This book systematically classifies the mathematical formalisms of computational models that are required for solving problems in mathematics, engineering and various other disciplines. It also provides numerical methods for solving these problems using suitable algorithms and for writing computer codes to find solutions. For discrete models, matrix algebra comes into play, while for continuum framework models, real and complex analysis is more suitable. The book clearly describes the method-algorithm-code approach for learning the techniques of scientific computation and how to arrive at accurate solutions by applying the procedures presented. It not only provides instructors with course material but also serves as a useful reference resource. Providing the detailed mathematical proofs behind the computational methods, this book appeals to undergraduate and graduate mathematics and engineering students. The computer codes have been written in the Fortran programming language, which is the traditional language for scientific computation. Fortran has a vast repository of source codes used in real-world applications and has continuously been upgraded in line with the computing capacity of the hardware. The language is fully backwards compatible with its earlier versions, facilitating integration with older source codes.

This book systematically classifies the mathematical formalisms of computational models that are required for solving problems in mathematics, engineering and various other disciplines. It also provides numerical methods for solving these problems using suitable algorithms and for writing computer codes to find solutions. For discrete models, matrix algebra comes into play, while for continuum framework models, real and complex analysis is more suitable. The book clearly describes the method-algorithm-code approach for learning the techniques of scientific computation and how to arrive at accurate solutions by applying the procedures presented. It not only provides instructors with course material but also serves as a useful reference resource. Providing the detailed mathematical proofs behind the computational methods, this book appeals to undergraduate and graduate mathematics and engineering students. The computer codes have been written in the Fortran programming language, which is the traditional language for scientific computation. Fortran has a vast repository of source codes used in real-world applications and has continuously been upgraded in line with the computing capacity of the hardware. The language is fully backwards compatible with its earlier versions, facilitating integration with older source codes.

Mechanics of solids as theories of Elasticity and Plasticity and the theories of fluid flows were developed centuries ago, but their combined constitutive filed theory appeared only in recent six decades. During its evolution as Continuum Mechanics, the approach was somewhat obscure compounded by obscure tensorial notations. Clearer versions of the theory appeared subsequently and at present standardization has been reached with the use of Cartesian tensors that are closely related to matrices. This text gives a clear presentation of this formalism of Continuum Mechanics that can be applied to not only classical solid and fluid mechanics, but shows the way to newer materials that are increasingly finding technical applications. The book will thus be useful as text for M.Sc. and M.Tech. students, and also researchers on mechanics of continuous materials of different varieties.

The science of Operations Research seeks efficiency and economy in organizational setups engaged in many economic activities. This book develops important mathematical models cropping up in different decision-making situations in a general manner and then proceeds to give algorithmic development of methods of solution. Though the methods of solution are very diverse in nature, the mathematical tools employed are mainly matrix algebra and elements of probability theory. NEW TO THE SECOND EDITION: Problems of Maximum Bipartite Matching and Equipment Replacement The Cutting-Plane Method for general integer programs This book will be useful as a text for a one-semester course in engineering and science and as a reference in economics and business administration.