Standard syllabus
Advanced engineering mathematics · Undergraduate · Math
Topics
Integral transforms and special functions
- Laplace transforms: advanced properties and convolution
- Inverse Laplace transforms and Bromwich integrals (introduction)
- Fourier transforms and discrete transforms
- Bessel functions and orthogonal expansions (introduction)
- Legendre polynomials and Sturm–Liouville problems (overview)
Partial differential equations
- Classification and canonical forms of second-order PDEs
- Separation of variables for heat, wave, and Laplace equations
- Nonhomogeneous PDEs and eigenfunction expansions
- Green's functions for boundary-value problems (introduction)
- Method of characteristics for first-order PDEs (brief)
Complex analysis for applications
- Analytic functions and Cauchy–Riemann equations (applied view)
- Contour integration and residue calculus for real integrals
- Conformal mapping in potential theory (introduction)
- Branch cuts and multivalued functions in engineering models
- Inverse problems and analytic continuation (overview)
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$1,162 · Advanced engineering mathematics · 18 tutoring hrs
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