Cambridge IISc Series – serie

The study of transport phenomena is an essential part of chemical engineering, as well as other disciplines concerned with material transformations such as biomedical engineering, microfluidics, reactor design and metallurgy. Material transformations require the motion of constituents relative to each other, the transfer of heat across materials and fluid flow. This lucid textbook introduces the student to the fundamentals and applications of transport phenomena in a single volume and explains how the outcomes of transformation processes depend on fluid flow and heat/mass transfer. It demonstrates the progression from physical concepts to the mathematical formulation, followed by the solution techniques for predicting outcomes in industrial applications. The ordering of the topics, gradual build-up of complexity and easy to read language make it a vital resource for anyone looking for an introduction to the domain. It also provides a foundation for advanced courses in fluid mechanics, multiphase flows and turbulence.

Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.

A comprehensive text in the field of biomaterials science and tissue engineering, covering fundamental principles and methods related to processing-microstructure-property linkages as applied to biomaterials science. Essential concepts and techniques of the cell biology are discussed in detail, with a focus quantitatively and qualitatively evaluating cell-material interaction. It gives detailed discussion on the processing, structure and properties of metals, ceramics and polymers, together with techniques and guidelines. Comprehensive coverage of in vitro and in vivo biocompatibility property evaluation of materials for bone, neural as well as cardiovascular tissue engineering applications, together with representative protocols. Supported by several multiple-choice questions, fill in the blanks, review questions, numerical problems and solutions to selected problems, this is an ideal text for undergraduate and graduate students in understanding fundamental concepts and the latest developments in the field of biomaterials science.

Written in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.

Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

This book presents a new methodology, known as Knowledge Driven Development, for managing project knowledge in an exhaustive and structured manner. The text highlights the importance of efficient project delivery methodology in the overall software development life cycle. Important topics such as requirement analysis, solution design, application design, and test design are discussed in depth. It establishes a connection between enterprise knowledge and project knowledge for continuous improvement and accelerated project delivery. Separate chapters on end-to-end project delivery, compliance and protocols and interface with existing methodologies makes it useful for the readers. Several case studies and examples are interspersed throughout the text for better understanding.

The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.

Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics - Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.

Suitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem. The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year graduate level course. To quickly get to the main points of the proof of the theorem, several topics that aid in the understanding of the proof are included in the appendices. These topics serve the purpose of providing familiarity with a large variety of tools used in the proof and adds to the flexibility of reading them independently.

The principles of classical physics, though superseded in specific fields by such theories as quantum mechanics and general relativity, are still of great importance in a broad range of applications. The book presents fundamental concepts of classical physics in a coherent and logical manner. It discusses important topics including the mechanics of a single particle, kinetic theory, oscillations and waves. Topics including the kinetic theory of gases, thermodynamics and statistical mechanics are discussed, which are normally not present in the books on classical physics. The fundamental concepts of energy, momentum, mass and entropy are explained with examples. Discussion on concepts of thermodynamics is presented along with the simplified explanation on Caratheodory's axioms. It covers chapters on wave motion and statistical physics, useful for the graduate students. Each concept is supported with real-life applications on several concepts including impulse and collision, Bernoulli's equation, and friction.