Advanced Mathematics for Engineering Students

"Overall, the reviewer considers this text to offer a good and useful coverage of advanced mathematics for engineers. It gives useful and succinct coverage of the topics included." --IEEE Pulse

Dr. Brent Lewis PhD, PEng is retired Dean, Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology (2013-2015); Professor and UNENE/NSERC Industrial Research Chair, Royal Military College of Canada (RMC) (1988-2013), Scientist and Section Head, Chalk River Laboratories (1980-1988). Dr. Lewis has authored 360 journal articles, conference proceedings and reports, has consulted extensively for the domestic and international nuclear fuel community, and participated in the severe accident research program of France's Commissariat à l'Energie Atomique in 1994-1995. He has also served on various committees and working groups, including several Standards Committees, the Executive Committee of the Material Science and Technology Division for the American Nuclear Society (ANS), the International Commission on Radiological Protection, the International Organization for Standardization, the International Space Station Multilateral Radiation Health Working Group for the Canadian Space Agency, UNENE and COG. As a result of his research work, he has received several awards from the ANS. Dr. Lewis was appointed a Fellow of the CNS in 2002. Dr. E. Nihan Onder earned a PhD degree in nuclear engineering from École Polytechnique of Montréal, an MSc degree in nuclear engineering from Istanbul Technical University (ITU) and a BSc degree in mining engineering in ITU. Between 2001 and 2005, she worked at the company Énergie & Analyse du Québec (ÉNAQ, was a subcontractor to Hydro-Québec) to perform safety analysis for the Gentilly-2 nuclear power plant in Trois-Rivières, Québec. In 2005, she joined the thermalhydraulics branch (THB) at the Canadian Nuclear Laboratories (CNL, formerly Atomic Energy of Canada Limited (AECL)). At the THB, she worked as an analyst, and from 2009 to 2013 was the head of the analysis section. During this time, she supervised students and junior staff. In 2008, she was selected by CNL to attend the World Nuclear University (WNU) 2008 summer institute, which is an intensive five-week leadership development programme, tailored for nuclear professionals. In 2013, she joined the fuel development branch (FDB) at CNL. Since then, she has been performing analysis for fuel performance. She has published numerous articles and co-authored a comprehensive textbook titled "Fundamentals of Nuclear Engineering¿, which was published by Wiley in 2017. Dr. Andrew Prudil Ph.D., PEng, graduated from the Queen's University Kingston in 2009 with a BASc degree in Engineering Physics with an emphasis on electrical engineering. In 2013 Andrew completed his PhD developing computational models of nuclear fuel behavior under the supervision of Dr. Lewis and P. Chan in the Chemistry and Chemical Engineering Department at the Royal Military College of Canada. Currently Andrew is a Nuclear Fuel Safety Research Scientist in the Computational Techniques group at Canadian Nuclear Laboratories in Chalk River. Andrew has published numerous peer reviewed papers related to nuclear fuel. He is an active member of the Canadian Nuclear Society, the Professional Engineers of Ontario, and adjunct professor at Ontario Tech in Oshawa.

1. Prologue
2. Ordinary Differential Equations
3. Laplace and Fourier Transform Methods
4. Matrices and Linear Systems of Equations
5. Analytical Methods for Solving Partial Differential Equations
6.Difference Numerical Methods for Differential Equations
7. Finite Element Technique
8. Treatment of Experimental Results
9. Numerical Analysis
10. Introduction to Complex Analysis
11. Nondimensionalisation
12. Nonlinear Differential Equations
13. Integral Equations
14. Calculus of Variations