Course Details

Methodology: Models, reality, properties of models, system characterization, steps in building in mathematical models, source of errors, dimensional analysis, model classification and illustration.
Case Studies related to R&D fields (one in each): Simulated Reality [Example: Traffic flow, Motion of Fibers, Behavior of Vehicles - Multi body systems, Behavior of Filters etc]; Optimization and Control [Example: Inverse problems and parameter identification, multi criteria optimization, Optimal shape design etc]; Multiscale models and algorithms [Example: Considering scenes of different scales nano, micro, mezzo and macro, Different algorithms on different scales and combining them]; Risks and decisions [Example: Portfolio optimization, Option pricing etc]; Data, text and Images [Example: Signal processing, Input-Output systems, Discover order in data sets, Image Denoising etc)
Modeling Lab [Thinking with Mathematical Models through Problems): Counting, Estimation, Structuring and Reasoning; Frame work through different mathematical (structural) equations and analysis; Optimization; Probabilities and Stochastic Processes.

Course References:

Reference Book:
1. "Mathematical modeling: Case Studies with Industry", Alister D.Fitt, CRS & Springer, 2008.
2. "Mathematical Modeling - A Case Study Approach", Reinhard Iliner, C.Sena Bohun, Samanta Mccallum and Thea van Roode, AMS, 2005.
3. "Mathematics and Technology", Christiane Rousseau and Yuan Saint-Aubin, Springer, 2008.
4. "Mathematical Models in Biology", Leah Edelstein-Kesht, SIAM, 2005.
5. "Principles of Mathematical Modeling", Cliev L.Dym, Elsevier, 2004.
6. "Mathematical Modeling of Earth's Dynamical Systems", Rudy Slingerland and Lee Kump, Princeton University Press, 2011. 7. "Mathematical Modeling for the Life Sciences", Jacques Istas, Springer, 2005