The Essential Guide to Analytical Problem-Solving in Applied Sciences
This textbook offers a wealth of analytical solutions to engineering and applied sciences problems, with a primary focus on heat transfer, groundwater flow, and contaminant transport in shallow subsurface environments. It emphasizes a deeper understanding of the mathematical framework underlying physical processes, inspiring an appreciation for the power and elegance of analytical modeling. Whether you are a student, instructor, researcher, or professional, this resource delivers the clarity and tools necessary to address ambiguities in existing models and unlock the methods to solving complex boundary value problems.
Key Features
1. Step-by-Step Mathematical Solutions
With clear, methodical explanations, this textbook breaks down complex boundary value problems, making them approachable even for readers without advanced mathematical background. It equips learners at all levels to master simulating physical problems using accessible programming tools such as MATLAB, Python, Maple, and Fortran.
2. Fourier Method
This textbook employs the Fourier method, an elegant mathematical approach to solving boundary value problems. By utilizing eigenfunction expansion and the fast Fourier transform (FFT), it provides a simpler and more traceable alternative to the intricate inverse Laplace transform. In particular, the FFT’s capability to address random time-dependent boundary conditions broadens its applicability far beyond conventional analytical techniques.
3. Multi-level Studies
The book is designed for students and researchers at all levels. It includes foundational topics ideal for undergraduate and postgraduate students, as well as advanced materials tailored for PhD candidates, postdocs, principal researchers, and experienced professionals. The content of this book is particularly well-suited for courses in civil, environmental, geothermal, geotechnical, and agricultural engineering, as well as in hydrology, geoscience, and geophysics. Moreover, its comprehensive approach and practical examples enriches the learning experience and provide valuable insights on analytical modelling across the diverse fields of applied sciences.
Elevate your analytical modeling expertise with this vital guide. Whether you are enriching your coursework or advancing your research, this book’s traceable methodology and comprehensive approach offer valuable insights across a wide range of applied sciences.
Rafid Al Khoury earned his Ph.D. in Computational Mechanics, graduating Cum Laude, from Delft University of Technology in 2002. After spending approximately three years in the commercial finite element industry, he returned to Delft University, joining the Computational Mechanics Chair at the Faculty of Civil Engineering and Geosciences. Since then, his research has focused on computational poromechanics, specializing in advanced modeling of multiphysics problems. Dr. Al Khoury has authored over 50 journal papers and two books on shallow geothermal systems and CO2 geosequestration. In relation to the subject of this book, he is internationally recognized for introducing analytical models for shallow geothermal systems using the spectral analysis method. He has published extensively in this field, including a book on shallow geothermal systems in 2012.
Cor Kasbergen earned his M.Sc. in Computer Science and Applied Mathematics from Delft University of Technology in 1993. Since then, he has been a researcher and lecturer at the Faculty of Civil Engineering and Geosciences at Delft University. He currently teaches undergraduate and postgraduate courses on continuum mechanics and computational pavement engineering. His primary research focuses on developing computational tools based on the finite element method and the spectral element method. His work emphasizes advanced mathematical derivations and the development of innovative computer codes for pavement mechanics and transport phenomena. Over the years, Cor Kasbergen has contributed to more than 130 journal and conference publications. In relation to the topic of this book, he has collaborated with Dr. Al Khoury on the computational verification of the models and the development of computer algorithms using both Fortran© and Maple©.
