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Innovation for national defense
Published in Adedeji B. Badiru, Cassie B. Barlow, Defense Innovation Handbook, 2018
Opportunity lost can be a recurring risk in industry. When new innovation knocks, it should be embraced. A good case example of opportunity lost and innovation ignored is the case of digital photography first developed (and ignored) at Kodak in the mid-1970s. Kodak ignored the new innovation, perhaps because it conflicted with their traditional market model. In 1998, Kodak had 170,000 employees and sold 85% of all photo paper worldwide. Within just a few years, Kodak’s business model disappeared and the company went out of its traditional business. Had Kodak aggressively embraced and leveraged the new digital photography in 1975, the future of the company might have taken a different positive and profitable path. If innovation is not timely embraced and capitalized on, what happened at Kodak can happen to many other companies in the prevailing digital engineering and manufacturing environment, particularly those dealing with artificial intelligence, health, autonomous and electric cars, (Science, Technology, Engineering, Mathematics [STEM]) education, 3D printing, agriculture, and knowledge-based jobs.
Solving the time-independent Schrödinger equation
Published in Nils O. Petersen, Foundations for Nanoscience and Nanotechnology, 2017
The complexity of arriving at this solution is beyond the scope of this text, but for those interested, the transformation and the solutions can be found in Applied Mathematics or Engineering texts such as that by Kreyszig’s Advanced Engineering Mathematics, where the problem is solved to understand the vibrations of vibrating planes, exemplified by objects such as drums. [See also Carl. W. David University of Connecticut Chemistry Educational Material http://digitalcommons.uconn.edu/cgi/viewcontent.cgi?article=1013&context=chem_educ.]
What is the problem in problem-based learning in higher education mathematics
Published in European Journal of Engineering Education, 2018
When discussing application of mathematics, one also needs to discuss the concept of engineering mathematics which is a term used to describe the mathematics applied by engineers. Engineering mathematics is therefore applied mathematics, for instance, mathematical modelling on complex problems. Christensen (2008) describes examples of Mathematics projects in applied mathematics at AAU. The work in engineering mathematics belongs to the second society but uses methods and theories developed by researchers in the third society. Alpers et al. (2013) describe and discuss the SEFI (European Society for Engineering Education) framework for mathematics curricula in engineering education in which they discuss the mathematics competencies also discussed above in this paper. A main message of their work is that the description of the mathematics competencies is not only relevant to mathematics education, but it is also a useful tool for mathematics education for engineers. They argue that even though content remains important, and students need some familiarity with the mathematics concepts and procedures prior to application, the knowledge ought to be embedded in view of the mathematical competencies in order to avoid that mathematics courses for engineering students are mainly restricted to contents. They also argue that ‘mathematics education must be integrated in the surrounding engineering study course to really achieve the ability to use mathematics in engineering contexts’ (Alpers et al. 2003, 7). The question of how mathematics curricula should be organised in engineering education is beyond the scope of this paper; however, what is essential for this paper is the emphasis on the application side of mathematics while maintaining that some level of knowledge of mathematics concepts and procedures are necessary too. It is also interesting that the SEFI framework uses a framework from mathematics in order to place limitations on how much mathematics content engineering students should learn. As argued by Antonsen (2009), the eight competencies from Niss and Jensen (2002) are different as four of them may be termed inner mathematical competencies (thinking, reasoning, representing, symbols, and formalism) as their focus from a mathematical point of view are relating to pure mathematics. Thus, in other contexts, the discussion of mathematics competencies are used to protect mathematics from being just a service subject where mathematics is mainly being used as a tool in other disciplines.