*The authors' enthusiasm for their subject is eloquently conveyed in this book, and draws the reader very quickly into active investigation of the problems posed.*

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# Guide to Mathematical Modelling

The authors' enthusiasm for their subject is eloquently conveyed in this book, and draws the reader very quickly into active investigation of the problems posed. By providing plenty of modelling examples from a wide variety of fields - most of which are familiar from everyday life - the book shows how to apply mathematical ideas to situations which would not previously have been considered to be 'mathematical' in character.
# A Biologist s Guide to Mathematical Modeling in Ecology and Evolution

Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
# Mathematical Modelling

An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.
# Introduction to Mathematical Modelling

Produced principally for undergraduate unit SIT194 (Introduction to mathematical modelling) offered by the Faculty of Science and Technology's School of Information Technology in Deakin University's Flexible Learning Program.
# Mathematical Modelling for Teachers

Mathematical Modelling for Teachers: Resources, Pedagogy and Practice provides everything that teachers and mathematics educators need to design and implement mathematical modelling activities in their classroom. Authored by an expert in Singapore, the global leader in mathematics education, it is written with an international readership in mind. This book focuses on practical classroom ideas in mathematical modelling suitable to be used by mathematics teachers at the secondary level. As they are interacting with students all the time, teachers generally have good ideas for possible mathematical modelling tasks. However, many have difficulty translating those ideas into concrete modelling activities suitable for a mathematics classroom. In this book, a framework is introduced to assist teachers in designing, planning and implementing mathematical modelling activities, and its use is illustrated through the many examples included. Readers will have access to modelling activities suitable for students from lower secondary levels (Years 7 and 8) onwards, along with the underlying framework, guiding notes for teachers and suggested approaches to solve the problems. The activities are grouped according to the types of models constructed: empirical, deterministic and simulation models. Finally, the book gives the reader suggestions of different ways to assess mathematical modelling competencies in students.
# Modeling Students Mathematical Modeling Competencies

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.
# Mathematical Modelling

Mathematical modelling is often spoken of as a way of life, referring to habits of mind and to dependence on the power of mathematics to describe, explain, predict and control real phenomena. This book aims to encourage teachers to provide opportunities for students to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education. Habits, misconceptions, and mindsets about mathematics can present obstacles to university students’ acceptance of a ‘‘models-and-modelling perspective’’ at this stage of mathematics education. Without prior experience in building, interpreting and applying mathematical models, many students may never come to view and regard modelling as a way of life. The book records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003. Examines mathematical modelling as a way of life, referring to habits of mind and dependence on the power of mathematics to describe, explain, predict and control real phenomena Encourages teachers to provide students with opportunities to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education Records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003
# Mathematical Modelling for Teachers

While there are many areas of focus in mathematics education, there are many good reasons for offering applicable mathematics education in schools. Let us just mention two of the most important reasons. On the one hand, a focus on the practical side of mathematics presents a convincing and motivating answer to the typical student question: ‘Why study mathematics?’ On the other hand, education policy seems inclined to move in this direction by implementing international testing, curricula and catalogues of skills. The most important feature of this book is that the authors speak directly to you, the mathematics teachers. The authors attempt to draw you into a continuous dialogue about activities you are asked to engage in as learners. You are asked to do something, and through doing and reflecting you will gain first-hand experience of new approaches and materials. In this way, you can learn to teach applicable mathematics to your students using your own experience as learners of applicable mathematics, motivated and supported by the book. Here applicable mathematics education is the phrase we use to describe reality-based mathematics education. Reality-based mathematics relies heavily on problem solving and a positive disposition to engage with mathematics. Modelling reality and simulating selected aspects of reality are other pillars of reality-based mathematics education.
# Mathematical Modeling

Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences. More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB® and Mathematica® are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project. Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams.
# Mathematical Modelling Techniques

Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.
# Introduction to Atmospheric Modelling

A compact, yet comprehensive, self-study guide that explores the power of mathematics to help us understand complex atmospheric phenomena.
# Mathematical Modelling and Simulation in Chemical Engineering

An easy to understand guide covering key principles of mathematical modelling and simulation in chemical engineering.
# Mathematical Modeling

