An Introduction To Mathematical Modeling

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An Introduction to Mathematical Modeling

Edward A. Bender
An Introduction to Mathematical Modeling Book PDF

Author : Edward A. Bender
Publisher : Courier Corporation
Page : 273 pages
File Size : 49,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486137124

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An Introduction to Mathematical Modeling by Edward A. Bender Pdf

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.

An Introduction to Mathematical Modeling of Infectious Diseases

Michael Y. Li
An Introduction to Mathematical Modeling of Infectious Diseases Book PDF

Author : Michael Y. Li
Publisher : Springer
Page : 156 pages
File Size : 46,8 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319721224

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An Introduction to Mathematical Modeling of Infectious Diseases by Michael Y. Li Pdf

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Introduction to Mathematical Modeling

Mayer Humi
Introduction to Mathematical Modeling Book PDF

Author : Mayer Humi
Publisher : CRC Press
Page : 484 pages
File Size : 40,5 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781498728027

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Introduction to Mathematical Modeling by Mayer Humi Pdf

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

Introduction to Mathematical Modeling and Computer Simulations

Vladimir Mityushev,Wojciech Nawalaniec,Natalia Rylko
Introduction to Mathematical Modeling and Computer Simulations Book PDF

Author : Vladimir Mityushev,Wojciech Nawalaniec,Natalia Rylko
Publisher : CRC Press
Page : 211 pages
File Size : 49,5 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351998758

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Introduction to Mathematical Modeling and Computer Simulations by Vladimir Mityushev,Wojciech Nawalaniec,Natalia Rylko Pdf

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.

An Introduction to Mathematical Modeling

J. Tinsley Oden
An Introduction to Mathematical Modeling Book PDF

Author : J. Tinsley Oden
Publisher : John Wiley & Sons
Page : 348 pages
File Size : 40,6 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9781118105740

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An Introduction to Mathematical Modeling by J. Tinsley Oden Pdf

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.

Mathematical Modeling in Systems Biology

Brian P. Ingalls
Mathematical Modeling in Systems Biology Book PDF

Author : Brian P. Ingalls
Publisher : MIT Press
Page : 423 pages
File Size : 42,5 Mb
Release : 2022-06-07
Category : Science
ISBN : 9780262545822

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Mathematical Modeling in Systems Biology by Brian P. Ingalls Pdf

An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.

Concepts of Mathematical Modeling

Walter J. Meyer
Concepts of Mathematical Modeling Book PDF

Author : Walter J. Meyer
Publisher : Courier Corporation
Page : 450 pages
File Size : 53,9 Mb
Release : 2012-10-23
Category : Mathematics
ISBN : 9780486137247

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Concepts of Mathematical Modeling by Walter J. Meyer Pdf

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition.

An Introduction to Mathematical Modelling

Neville D. Fowkes,John J. Mahony
An Introduction to Mathematical Modelling Book PDF

Author : Neville D. Fowkes,John J. Mahony
Publisher : Wiley
Page : 464 pages
File Size : 48,7 Mb
Release : 1994-08-16
Category : Technology & Engineering
ISBN : 0471943096

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An Introduction to Mathematical Modelling by Neville D. Fowkes,John J. Mahony Pdf

Demonstrates the challenges and fascinations of mathematical modelling and enables students to develop the skills required to examine real life problems. The various techniques and skills are introduced to the reader through the discussion of a variety of carefully selected problems and exercises, largely drawn from industrial contexts. Maple is used for the problems discussed and for many of the exercises, with suggestions and commands provided for readers unfamiliar with this software package.

Modelling Nature

Edward Gillman,Michael Gillman
Modelling Nature Book PDF

Author : Edward Gillman,Michael Gillman
Publisher : CABI
Page : 281 pages
File Size : 40,9 Mb
Release : 2019-05-30
Category : Science
ISBN : 9781786393104

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Modelling Nature by Edward Gillman,Michael Gillman Pdf

This short textbook introduces students to the concept of describing natural systems using mathematical models. We highlight the variety of ways in which natural systems lend themselves to mathematical description and the importance of models in revealing fundamental processes. The process of science via the building, testing and use of models (theories) is described and forms the structure of the book. The book covers a broad range from the molecular to ecosystems and whole-Earth phenomena. Themes running through the chapters include scale (temporal and spatial), change (linear and nonlinear), emergent phenomena and uncertainty. Mathematical descriptions are kept to a minimum and we illustrate mechanisms and results in graphical form wherever possible. Essential mathematical details are described fully, with the use of boxes. The mathematics supports but does not lead the text.

Mathematical Modeling and Simulation

Kai Velten
Mathematical Modeling and Simulation Book PDF

Author : Kai Velten
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 42,9 Mb
Release : 2009-06-01
Category : Science
ISBN : 9783527627615

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Mathematical Modeling and Simulation by Kai Velten Pdf

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).

