Applied Mathematics
MP232: Mathematical Methods II (5 ECTS)
This is a mathematical methods course that considers the following topics: Laplace transforms, vector calculus, multiple integration and integral theorems
Taught in Semester(s) II. Examined in Semester(s) II.
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 the Laplace transforms of some elementary functions;
- calculate the inverse Laplace transform of some elementary functions using standard techniques;
- solve various initial value problems for ordinary differential equations using Laplace transforms;
- calculate the gradient and directional derivative of a scalar field and be able to interpret these quantities;
- calculate the divergence and curl of a vector field and be able to interpret these quantities;
- find the normal of a surface, find the tangent plane to a surface, and calculate surface integrals;
- calculate volume integrals and be able to verify the divergence theorem for elementary volumes and vector fields;
- verify Stoke's theorem for elementary vector fields and surfaces.
Indicative Content
- Laplace transforms: Laplace transforms of elementary functions, the shift theorems, inverse Laplace transforms, Laplace transforms of derivatives, the convolution theorem,solving initial value problems for ordinary differential equations using Laplace transforms.
- Curves and line integrals.
- The divergence, the gradient and the curl, conservative vector fields.
- Parametrisation of surfaces, normal to a surface, tangent plane to a surface, surface integrals.
- Volume integrals, the divergence theorem, examples.
- Stoke's theorem, examples.
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.
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