Department of Mathematics
MATH335 - Mathematical
Methods
Unit Syllabus
Special Functions:
- Second order linear ordinary differential equations, power series solutions.
- Legendre functions.
- Bessel functions.
- Classical Orthogonal polynomials.
- Gamma function.
- Sturm-Liouville problems, properties of the solutions, eigenvalues, eigenfunctions.
- Series expansions in orthogonal functions.
Ordinary Differential Equations:
- Introduction. First order equations.
- Existence & uniqueness, successive approximations.
- Second order linear equations, fundamental sets, reduction of order.
- Higher order linear equations. > Linear equations with constant coefficients.
- First-order linear systems: fundamental set of solutions. Systems with constant coefficients
- Critical points and stability. The phase plane and stability of linear systems.
- Non-linear systems and stability.
- Limit cycles and stability.
