A Textbook of Computer Based Numerical and Statistical Techniques
by A.K. Jaiswal and Anju Khandelwal
Early Days in Complex Dynamics (History of Mathematics)
by Daniel S. Alexander, Felice Lavernaro, and Alssandro Rosa
The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book by Alexander, Iavernaro, and Rosa paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others. A...
Lecture Notes in Numerical Analysis with Mathematica
by Tadeusz StyŚ and Krystyna StyŚ
Theory and Numerical Approximations of Fractional Integrals and Derivatives
by Changpin Li and Min Cai
Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus and provides a detailed treatment of existing numerical approximations. Theory and Numerical Approximations of...
Reliable Methods for Computer Simulation (Studies in Mathematics and Its Applications, #33)
by Professor Department of Mathematics P Neittaanmaki, Pekka Neittaanm Ki, and Sergey R Repin
Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such...
Introduction to Numerical Analysis and Scientific Computing
by Nabil Nassif and Dolly Khuwayri Fayyad
Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple and double-precision standards as used in scientific computer environments such as MATLAB (R) version 7. Drawing on their years of teaching students in...
Eine Algorithmisch Orientierte Einf hrung (de Gruyter Lehrbuch)
by Peter Deuflhard and Andreas Hohmann
An Introduction to Numerical Computations
by Sidney J. Yakowitz and Ferenc Szidarovszky
This introduction to modern numerical methods encourages students in mathematics, physics, engineering, computer science or physical science to develop computational intuition and self-reliance by comparing the performance of various methods in solving a given problem. Number representation and round-off are presented in a hypothetical computer decimal word, instead of in binary representation, to simplify the explanation of origins and propagation of round-off error. Linear equations are studie...
This book examines how nonlinear optimization techniques can be applied to training and testing neural networks. It includes both well-known and recently-developed network training methods including deterministic nonlinear optimization methods, stochastic nonlinear optimization methods, and advanced training schemes which combine both deterministic and stochastic components. The convergence analysis and convergence proofs of these techniques are presented as well as real applications of neural n...
Elementary Numerical Analysis (Classics in Applied Mathematics)
by S.D. Conte and Carl De Boor
This book provides a thorough and careful introduction to the theory and practice of scientific computing at an elementary, yet rigorous, level, from theory via examples and algorithms to computer programs. The original FORTRAN programs have been rewritten in MATLAB and now appear in a new appendix and online, offering a modernized version of this classic reference for basic numerical algorithms.
Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is...
Health, for Better, for Worse (Open Mathematics, Course MU120)
Numerical Analysis
by Walter Albert Watson, etc., T. Philipson, and P. J. Oates
Numerical Computation of Internal and External Flows, Second Edition
by Charles Hirsch
The second edition of this book is a self-contained introduction to computational fluid dynamics (CFD). It covers the fundamentals of the subject and is ideal as a text or a comprehensive reference to CFD theory and practice. New approach takes readers seamlessly from first principles to more advanced and applied topics. Presents the essential components of a simulation system at a level suitable for those coming into contact with CFD for the first time, and is ideal for those who need a compr...
Scientific Programming: C-language, Algorithms And Models In Science
by Enzo Marinari, Luciano Maria Barone, Giovanni Organtini, and Federico Ricci-tersenghi
The book teaches a student to model a scientific problem and write a computer program in C language to solve that problem. To do that, the book first introduces the student to the basics of C language, dealing with all syntactical aspects, but without the pedantic content of a typical programming language manual. Then the book describes and discusses many algorithms commonly used in scientific applications (e.g. searching, graphs, statistics, equation solving, Monte Carlo methods etc.).Th...
This text presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting theory.The applied techniques include those that arise in the present literature. The supporting mathematical theory includes the general convergence theory. This material should be readily accessible to stud...