Advanced engineering mathematics
Graduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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$1,162 · Advanced engineering mathematics · 18 tutoring hrs
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Topics typically covered
Standard syllabus
Integral transforms and complex methods
- Laplace and Fourier transforms: advanced properties and inversion
- Mellin transforms (introduction)
- Complex contour integration for transform inversion
- Wiener–Hopf methods (introduction)
- Discrete transforms and FFT applications at scale
Special functions and orthogonal expansions
- Bessel, Legendre, and Hermite functions; recurrence and orthogonality
- Sturm–Liouville problems and eigenfunction expansions
- Green's functions for boundary-value problems
- Multidimensional separation of variables
- Asymptotics of special functions (introduction)
PDE methods for engineers
- Classification and canonical forms of linear PDEs
- Method of characteristics for first-order systems
- Variational formulations of elliptic problems (introduction)
- Integral equation formulations (introduction)
- Well-posedness and engineering interpretation of boundary conditions
STEM / applied
Computational engineering mathematics
- Spectral methods for PDEs (introduction)
- Finite element and finite volume overview for multiphysics
- High-performance computing for large simulations
- Uncertainty propagation in engineering models
- Coupled field problems: thermal–structural, electro-mechanical (overview)
Case studies
- Signal and image processing pipelines using transform methods
- Structural dynamics and modal superposition
- Electromagnetics and waveguides (mathematical models)
- Transport phenomena and diffusion with sources
- Benchmark problems linking analytical and numerical solutions
Notes
Topics reflect common graduate advanced engineering mathematics syllabi at US universities, often serving engineering PhD students alongside applied math offerings.