The chapter on statistical-physics simulations has been enlarged, mainly by a dis cussion of multispin coding techniques for the Ising model (bit-by-bit parallel oper ations). In the chapter about Reduce, some details of the presentation have been cor rected or clarified. The new operator MATEIGEN for the computation of eigenvec tors of matrices is explained. The first chapter and the appendix remain unchanged. Needless to say, the field of computational science is advancing so quickly, for ex ample with the development of parallel, as opposed to vectorized, algorithms, that it will not be too long before a further edition is called for. Cologne, March 1989 The authors Preface to the First Edition Computers play an increasingly important role in many of today's activities, and correspondingly physicists find employment after graduation in computer related jobs, often quite remote from their physics education. The present lectures, on the other hand, emphasize how we can use computers for the purposes of fundamental research in physics. Thus we do not deal with programs designed for newspapers, banks, or travel agencies, i.e., word processing and storage of large amounts of data.

Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.

Daniel Maki and Maynard Thompson provide a conceptual framework for the process of building and using mathematical models, illustrating the uses of mathematical and computer models in a variety of situations.

This text is based on the authors' broad experience in teaching the application of computers to physics. It takes the reader from the introductory simulation of classical mechanical problems (part one) to current research in statistical physics. The Ising model, cellular automata, percolation, Eden clusters and the Kauffman model are presented with exercises and programs for hands-on use with the aim of enabling and encouraging the student to write her/his own programs. The third part gives a detailed course into algebraic formula manipulation using the computer algebra system REDUCE, again with numerous examples and exercises. These "lectures for beginners" do not require any previous knowledge of computer languages, but a brief introduction to FORTRAN and BASIC can be found in the appendix.

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

Computational methods pertaining to many branches of science, such as physics, physical chemistry and biology, are presented. The text is primarily intended for third-year undergraduate or first-year graduate students. However, active researchers wanting to learn about the new techniques of computational science should also benefit from reading the book. It treats all major methods, including the powerful molecular dynamics method, Brownian dynamics and the Monte-Carlo method. All methods are treated equally from a theroetical point of view. In each case the underlying theory is presented and then practical algorithms are displayed, giving the reader the opportunity to apply these methods directly. For this purpose exercises are included. The book also features complete program listings ready for application.

Papers direct the focus of interest to the development and use of conceptual models in information systems of various kinds and aim at improving awareness about general or specific problems and solutions in conceptual modelling.

This book is written to introduce computer simulations to undergraduate college students, freshmen to seniors, in STEM fields. The book starts with concepts from Basic Mathematics: Geometry, Algebra and Calculus, Properties of Elementary Functions (Polynomials, Exponential, Hyperbolic and Trigonometric Functions) are studied and simple differential equations representing these functions are derived. Numerical approximations of first and second order differential equations are studied in terms of finite differences on uniform grids. Computer solutions are obtained via recursive relations or solutions of simultaneous algebraic equations. Comparisons with the exact solutions (known a priori) allow the calculations of the error due to discretization. After the students build confidence in this approach, more problems where the solutions are not known a priori are tackled with applications in many fields. Next, the book gradually addresses linear differential equations with variable coefficients and nonlinear differential equations, including problems of bifurcation and chaos.Applications in Dynamics, Solid Mechanics, Fluid Mechanics, Heat Transfer, Chemical Reactions, and Combustion are included. Biographies of 50 pioneering mathematicians and scientists who contributed to the materials of the book are briefly sketched, to shed light on the history of these STEM fields.Finally, the main concepts discussed in the book, are summarized to make sure that the students do not miss any of them. Also, references for further readings are given for interested readers.