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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.
Applied mathematics, modelling, and computer simulation are central to many aspects of engineering and computer science, and continue to be of intrinsic importance to the development of modern technologies. This book presents the proceedings of AMMCS 2023, the 3rd International Conference on Applied Mathematics, Modeling and Computer Simulation, held on 12 and 13 August 2023 in Wuhan, China. The conference provided an ideal opportunity for scholars and researchers to communicate important recent developments in their areas of specialization to their colleagues, and to scientists in related disciplines. More than 250 submissions were received for the conference, of which 133 were selected for presentation at the conference and inclusion here after a thorough peer-review process. These range from the theoretical and conceptual to strongly pragmatic papers addressing industrial best practice, and cover topics such as mathematical modeling and application; engineering applications and scientific computations; and the simulation of intelligent systems. The book explores practical experiences and enlightening ideas, and will be of interest to researchers, practitioners, and to all those working in the fields of applied mathematics, modeling and computer simulation.
The aim of this book is to introduce the subject of mathematical modeling in the life sciences. It is intended for students of mathematics, the physical sciences, and engineering who are curious about biology. Additionally, it will be useful to students of the life sciences and medicine who are unsatisfied with mere description and who seek an understanding of biological mechanism and dynamics through the use of mathematics. The book will be particularly useful to premedical students, because it will introduce them not only to a collection of mathematical methods but also to an assortment of phenomena involving genetics, epidemics, and the physiology of the heart, lung, and kidney. Because of its introductory character, mathematical prerequisites are kept to a minimum; they involve only what is usually covered in the first semester of a calculus sequence. The authors have drawn on their extensive experience as modelers to select examples which are simple enough to be understood at this elementary level and yet realistic enough to capture the essence of significant biological phenomena drawn from the areas of population dynamics and physiology. Because the models presented are realistic, the book can serve not only as an introduction to mathematical methods but also as a mathematical introduction to the biological material itself. For the student, who enjoys mathematics, such an introduction will be far more stimulating and satisfying than the purely descriptive approach that is traditional in the biological sciences.
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 concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).
This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.
The result of lectures given by the authors at New York University, the University of Utah, and Michigan State University, the material is written for students who have had only one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well as solutions to selected exercises, so as to lead readers to discover interesting extensions of that material. Throughout, illustrations depict physiological processes, population biology phenomena, corresponding models, and the results of computer simulations. Topics covered range from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models.
Very broad overview of the field intended for an interdisciplinary audience; Lively discussion of current challenges written in a colloquial style; Author is a rising star in this discipline; Suitably accessible for beginners and suitably rigorous for experts; Features extensive four-color illustrations; Appendices featuring homework assignments and reading lists complement the material in the main text