Santanu Saha Ray Livres

The book explores advanced analytical and numerical methods, particularly wavelet techniques, to analyze nuclear reactor behavior. By utilizing fractional calculus, it offers a more accurate representation of reactor kinetics compared to traditional methods. The text provides both analytical and numerical solutions, enhancing understanding of fractional order control, which is crucial for optimizing overall plant efficiency. This approach highlights the significance of modern mathematical frameworks in the field of nuclear engineering.

The book explores innovative analytical and numerical techniques for addressing partial and fractional differential equations. It highlights specific numerical methods, including Euler-Maruyama and strong-order Taylor methods, for solving stochastic point kinetic equations relevant to nuclear reactor dynamics. Additionally, it presents new exact solutions for a range of fractional differential equations, such as the time-fractional Burgers-Hopf equation and various (3+1)-dimensional equations, showcasing the depth and applicability of these methods in advanced mathematical contexts.

Focusing on the theory of graphs and algorithms, this book offers rigorously explained theorem proofs alongside elegantly defined examples. It covers essential algorithms while employing straightforward and logical mathematical language, making complex concepts accessible. The clear presentation aids in understanding the practical applications of graph theory and algorithms.

Stochastic partial differential equations (SPDEs) represent a significant advancement in modeling systems where parameters are uncertain, particularly in fields like physics and economics. These equations blend deterministic partial differential equations with stochastic processes, incorporating elements of both finite and infinite dimensions. The use of white noise, despite being a mathematical abstraction, effectively captures rapid random fluctuations, making SPDEs a powerful tool for understanding complex systems influenced by randomness.

Focusing on numerical methods, this textbook offers an in-depth exploration of algorithms and their implementation in computer programs, specifically tailored for science and engineering applications. It enhances students' grasp of how to construct numerical algorithms and understand their practical uses. The book is rich with worked examples, exercises at the end of each chapter, and includes Mathematica® programs, ensuring a comprehensive learning experience while covering standard algorithms for numerical computation.

The book has many important features which make it suitable for both undergraduate and postgraduate students in various branches of engineering and general and applied sciences. The important topics interrelating Mathematics & Computer Science are also covered briefly. The book is useful to readers with a wide range of backgrounds including Mathematics, Computer Science/Computer Applications and Operational Research. While dealing with theorems and algorithms, emphasis is laid on constructions which consist of formal proofs, examples with applications. Uptill, there is scarcity of books in the open literature which cover all the things including most importantly various algorithms and applications with examples.