Applied Mathematics
MP345: Mathematical Methods I (5 ECTS)
This course introduces some advanced methods of mathematical physics for solving ordinary differential equations, and presents some applications of complex analysis.
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:
- 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
This is a course on mathematical methods, and amongst the topics covered are:
- solution methods for second order linear differential equations with constant coefficients and special ODEs;
- power series and Frobenius series solutions of second order linear ordinary differential equations with variable coefficients;
- orthogonality relations for trigonometric functions, Legendre functions, and Bessel functions;
- the calculation of some real integrals using complex contour integration;
- complex analytic functions.
Module Resources
E. Kreyszig, Advanced Engineering Mathematics, Wiley
Back