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| functions and modeling math: Modeling, Functions, and Graphs Katherine Franklin, Katherine Yoshiwara, Irving Drooyan, 1991 While maintaining its focus on functions and graphs this book gives the adequately prepared algebra student the right start and flexible goals. |
| functions and modeling math: Elementary Mathematical Modeling Mary Ellen Davis, Charles Henry Edwards, 2007 For introductory college math course at the college algebra level for non-calculus bound students. Designed for students who are not headed for calculus-based curricula - but who still need a solid quantitative foundation for subsequent studies and for life as educated citizens - this introduction to mathematical modeling offers an alternative approach to college algebra. The authors use elementary functions to describe and explore real-world data and phenomena. Students learn how to construct useful mathematical models, to analyze them critically, and to communicate quantitative concepts effectively. The Second Edition is even more student-friendly, with more concrete language and examples throughout. |
| functions and modeling math: Calculus: Functions and models James Stewart, 2012 |
| functions and modeling math: Functions, Data and Models Sheldon P. Gordon, Florence S. Gordon, 2010 Focuses primarily on mathematical concepts and mathematical thinking, thereby achieving a balance among geometric, numerical, symbolic, and statistical approaches, rather than focusing on algebraic manipulation. Gordon incorporates a significant amount of statistical reasoning and methods as natural applications of more standard college algebra topics. --From publisher description. |
| functions and modeling math: College Algebra Jay Abramson, 2018-01-07 College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory |
| functions and modeling math: Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition Dan Kalman, Sacha Forgoston, Albert Goetz, 2019-08-02 Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the methodology of mathematical modeling, which plays a role in nearly all real applications of mathematics. A course based on this text would have as its primary goal preparing students to be competent consumers of mathematical modeling in their future studies. Such a course would also provide students with an understanding of the modeling process and a facility with much of the standard, non-trigonometric, content of college algebra and precalculus. This book builds, successively, a series of growth models defined in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth. Students discover and come to understand linear, polynomial, exponential, and logarithmic functions in the context of analyzing these models of intrinsically—and scientifically—interesting phenomena including polar ice extent, antibiotic resistance, and viral internet videos. Students gain a deep appreciation for the power and limitations of mathematical modeling in the physical, life, and social sciences as questions of modeling methodology are carefully and constantly addressed. Realistic examples are used consistently throughout the text, and every topic is illustrated with models that are constructed from and compared to real data. The text is extremely attractive and the exposition is extraordinarily clear. The lead author of this text is the recipient of nine MAA awards for expository writing including the Ford, Evans, Pólya, and Allendoerfer awards and the Beckenbach Book prize. Great care has been taken by accomplished expositors to make the book readable by students. Those students will also benefit from more than 1,000 carefully crafted exercises. |
| functions and modeling math: Modeling Life Alan Garfinkel, Jane Shevtsov, Yina Guo, 2017-09-06 This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science? |
| functions and modeling math: R for Data Science Hadley Wickham, Garrett Grolemund, 2016-12-12 Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you've learned along the way. You'll learn how to: Wrangle—transform your datasets into a form convenient for analysis Program—learn powerful R tools for solving data problems with greater clarity and ease Explore—examine your data, generate hypotheses, and quickly test them Model—provide a low-dimensional summary that captures true signals in your dataset Communicate—learn R Markdown for integrating prose, code, and results |
| functions and modeling math: Algebra and Trigonometry Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Rick Norwood, Melonie Rasmussen, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2015-02-13 The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. While the breadth of topics may go beyond what an instructor would cover, the modular approach and the richness of content ensures that the book meets the needs of a variety of programs.--Page 1. |
| functions and modeling math: Mathematical Modeling Christof Eck, Harald Garcke, Peter Knabner, 2017-04-11 Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively. |
| functions and modeling math: Fitting Models to Biological Data Using Linear and Nonlinear Regression Harvey Motulsky, Arthur Christopoulos, 2004-05-27 Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists. |
| functions and modeling math: Introduction to Mathematical Modeling and Computer Simulations Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko, 2018-02-19 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. |
| functions and modeling math: Functions Modeling Change Eric Connally, Deborah Hughes-Hallett, 2017-09-13 The 5th edition of this market-leading text helps instructors instill key algebra and trig concepts and helps students develop critical thinking skills. Functions Modeling Change, 5th Edition, is designed to accomplish the main goals of the Precalculus course: to build a solid mathematical foundation and prepare students for Calculus. The authors achieve this by focusing on a small number of key topics, thereby emphasizing depth of understanding rather than breadth of coverage. Functions Modeling Change, 5th Edition, presents each function symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples, and problems enable students to create mathematical models that relate to the world around them. |
| functions and modeling math: Guide to Mathematical Modelling David A Towers, Dilwyn Edwards, Mike Hamson, 2020-06-06 A basic introduction to Mathematical Modelling, this book encourages the reader to participate in the investigation of a wide variety of modelling examples. These are carefully paced so that the readers can identify and develop the skills which are required for successful modelling. The examples also promote an appreciation of the enormous range of problems to which mathematical modelling skills can be usefully applied. |
