Mathematical Methods for Computing
Mathematical Modeling
Course Supervisor: Dr. Sohail Iqbal
Mathematical Modeling
Fundamental and quantitative way to understand and analyze complex systems and phenomena
Complement to Theory and Experiments, and often Integrate them
Becoming widespread in: Computational Physics, Chemistry, Mechanics, Materials, …, Biology
What are the goals of Modeling studies?
Appreciation of broad use of modeling
Hands-on an experience with simulation techniques
Develop communication skills working with practicing professionals
Mathematical Modeling?
Mathematical modeling seeks to gain an understanding of science through the use of mathematical models on computers.
Mathematical modeling involves teamwork
Theory
Experiment
Computation
Mathematical Modeling
Complements, but does not replace, theory and experimentation in scientific research.
Mathematical Modeling
Is often used in place of experiments when experiments are too large, too expensive, too dangerous, or too time consuming.
Can be useful in “what if” studies; e.g. to investigate the use of pathogens (viruses, bacteria) to control an insect population
Is a modern tool for scientific investigation.
Mathematical Modeling
Has emerged as a powerful, indispensable tool for studying a variety of problems in scientific research, product and process development, and manufacturing.

Seismology
Climate modeling
Economics
Environment
Material research
Drug design
Manufacturing
Medicine
Biology
Example: Industry
http://www.boeing.com/commercial/777family/index.html?
First jetliner to be digitally designed, “pre-assembled” on computer, eliminating need for costly, full-scale mockup.
Computational modeling improved the quality of work and reduced changes, errors, and rework.
Example: Roadmaps of the Human Brain
Cortical regions activated as a subject remembers the letters x and r.
Real-time Magnetic Resonance Imaging (MRI) techno-logy…