M.E. 8000, a 2nd Advanced Engineering Mathematics course and a follow-up to M.E. 7000, was first offered in the Spring 2012 semester. It was offered in the Spring 2014, Spring 2016, and Spring 2018 semesters. It is unknown when it will be offered next. The course outline for the Spring 2018 version of ME 8000 is provided below.
ME 8000 Course Outline – Spring 2018
| Meeting | Meeting Topics | Lecture Handouts | Lecture Notes | HW Assignments | HW Solutions | Quiz | Quiz Solution |
| 1 | Â Integral Equations: Introduction, Green’s Function | ||||||
| 2 | Â Integral Equations: Fredholm equations, Hilbert-Schmidt Theory | ||||||
| 3 | Â Integral Equations: Iterative and Approximate methods | ||||||
| 4 | Â Calculus of Variations: Maxima and Minima; Statement of the Basic Problem | ||||||
| 5 | Â Calculus of Variations: Constraints; Natural Boundary Conditions; Higher Order Problems | ||||||
| 6 |  Calculus of Variations: Hamilton’s Principle; Deformable Bodies; Approximate Methods | ||||||
| 7 |  Mid-Term Examination – In-Class | ||||||
| 8 | Â Analytical Functions: Complex Variables, Cauchy -Riemann eqns, Cauchy integrals, Line integrals | ||||||
| 9 | Â Analytical Functions: Laurent Series, Singularities, Residues | ||||||
| 10 | Â Analytical Functions: Real Definite Integrals, Practical Applications, Conformal Mapping | ||||||
| 11 | Â Perturbation Theory – Introduction, Asymptotic Series, Asymptotic Expansions | ||||||
| 12 | Â Perturbation Theory – Quadratic Eqns, Higher Order Eqns, Transcendental Eqns | ||||||
| 13 | Â Perturbation Theory – Integrals | ||||||
| 14 | Perturbation Theory – Ordinary Differential Equations | ||||||
| 15 | Final Examination – in class |