Mathematics or generally applied mathematics is extensively used in every engineering expertise. Mathematics is well-thought-out to be the base of all sciences. It has solicitation in practically all the fields of science as well as non-scientific study.
The book covers some real-world applications of Engineering Mathematics. This book starts with a discussion on some axisymmetric stress analysis problems where there is contact along an inner region of a cylindrical boundary and hence results in mixed boundary conditions (which might be non-linear) on the inner boundary wall. Further, the book emphasizes on Laplace transform collocation method for solving the hyperbolic telegraph equation. Block Backward differentiation formulas for fractional differential equations are also given. The Kortweg–de Vries equations play an important role in model different physical phenomena in nature. This book investigates the analytical solution to the system of nonlinear fractional Kortweg–de Vries, partial differential equations. The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this book, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation. As a safety and reliability analysis technique, failure mode and effects analysis (FMEA) has been used extensively in several industries for the identification and elimination of known and potential failures. However, some shortcomings associated with the FMEA method have limited its applicability. This book aims at presenting a comprehensive FMEA model that could efficiently handle the preference interdependence and psychological behavior of experts in the process of failure modes ranking.
This book also aims to the study of the Cubic B-splines to find the numerical solution of linear and non-linear 8th order BVPs that arises in the study of astrophysics, magnetic fields, astronomy, and beam theory, cylindrical shells, hydrodynamics, and hydro-magnetic stability, engineering, applied physics, fluid dynamics, and applied mathematics. In the present book, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using the Natural transform decomposition method. In conclusion, the book explores the new meaning of integral and derivative actions, and gains, derived by the consideration of non-integer integration and differentiation orders, i.e., for fractional-order PID controllers. Similarities and differences between classical and fractional PIDs, as well as illustrative control examples, are given for the best understanding of new possibilities of control with the latter. It is hoped that this book will serve to students, practitioners, scientists, and engineers as well as for those who are involved in the associated area.