Program Statistics
Visit Master's Program Statistics and PhD Program Statistics for statistics such as program admissions, enrollment, student demographics and more.
Engineering Sciences and Applied Mathematics
Degree Types: PhD, MS
The program in Engineering Science and Applied Mathematics educates students in mathematical methods and their application to various scientific and engineering fields.
Our program emphasizes techniques associated with asymptotic analysis, bifurcation theory, dynamical systems, numerical analysis, ordinary and partial differential equations, singular perturbations, stability theory, and stochastic processes. These techniques are employed to address problems arising in science and engineering including fluid mechanics, microbiology, neurobiology, ecology, geophysics, materials, diffusion processes, fiber optics, interfacial phenomena, pattern formation, solid mechanics, solidification theory, wave phenomena, and social sciences.
Students are given broad-based training encompassing mathematical methods and fields of science or engineering where significant applications of mathematics are made.
Additional resources:
Program Contact
Contact Ted Shaeffer
Program Assistant
847-491-3345
Degree Requirements
The following requirements are in addition to, or further elaborate upon, those requirements outlined in The Graduate School Policy Guide.
Master's
Total Units Required: 12
| Course | Title |
|---|---|
| ES_APPM 311-0 | Methods of Applied Mathematics |
| or ES_APPM 411-1 | Differential Equations of Mathematical Physics |
| ES_APPM 420-1 | Asymptotic and Perturbation Methods in Applied Mathematics |
| ES_APPM 446-1 | Numerical Solution of Partial Differential Equations |
| 1 unit from this list: | |
ES_APPM 312-0 | Complex Variables |
ES_APPM 322-0 | Applied Dynamical Systems |
ES_APPM 345-0 | Applied Linear Algebra |
ES_APPM 411-1 | Differential Equations of Mathematical Physics Only if ES_APPM 311-0 is used above as a core requirement. |
ES_APPM 411-2 | Differential Equations of Mathematical Physics |
ES_APPM 412-0 | Methods of Nonlinear Analysis |
ES_APPM 420-2 | Asymptotic and Perturbation Methods in Applied Mathematics |
ES_APPM 429-0 | Hydrodynamic Stability Theory |
ES_APPM 440-0 | Integral Equations & Applications |
ES_APPM 442-0 | Stochastic Differential Equations |
| 2 units from this list: | |
ES_APPM 444-0 | High Performance Scientific Computing |
ES_APPM 445-0 | Iterative Methods for Elliptic Equations |
ES_APPM 446-2 | Numerical Solution of Partial Differential Equations |
ES_APPM 447-0 | Boundary Integral Method |
ES_APPM 448-0 | Numerical Methods for Random Processes |
ES_APPM 449-0 | Numerical Methods for Moving Interfaces |
| Mathematical Modeling Electives (approved; 3 units) | |
| Mathematical Content Electives (approved; 3 units) | |
Other MS Degree Requirements
- Mathematical Content Electives Theme: Courses selected to complete the Mathematical Content Electives must have mathematically focused content related by a defined theme chosen by the student.
- Mathematical Modeling Electives Theme: Courses selected to complete the Mathematical Modeling Electives must be application areas that use mathematical methods and be related by a defined theme chosen by the student.
- At least three of the six courses used to satisfy the mathematical content and mathematical modeling themes must be at the 400/500 level.
- Master's Thesis (optional): Up to two units of the Mathematical Modeling Electives Theme may be replaced with ES_APPM 590-0 Research for work culminating in a Master's thesis consisting of original research and approved by a thesis committee.
Degree Requirements
The following requirements are in addition to, or further elaborate upon, those requirements outlined in The Graduate School Policy Guide.
PhD
Total Units Required: 18
| Course | Title |
|---|---|
| ES_APPM 411-1 | Differential Equations of Mathematical Physics |
| ES_APPM 411-2 | Differential Equations of Mathematical Physics |
| ES_APPM 420-1 | Asymptotic and Perturbation Methods in Applied Mathematics |
| ES_APPM 421-1 | Models in Applied Mathematics |
| ES_APPM 446-1 | Numerical Solution of Partial Differential Equations |
| GEN_ENG 519-0 | Responsible Conduct for Research Training |
| Electives (approved; 13 units) Up to 3 units may be taken outside of ES_APPM | |
Other PhD Degree Requirements
- Examinations: written preliminary examinations in differential equations, advanced calculus, complex variables and linear algebra; oral qualifying examination for admission to candidacy
- English Language Proficiency: meet The Graduate School's spoken English proficiency requirement to be a teaching assistant
- PhD Dissertation: original research, defended before student's doctoral committee
- Final Evaluations: oral presentation and faculty evaluation when all other requirements complete