Mathematical Modeling and Computational Science

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Mathematical Modeling and Computational Science
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Mathematical Modeling

• A mathematical model is the use of mathematical
  language to describe the behavior of a system.
• Mathematical models are used in particularly in
  the sciences such biology, electrical
  engineering, physics but also in other fields
  such as economics, sociology and political
  science

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Mathematical Modeling

• is a mathematical description of a physical
  situation.

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Numerical Analysis

• this refers to the analysis of mathematical
  problems by numerical means, especially
  mathematical problems arising from models based
  on calculus.

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Numerical Analysis

• effective numerical analysis requires
• an understanding of the computational tool being
  used, be it a calculator or a computer.
• an understanding of the problem to be solved.
• construction of an algorithm which will solve
  the given mathematical problem to a given desired
  accuracy and within the limits of the resources
  that are available.

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Computational Science

• is the field of study concerned with
  constructing mathematical models and numerical
  solution techniques and using computers to
  analyze and solve scientific and engineering
  problems

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Computational Science

• application programs often model real-world
  changing conditions, such as weather, air flow
  around a plane, automobile body distortions in a
  crash, the motion of stars in a galaxy, an
  explosive device, etc

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Computational Science

• focuses on a scientific and engineering problem
  and draws from computer science and mathematics
  to gain an improved understanding of the problem.

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Traditional areas of Computational Science

• Computational fluid dynamic
• Atmospheric science
• Seismology
• Structural analysis
• Chemistry
• Magnetohydrodynamics
• Reservoir modeling
• Global ocean/climate modeling
• Environmental studies
• Nuclear engineering

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Nontraditional and emerging areas of
computational science

• Biology
• Economics
• Materials research
• Medical imaging
• Animal science
• Music
• Visual arts