Computational Methods in Engineering

The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial valueproblems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.

Introduction.- Solution of linear equations.- Computation of eigenvalues.- Solution of algebraic equations.-  Interpolation.

S.P. Venkateshan obtained his Ph.D. from the Indian Institute of Science, Bangalore, in 1977. After spending three years at Yale University, he joined the Indian Institute of Technology Madras in 1982. He retired as Professor and Head of the Department of Mechanical Engineering in November 2012. Subsequently, he served IIT Madras as Professor Emeritus till November 2016. Since December 2016, he has been Professor Emeritus and Advisor at IIITDM Kancheepuram. He has continued teaching and research during this period. Prof. Venkateshan has taught subjects like heat transfer, thermodynamics, measurements, and computational methods. His research areas are radiation heat transfer, conjugate heat transfer–experimental and numerical, measurement of thermo-physical properties by inverse heat transfer methods, and instrumentation. He has supervised 30 doctoral and 25 Master by research candidates at IIT Madras. In addition to more than 200 published research papers to his credit, Prof. Venkateshan has also authored two books— Heat Transfer and Mechanical Measurements.

Prasanna Swaminathan obtained his Ph.D. from the Indian Institute of Technology Madras in 2013. After working as a postdoctoral researcher in different laboratories in the Paris region, he joined as a full-time researcher at LSPM, a CNRS laboratory associated with University Sorbonne Paris Nord, Paris, in 2016. His main area of interest is modeling and designing microwave-based plasma sources for the elaboration of novel materials such as CVD diamond and graphene.