Modern Methods in Mathematical Physics

Vladimir Ryzhov works at the SMTU since 1984, and is Head of Applied Math and Math Modeling Department, Director of «e-Learning, Science & Technology Center», Professor, Doctor of Technical Sciences. His teaching background is engaged in developing innovative methods and models of training on subjects of the department with a special focus on e-learning courses. He developed methods of knowledge testing for research engineering disciplines. He has extensive experience in educational (academic and corporative) and research projects management. He trains Ph.D. students in fluid mechanics. He is a member of the Academic Degree Councils and has a large experience in Ph.D. thesis quality assessment. He is an author of more than 100 scientific publications. He was the coordinator of international projects (TEMPUS, ERASMUS programs). Tatiana Fedorova works at the SMTU since 1994, is Associate Professor of the Department of Applied Mathematics and Mathematical Modeling, and holds Ph.D. in theoretical physics. The area of her research experience lies in the field of many-body interactions in complex systems. She teaches a wide range of disciplines at graduate and postgraduate levels. She has a special interest in developing e-learning courses of theoretical orientation. She is involved in graduate and postgraduate student supervision in the fields of mathematical and computer modeling. She is an author of 25 articles. She has extensive experience in teamwork and international cooperation.Kirill Safronov works at the SMTU since 2015 and is an Assistant Professor of Applied Mathematics and Mathematical Modeling Department. He has held the position of an Assistant Professor. He is engaged in developing innovative methods and models of teaching on mathematical subjects. He has work experience in the primary field of the department (he works for Wärtsila Ltd as a Modeling Engineer). He is a developer of syllabi of the practice-oriented computer modeling and simulation courses.Professor Ir. Dr. Shaharin Anwar Sulaiman serves the Department of Mechanical Engineering at Universiti Teknologi PETRONAS. He holds a B.Sc., M.Sc., and Ph.D. in Mechanical Engineering from the USA and the UK. He was a Mechanical and Electrical (M&E) Engineer in YTL Construction prior to joining the academics in 1998. His research interests include air-conditioning, biomass energy, solar photovoltaic, combustion, and flow assurance. He published a few books: Engineers in Society (2010), Gas District Cooling in Malaysia (2011), Downdraft Gasification of Oil Palm Frond (2012), and Energy Efficiency Improvements: Miscellanea (2014). He was also UTP’s Director of Mission-Oriented Research (MOR) for Hybrid Energy Systems in UTP from 2009 to 2017.Dr. Samsul Ariffin Abdul Karim is a senior lecturer at Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS (UTP), Malaysia. He obtained his PhD in Computational Mathematics and Computer-Aided Geometric Design (CAGD) from Universiti Sains Malaysia (USM). He is Professional Technologists registered with the Malaysia Board of Technologists (MBOT). His research interests include curves and surfaces designing, geometric modeling, and wavelets applications in image compression and statistics.

“The methods in Modern Methods are not particularly modern, dating back a century, though of course, the use of Mathematica is more modern. The use of Mathematica is a major strength of the book. The authors present many examples, and give the reader the tools to pursue more examples, making its subject more tangible.” (John D. Cook, MAA Reviews, June 17, 2023)

• Introduction.- Fundamentals. Classification of integral equations.- Integral equations with difference kernels.