Industrial mathematics. Case studies in diffusion of heat and matter (Q2761566)

This is an excellent text aimed primarily at engineering students with substantial interest in mathematics and mathematics students wishing to apply their knowledge in industry. The main goal is to provide students with efficient training through mathematical modeling of real-life applications and successful application of different solution techniques to various types of partial differential equations arising in case studies in the diffusion of heat and matter. The book prepares graduates for the work in industry teaching them how to examine practical problems, state them clearly in mathematical terms deducing necessary equations and using dimensionless variables, analyze mathematical models and select appropriate methods for their study, find the solutions and make relevant predictions about their behavior translating mathematical terms back to real-world context. NEWLINENEWLINENEWLINEThe book is divided into seven chapters. The first one is introductory and contains an overview of the case studies, provides basic information on diffusion and heat conduction equations and methods used for their solving, explains scaling of equations and dimensional analysis. NEWLINENEWLINENEWLINEThe next five chapters constitute the core part of the book. Each of them is self-contained, deals with a different case study and introduces a new important mathematical technique. These chapters are virtually independent and can be practically studied in arbitrary order. NEWLINENEWLINENEWLINEChapter two deals with continuous casting introducing free boundary value problems for partial differential equations and the Boltzmann similarity solution as a method for solving them. Water filtration is discussed in Chapter three, and the method of stretching transformations, an extension of the technique exploited in Chapter two, is used to reduce the partial differential equation to an ordinary differential equation. Chapter four is concerned with laser drilling, and the method of regular perturbations is developed as a tool for obtaining a sequence of approximate equations. Factory fires are studied in Chapter five and the bifurcation analysis frequently used for discussing problems involving parameters is introduced. Irrigation is dealt with in Chapter 6. Using the fact that the problem is governed by linear equations having periodic structure, solutions are sought as series of trigonometric functions (Fourier series). NEWLINENEWLINENEWLINEThe last chapter presents a brief survey of numerous mathematical techniques used in applied problems that have not been discussed in the book and prompts various applications of mathematical techniques in other industries. NEWLINENEWLINENEWLINEThe textbook is written in a lucid manner, with all the information lined up logically and all necessary explanations given. Each chapter contains well-designed examples, helpful graphic support, sufficient number of exercises for self study, and useful suggestions for further reading. The book is written and typeset so nicely, that it is a real pleasure to read it. The prerequisites are not very restrictive and require some basic knowledge of differential equations, linear algebra and numerical analysis, while all new techniques are introduced at the acceptable level of difficulty. NEWLINENEWLINENEWLINEThis textbook is highly recommended reading for all students of mathematics, science and engineering, and will certainly benefit anyone who wishes to understand better how mathematical techniques are ''projected'' onto the real-world problems. You will definitely understand much more about mathematical modeling and may even start loving it after having read this very nice book.