00.
LecturersDr A N Wright (Module coordinator), Dr A P Naughton, Dr A L Haynes
Click here for access to past examination papers for this module.
Click here to see the University Course Catalogue entry.
Revised: PMH (December 2013)