A Historical Introduction to Mathematical Modeling of Infectious Diseases

Ivo M. Foppa
A Historical Introduction to Mathematical Modeling of Infectious Diseases Book PDF

Author : Ivo M. Foppa
Publisher : Academic Press
Page : 214 pages
File Size : 53,7 Mb
Release : 2016-10-18
Category : Mathematics
ISBN : 9780128024997

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A Historical Introduction to Mathematical Modeling of Infectious Diseases by Ivo M. Foppa Pdf

A Historical Introduction to Mathematical Modeling of Infectious Diseases: Seminal Papers in Epidemiology offers step-by-step help on how to navigate the important historical papers on the subject, beginning in the 18th century. The book carefully, and critically, guides the reader through seminal writings that helped revolutionize the field. With pointed questions, prompts, and analysis, this book helps the non-mathematician develop their own perspective, relying purely on a basic knowledge of algebra, calculus, and statistics. By learning from the important moments in the field, from its conception to the 21st century, it enables readers to mature into competent practitioners of epidemiologic modeling. Presents a refreshing and in-depth look at key historical works of mathematical epidemiology Provides all the basic knowledge of mathematics readers need in order to understand the fundamentals of mathematical modeling of infectious diseases Includes questions, prompts, and answers to help apply historical solutions to modern day problems

Introduction to Mathematical Modeling of Crop Growth

Christopher B. S. Teh
Introduction to Mathematical Modeling of Crop Growth Book PDF

Author : Christopher B. S. Teh
Publisher : Dissertation.com
Page : 278 pages
File Size : 54,5 Mb
Release : 2006
Category : Technology & Engineering
ISBN : 9781581129991

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Introduction to Mathematical Modeling of Crop Growth by Christopher B. S. Teh Pdf

Learning mathematical modeling need not be difficult. Unlike other books, this book not only lists the equations one-by-one, but explains in detail how they are each derived, used, and finally assembled into a computer program for model simulations. This book shows how mathematics is applied in agriculture, in particular to modeling the growth and yield of a generic crop. Topics covered are agriculture meteorology, solar radiation interception and absorption, evapotranspiration, energy and soil water balance, soil water flow, photosynthesis, respiration, and crop growth development. Rather than covering many modeling approaches but in superficial detail, this book selects one or two widely-used modeling approaches and discusses about them in depth. Principles learned from this book equips readers when they encounter other modeling approaches or when they develop their own crop models.

An Introduction to Mathematical Epidemiology

Maia Martcheva
An Introduction to Mathematical Epidemiology Book PDF

Author : Maia Martcheva
Publisher : Springer
Page : 453 pages
File Size : 51,8 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9781489976123

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An Introduction to Mathematical Epidemiology by Maia Martcheva Pdf

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.

The Nature of Mathematical Modeling

Neil A. Gershenfeld
The Nature of Mathematical Modeling Book PDF

Author : Neil A. Gershenfeld
Publisher : Cambridge University Press
Page : 268 pages
File Size : 40,6 Mb
Release : 1999
Category : Science
ISBN : 0521570956

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The Nature of Mathematical Modeling by Neil A. Gershenfeld Pdf

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems.

Mathematical Modeling

Sandip Banerjee
Mathematical Modeling Book PDF

Author : Sandip Banerjee
Publisher : CRC Press
Page : 419 pages
File Size : 52,6 Mb
Release : 2021-11-11
Category : Mathematics
ISBN : 9781351022934

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Mathematical Modeling by Sandip Banerjee Pdf

Mathematical Modeling: Models, Analysis and Applications, Second Edition introduces models of both discrete and continuous systems. This book is aimed at newcomers who desires to learn mathematical modeling, especially students taking a first course in the subject. Beginning with the step-by-step guidance of model formulation, this book equips the reader about modeling with difference equations (discrete models), ODE’s, PDE’s, delay and stochastic differential equations (continuous models). This book provides interdisciplinary and integrative overview of mathematical modeling, making it a complete textbook for a wide audience. A unique feature of the book is the breadth of coverage of different examples on mathematical modelling, which include population models, economic models, arms race models, combat models, learning model, alcohol dynamics model, carbon dating, drug distribution models, mechanical oscillation models, epidemic models, tumor models, traffic flow models, crime flow models, spatial models, football team performance model, breathing model, two neuron system model, zombie model and model on love affairs. Common themes such as equilibrium points, stability, phase plane analysis, bifurcations, limit cycles, period doubling and chaos run through several chapters and their interpretations in the context of the model have been highlighted. In chapter 3, a section on estimation of system parameters with real life data for model validation has also been discussed. Features Covers discrete, continuous, spatial, delayed and stochastic models. Over 250 illustrations, 300 examples and exercises with complete solutions. Incorporates MATHEMATICA® and MATLAB®, each chapter contains Mathematica and Matlab codes used to display numerical results (available at CRC website). Separate sections for Projects. Several exercise problems can also be used for projects. Presents real life examples of discrete and continuous scenarios. The book is ideal for an introductory course for undergraduate and graduate students, engineers, applied mathematicians and researchers working in various areas of natural and applied sciences.