A streamlined approach to learning partial differential equations (PDEs) makes this book ideal for undergraduate courses. It focuses on enhancing students' problem-solving skills through clear explanations and practical worked examples, allowing them to witness the techniques in action.
Stories, Challenges, and Adventures in Mathematics
The narrative presents a humorous exploration of the significance of mathematics through the character JJ, who provides a satirical critique of society's views on numeracy and logic. Blending factual information with light scholarly arguments and engaging challenges, it invites readers to reflect on their relationship with math while enjoying a fun and thought-provoking journey.
Focusing on the deformation of elastic plates, this book presents advanced analytic techniques to address fundamental boundary value problems, specifically for plates exhibiting transverse shear deformation. By offering a more comprehensive understanding of bending processes compared to Kirchhoff's classical theory, it serves as a valuable resource for applied mathematicians and engineers involved in diverse fields such as microchip production, skyscraper construction, and aircraft design.
Thin Plates on an Elastic Foundation
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.
This textbook caters to the needs of today’s students, making it ideal for a first course in elementary differential equations for future engineers, scientists, and mathematicians. Accessible to anyone with a basic understanding of precalculus algebra and calculus, it adopts a concise, straightforward approach to differential equations, allowing students to gain solid experience in classical solution techniques. With a lighter emphasis on physical interpretations, a manageable page count, and a highly readable style, it features over 1000 exercises designed for completion without a calculator. The second edition includes a new chapter on numerical methods and separates the “pure” and “applied” content by discussing selected mathematical models in distinct chapters. Most of the 246 worked examples conclude with Mathematica® commands for result verification. This text serves as a self-contained resource for average students to learn the fundamentals, while also providing a stepping stone for those interested in more advanced material. Additionally, practitioners encountering differential equations in their work will find it a convenient reference.