Applied Mathematics
MP553: Advanced Applied Mathematics for Engineers 1 ( ECTS)
This course introduces some advanced methods of applied mathematics for solving ordinary differential equations and using complex analysis, with a view to engineering applications. The topics covered include: 1. Linear Second Order Ordinary Differential Equations; 2. Power Series Solutions; 3. The Frobenius Method; 4. Special Equations; 5. Complex Analysis; 6. Application to vibrations, waves, flows.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 34 hours (24 Lecture hours, 10 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Find the general solution to a second-order linear differential equation with constant coefficients when it is homogeneous, and a particular solution when it is inhomogeneous;
- Find a second, linearly independent, solution to a second-order differential equation when one is known;
- Compute the first few terms of a power series or Frobenius series solution to a second-order linear equation with variable coefficients, when it exists;
- Derive orthogonality relations for trigonometric, Legendre and Bessel functions;
- Compute real integrals using the theorems of complex contour integration;
- Draw fields described by complex analytic functions.
Indicative Content
ordinary differential equations; series solutions; special functions; vibrations, waves, flows.
Module Resources
E. Kreyszig, Advanced Engineering Mathematics, Wiley
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