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Department of Mathematics
MATH335 - Mathematical
Methods
Unit Syllabus
Fourier Analysis:
- Algebraic background to Fourier series.
- Fourier series, pointwise convergence,
Dirichlet's theorem, uniform convergence, Parseval's identity,
uniqueness.
- Gibbs phenomenon, differentiation and
integration of Fourier series.
- Fourier transforms, inverse Fourier
transforms, Plancherel's identity, convolution.
- Use of the residue theorem to calculate
Fourier transforms.
- Applications to partial differential
equations and signal processing.
Ordinary Differential Equations:
- First order linear equations, isoclines,
linear equations, existence and uniqueness of solutions, successive
approximations.
- Second order linear equations, fundamental
sets, reduction of order, non-homogeneous equations, variation
of parameters, Green's functions.
- Higher order linear equations.
- Linear equations with constant coefficients.
- First order linear systems, fundamental
set of solutions.
- First order linear systems with constant
coefficients, matrix exponentials.
- Critical points and stability, the phase
plane, stability of linear systems.
- Non-linear systems and stability.
- Limit cycles and stability.
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