This book is a logical, well-organized guide to various mathematical modeling techniques and applications for evaluating and solving problems in the diverse field of mathematics. A highly-qualified lecturer in the area of mathematics education and modeling, the author provides a unique pedagogical approach to using GeoGebra and WolframAlpha in courses that require problem solving and evaluation through mathematical modeling. The main software presented in the book is GeoGebra, which is a fast-growing, free program and can be used within numerous areas of mathematics such as algebra, geometry, geometry 3D, functions, statistics, spreadsheet calculations, and symbolic algebra. The book provides detailed information on how to use GeoGebra to teach mathematics, as well as a technical guide to using GeoGebra for mathematical modeling. Beginning with the basics of GeoGebra, the book introduces specific GeoGebra exercises and additional resources for further study. The book then moves on to comprehensive modeling examples that correspond to different levels of mathematics experience. Each chapter builds on the previous chapter’s level, and includes numerous examples of solved modeling tasks with at least one, sometimes several, solution suggestions. These solutions are detailed both mathematically and in a GeoGebra sense to engage readers with the necessary skills for future problem solving and mathematical modeling. Subsequently, the book addresses how to organize practical work and gives examples of various approaches to teaching modeling in the classroom. Finally, the book illustrates the methods for evaluating models, including relative error, correlation, square sum of errors, regression, and confidence interval.
# A Guide to Mathematical Models Used in Steam Electric Power Plant Environmental Impact Assessment

# Guide to Load Analysis for Durability in Vehicle Engineering

The overall goal of vehicle design is to make a robust and reliable product that meets the demands of the customers and this book treats the topic of analysing and describing customer loads with respect to durability. Guide to Load Analysis for Vehicle and Durability Engineering supplies a variety of methods for load analysis and also explains their proper use in view of the vehicle design process. In Part I, Overview, there are two chapters presenting the scope of the book as well as providing an introduction to the subject. Part II, Methods for Load Analysis, describes useful methods and indicates how and when they should be used. Part III, Load Analysis in view of the Vehicle Design Process, offers strategies for the evaluation of customer loads, in particular characterization of customer populations, which leads to the derivation of design loads, and finally to the verification of systems and components. Key features: • Is a comprehensive collection of methods for load analysis, vehicle dynamics and statistics • Combines standard load data analysis methods with statistical aspects on deriving test loads from surveys of customer usage • Sets the methods used in the framework of system dynamics and response, and derives recommendations for the application of methods in engineering practice • Presents a reliability design methodology based on statistical evaluation of component strength and customers loads • Includes case studies and illustrative examples that translate the theory into engineering practice Developed in cooperation with six European truck manufacturers (DAF, Daimler, Iveco, MAN, Scania and Volvo) to meet the needs of industry, Guide to Load Analysis for Vehicle and Durability Engineering provides an understanding of the current methods in load analysis and will inspire the incorporation of new techniques in the design and test processes.
# A Practical Guide to Ecological Modelling

Mathematical modelling is an essential tool in present-day ecological research. Yet for many ecologists it is still problematic to apply modelling in their research. In our experience, the major problem is at the conceptual level: proper understanding of what a model is, how ecological relations can be translated consistently into mathematical equations, how models are solved, steady states calculated and interpreted. Many textbooks jump over these conceptual hurdles to dive into detailed formulations or the mathematics of solution. This book attempts to fill that gap. It introduces essential concepts for mathematical modelling, explains the mathematics behind the methods, and helps readers to implement models and obtain hands-on experience. Throughout the book, emphasis is laid on how to translate ecological questions into interpretable models in a practical way. The book aims to be an introductory textbook at the undergraduate-graduate level, but will also be useful to seduce experienced ecologists into the world of modelling. The range of ecological models treated is wide, from Lotka-Volterra type of principle-seeking models to environmental or ecosystem models, and including matrix models, lattice models and sequential decision models. All chapters contain a concise introduction into the theory, worked-out examples and exercises. All examples are implemented in the open-source package R, thus taking away problems of software availability for use of the book. All code used in the book is available on a dedicated website.
# Criteria for Movements of Moored Ships in Harbours

# Mathematical Modelling of Zombies

In this terrible new COVID-19 world, the University of Ottawa is doing its part by offering a 50% discount on this very important book. We decided not to rewrite the witty book description, though we realize it is tone-deaf at the present moment, as we wanted to give readers a sense of the tone of this title. But don’t be deceived: while a fun read, this book will help you better understand how epidemiologists, governments and health care planners use mathematical models to figure out how quickly epidemics and pandemics spread, in order to plan appropriately. Reading has perhaps never been as important, and this book should be at the top of your reading list. You’re outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course. Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a “hook,” you’ll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you’ll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included). In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You’ll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.). So if the zombies turn up, reach for this book. The future of the human race may depend on it.
# Mathematical Modelling

An important component of mathematical education at all levels the use of mathematics to model real-world situation. In this book the emphasis is on developing models which provide a means to analysis and answer questions posed in practical settings. It provides a pendium of case studies of mathematical models of varying degrees of sophistication and practicality. Teachers and students of mathematical modelling will find it a rich source of examples ranging from insulating houses to basketball and from modelling epidemics to studying the generation of windmill power.
# Mathematical Modelling Computing in Biology and Medicine