June 23, 2013
June 23, 2013
June 26, 2013
23.436.1 - 23.436.9
ASEE ABSTRACT:DIMENSIONAL ANALYSIS IN MATHEMATICS FOR ENGINEERSEngineering theory and practice requires the application of various mathematicalmethods to process signals and information that represent physical quantities. Theinteraction between physical quantities is often obscured within the complexity ofadvanced mathematical computations leading to possibly meaningless results. Asan example, the use of singular value decomposition or eigensystems has beenshown to lead to physically inconsistent results in systems with different units.The importance of adequate handling of physical units in scientific and technologicaldevelopments and endeavors can lead to costly and serious failures as evidenced bythe loss of the Mars Climate Orbiter that crashed on the red planet in September1999. The reason given by NASA for this failure is system integration ofincompatible physical systems of units used by two separate divisions of the overalldesign and development team. This costly oversight serves as an example of apervasive careless attitude towards physical units even in well-established andprestigious research centers.Modern software and hardware tools are now commonly used in the treatment,analysis, and design of engineering systems. These tools convert all data tonumerical values for processing and may not be designed to perform adequatedimensional analysis to ensure the physical integrity of results.The proposed research makes the case for the integration of dimensional analysis inthe mathematical preparation of engineering students. While this topic should beinfused in an engineering curriculum, it requires particular attention in the courseswhere advanced mathematical methods are covered such as Differential Equations,Linear Algebra, or Numerical Analysis.A new course on Advanced Engineering Mathematics has been developed at ourinstitution for the benefit of two new engineering programs: Software Engineeringand Electrical and Computer Engineering. This work will describe and discussteaching dimensional analysis as an integral part of mathematics for engineeringcourses and our new advanced engineering mathematics course in particular.
Manseur, Z. (2013, June), DIMENSIONAL ANALYSIS IN MATHEMATICS FOR ENGINEERS Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. https://peer.asee.org/19450
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