Applied Mathematics
MP231: Mathematical Methods I (5 ECTS)
This course covers mathematical methods (principally from Calculus) that are important in applications. Included are differentiation and integration of functions of multiple variables and associated applications such as optimization (Lagrange Multipliers), critical points, Fourier series, and area/volume calculations.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Calculate partial differentials of a function of two or three variables, and determine the critical points of functions of two variables, including constrained systems using Lagrange multipliers.
- Determine Fourier series for periodic functions; utilize even/odd properties of functions to optimize Fourier series calculations; define the periodic extension of a function defined in an interval.
- Carry out multiple integrals of a function; interpret results in terms of area and/or volume; calculate the area bounded by multiple curves.
- Exhibit Green's theorem by calculating the relevant double integral and single (line) integrals.
Indicative Content
- Partial differentiation;
- Critical points in the plane and Lagrange multipliers;
- Optimisation with the Lagrange multiplier method;
- Fourier Series;
- Double and line integrals in the plane;
- Green’s theorem in the plane.
Module Resources
Glyn James : 'Modern Engineering Mathematics' Pearson-Prentice Hall 4th edition.
Advanced Engineering Mathematics, 10th Edition, E. Kreyszig, John Wiley & Sons.
Riley, Hobson & Bence: 'Mathematical Methods for Physics and Engineering', Cambridge University Press (2002)
Back