Numerical Methods and Methods of Approximation in Science and Engineering

Karan S. Surana, born in India, went to undergraduate school at Birla Institute of Technology and Science (BITS), Pilani, India, and received a B.E. degree in Mechanical Engineering in 1965. He then attended the University of Wisconsin, Madison, where he obtained M.S. and Ph.D. degrees in Mechanical Engineering in 1967 and 1970, respectively. He worked in industry, in research and development in various areas of computational mechanics and software development, for fifteen years: SDRC, Cincinnati (1970{1973), EMRC, Detroit (1973{1978); and McDonnell-Douglas, St. Louis (1978{1984). In 1984, he joined the Department of Mechanical Engineering faculty at University of Kansas, where he is currently the Deane E. Ackers University Distinguished Professor of Mechanical Engineering. His areas of interest and expertise are computational mathematics, computational mechanics, and continuum mechanics. He is author of over 350 research reports, conference papers, and journal articles. He has served as advisor and chairman of 50 M.S. students and 22 Ph.D. students in various areas of Computational Mathematics and Continuum Mechanics, and has delivered many plenary and keynote lectures in various national and international conferences and congresses on computational mathematics, computational mechanics, and continuum mechanics. He has served on international advisory committees of many conferences and has co-organized minisymposia on k-version of the finite element method, computational methods, and constitutive theories at U.S. National Congresses of Computational Mechanics, organized by the U.S. Association of Computational Mechanics (USACM). He is a member of International Association of Computational Mechanics (IACM) and USACM, and a fellow and life member of ASME. Dr. Surana's most notable contributions include: large deformation finite element formulations of shells; the k-version of the finite element method; operator classication and variationally consistent integral forms in methods of approximations for BVPs and IVPs; and ordered rate constitutive theories for solid and fluent continua. His most recent (and present) research work is in non-classical internal polar continuum theories and non-classical Cosserat continuum theories for solid and fluent continua and associated ordered rate constitutive theories. He is the author of three recently published textbooks from Taylor & Francis/CRC Press: Advanced Mechanics of Continua; The Finite Element Method for Boundary Value Problems: Mathematics and Computations; and The Finite Element Method for Initial Value Problems: Mathematics and Computations.

Preface

About the Author

1 Introduction

2 Linear Simultaneous Algebraic Equations

3 Nonlinear Simultaneous Equations

4 Algebraic Eigenvalue Problems

5 Interpolation and Mapping

6 Numerical Integration or Quadrature

7 Curve Fitting

8 Numerical Differentiation

9 Numerical Solutions of BVPs

10 Numerical Solution of Initial Value Problems

11 Fourier Series

BIBLIOGRAPHY

INDEX