Advanced Mathematics for Engineering Students
The Essential Toolbox
- 1st Edition - May 20, 2021
- Imprint: Butterworth-Heinemann
- Authors: Brent J. Lewis, E. Nihan Onder, Andrew Prudil
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 2 3 6 8 1 - 9
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 2 3 6 8 2 - 6
Advanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics. Derived from two semester advanced mathematics course… Read more
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Request a sales quoteAdvanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics. Derived from two semester advanced mathematics courses at the author’s university, the book delivers the mathematical foundation needed in an engineering program of study. Other treatments typically provide a thorough but somewhat complicated presentation where students do not appreciate the application. This book focuses on the development of tools to solve most types of mathematical problems that arise in engineering – a “toolbox” for the engineer. It provides an important foundation but goes one step further and demonstrates the practical use of new technology for applied analysis with commercial software packages (e.g., algebraic, numerical and statistical).
- Delivers a focused and concise treatment on the underlying theory and direct application of mathematical methods so that the reader has a collection of important mathematical tools that are easily understood and ready for application as a practicing engineer
- The book material has been derived from class-tested courses presented over many years in applied mathematics for engineering students (all problem sets and exam questions given for the course(s) are included along with a solution manual)
- Provides fundamental theory for applied mathematics while also introducing the application of commercial software packages as modern tools for engineering application, including: EXCEL (statistical analysis); MAPLE (symbolic and numeric computing environment); and COMSOL (finite element solver for ordinary and partial differential equations)
3rd and 4th year undergraduate engineering students; practicing engineers needing to catch up on useful techniques and current commercial software applications
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Acknowledgments
- List of tables
- List of figures
- Bibliography
- Chapter 1: Prologue
- 1.1. Introduction
- Bibliography
- Chapter 2: Ordinary differential equations
- 2.1. First-order equations
- 2.2. Second-order linear differential equations
- 2.3. Higher-order linear differential equations
- 2.4. Systems of differential equations
- 2.5. Series solutions and special functions
- Problems
- Chapter 3: Laplace and Fourier transforms
- 3.1. Laplace transform methods
- 3.2. Fourier transform methods
- 3.3. Discrete Fourier transforms and fast Fourier transforms
- Problems
- Bibliography
- Chapter 4: Matrices, linear systems, and vector analysis
- 4.1. Determinants
- 4.2. Inverse of a matrix
- 4.3. Linear systems of equations
- 4.4. Vector analysis
- Problems
- Bibliography
- Chapter 5: Partial differential equations
- 5.1. Derivation of important partial differential equations
- 5.2. Analytical methods of solution
- Problems
- Bibliography
- Chapter 6: Difference numerical methods
- 6.1. Ordinary differential equations
- 6.2. Partial differential equations
- Problems
- Bibliography
- Chapter 7: Finite element methods
- 7.1. COMSOL application methodology
- 7.2. General theory of finite elements
- Problems
- Bibliography
- Chapter 8: Treatment of experimental results
- 8.1. Definitions
- 8.2. Uses of statistics
- 8.3. Regression analysis and software applications
- 8.4. Propagation of errors
- Problems
- Bibliography
- Chapter 9: Numerical analysis
- 9.1. Finding zeros of functions
- 9.2. Interpolation
- 9.3. Splines
- 9.4. Data smoothing
- 9.5. Numerical integration and differentiation
- Problems
- Bibliography
- Chapter 10: Introduction to complex analysis
- 10.1. Complex functions
- 10.2. Complex integration
- 10.3. Taylor and Laurent series
- 10.4. Residue integration method
- 10.5. Residue theorem
- 10.6. Applications of conformal mapping
- Problems
- Bibliography
- Chapter 11: Nondimensionalization
- 11.1. Dimensional analysis
- 11.2. Buckingham's π theorem – dimensional analysis
- 11.3. Similarity laws
- 11.4. Nondimensionalization technique
- Problems
- Bibliography
- Chapter 12: Nonlinear differential equations
- 12.1. Analytical solution
- 12.2. Numerical solution
- Problems
- Bibliography
- Chapter 13: Integral equations
- 13.1. Integral equations
- 13.2. Green's function
- Problems
- Bibliography
- Chapter 14: Calculus of variations
- 14.1. Euler–Lagrange equation
- 14.2. Lagrange multipliers
- Problems
- Bibliography
- Appendix A: Maple software package
- A.1. Maple commands
- Bibliography
- Appendix B: Geodesic formulation
- B.1. Tensors
- B.2. Lagrangian and action
- Bibliography
- Bibliography
- Bibliography
- Index
- Edition: 1
- Published: May 20, 2021
- Imprint: Butterworth-Heinemann
- No. of pages: 432
- Language: English
- Paperback ISBN: 9780128236819
- eBook ISBN: 9780128236826
BL
Brent J. Lewis
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.
Affiliations and expertise
Formerly, Royal Military College, Kingston, CanadaEO
E. Nihan Onder
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.
Affiliations and expertise
Fuel Development Branch, Canadian Nuclear Laboratories, CanadaAP
Andrew Prudil
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.
Affiliations and expertise
Computational Techniques Group, Canadian Nuclear Laboratories, Chalk River, Ontario, CanadaRead Advanced Mathematics for Engineering Students on ScienceDirect