| functions and modeling math: Domain Modeling Made Functional Scott Wlaschin, 2018-01-25 You want increased customer satisfaction, faster development cycles, and less wasted work. Domain-driven design (DDD) combined with functional programming is the innovative combo that will get you there. In this pragmatic, down-to-earth guide, you'll see how applying the core principles of functional programming can result in software designs that model real-world requirements both elegantly and concisely - often more so than an object-oriented approach. Practical examples in the open-source F# functional language, and examples from familiar business domains, show you how to apply these techniques to build software that is business-focused, flexible, and high quality. Domain-driven design is a well-established approach to designing software that ensures that domain experts and developers work together effectively to create high-quality software. This book is the first to combine DDD with techniques from statically typed functional programming. This book is perfect for newcomers to DDD or functional programming - all the techniques you need will be introduced and explained. Model a complex domain accurately using the F# type system, creating compilable code that is also readable documentation---ensuring that the code and design never get out of sync. Encode business rules in the design so that you have compile-time unit tests, and eliminate many potential bugs by making illegal states unrepresentable. Assemble a series of small, testable functions into a complete use case, and compose these individual scenarios into a large-scale design. Discover why the combination of functional programming and DDD leads naturally to service-oriented and hexagonal architectures. Finally, create a functional domain model that works with traditional databases, NoSQL, and event stores, and safely expose your domain via a website or API. Solve real problems by focusing on real-world requirements for your software. What You Need: The code in this book is designed to be run interactively on Windows, Mac and Linux.You will need a recent version of F# (4.0 or greater), and the appropriate .NET runtime for your platform.Full installation instructions for all platforms at fsharp.org. |
| functions and modeling math: An Introduction to Mathematical Modeling Edward A. Bender, 2012-05-23 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. |
| functions and modeling math: Mathematical Modeling in Economics, Ecology and the Environment N.V. Hritonenko, Yuri P. Yatsenko, 2013-04-17 The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ... |
| functions and modeling math: Mathematical Modeling Jonas Hall, Thomas Lingefjärd, 2016-06-13 A logical problem-based introduction to the use of GeoGebra for mathematical modeling and problem solving within various areas of mathematics A well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, Mathematical Modeling: Applications with GeoGebra presents a unique approach to software applications in GeoGebra and WolframAlpha. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebra can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations. Each chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, Mathematical Modeling: Applications with GeoGebra also includes: Over 400 diagrams and 300 GeoGebra examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content Numerous real-world exercises with solutions to help readers learn mathematical modeling techniques A companion website with GeoGebra constructions and screencasts Mathematical Modeling: Applications with GeoGebrais ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics. |
| functions and modeling math: A Primer on Mathematical Modelling Alfio Quarteroni, Paola Gervasio, 2020-10-09 In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models. |
| functions and modeling math: Mathematical models Gerd Fischer, 1986 |
| functions and modeling math: Mathematical Modeling of Earth's Dynamical Systems Rudy Slingerland, Lee Kump, 2011-03-28 A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html |
| functions and modeling math: Mathematical Models in Biology Elizabeth Spencer Allman, John A. Rhodes, 2004 This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal. |
| functions and modeling math: Functions Modeling Change Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason, 2019-02-20 An accessible Precalculus text with concepts, examples, and problems The sixth edition of Functions Modeling Change: A Preparation for Calculus helps students establish a foundation for studying Calculus. The text covers key Precalculus topics, examples, and problems. Chapters examine linear, quadratic, logarithmic, exponential, polynomial, and rational functions. They also explore trigonometry and trigonometric Identities, plus vectors and matrices. The end of each chapter offers details on how students can strengthen their knowledge about the topics covered. |
| functions and modeling math: Modelling and Applications in Mathematics Education Peter L. Galbraith, Hans-Wolfgang Henn, Mogens Niss, 2007-12-05 The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students. |
| functions and modeling math: Modeling with Logarithms Jack Burrill, Miriam Clifford, James M. Landwehr, 1999 |
| functions and modeling math: Functions and Change Bruce Crauder, Benny Evans, Alan Noell, 2014 |
| functions and modeling math: Mathematical Models in Biology Leah Edelstein-Keshet, 1988-01-01 Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field. |
| functions and modeling math: Dynamic Models in Biology Stephen P. Ellner, John Guckenheimer, 2011-09-19 From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering. |
| functions and modeling math: Principles of Mathematical Modeling Clive Dym, 2004-08-10 Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and own the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics. - Serves as an introductory text on the development and application of mathematical models - Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems - Offers more than 360 problems, providing ample opportunities for practice - Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences - Uses straightforward language and explanations that make modeling easy to understand and apply New to this Edition: - A more systematic approach to mathematical modeling, outlining ten specific principles - Expanded and reorganized chapters that flow in an increasing level of complexity - Several new problems and updated applications - Expanded figure captions that provide more information - Improved accessibility and flexibility for teaching |
| functions and modeling math: A First Course in Mathematical Modeling Frank R. Giordano, William P. Fox, Steven B. Horton, Maurice D. Weir, 2008-07-03 Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| functions and modeling math: Modeling and Simulation in Python Allen B. Downey, 2023-05-30 Modeling and Simulation in Python teaches readers how to analyze real-world scenarios using the Python programming language, requiring no more than a background in high school math. Modeling and Simulation in Python is a thorough but easy-to-follow introduction to physical modeling—that is, the art of describing and simulating real-world systems. Readers are guided through modeling things like world population growth, infectious disease, bungee jumping, baseball flight trajectories, celestial mechanics, and more while simultaneously developing a strong understanding of fundamental programming concepts like loops, vectors, and functions. Clear and concise, with a focus on learning by doing, the author spares the reader abstract, theoretical complexities and gets right to hands-on examples that show how to produce useful models and simulations. |
| functions and modeling math: Handbook of Mathematical Functions Milton Abramowitz, Irene A. Stegun, 1965-01-01 An extensive summary of mathematical functions that occur in physical and engineering problems |
| functions and modeling math: Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations Steven R. Dunbar, 2019-04-03 Mathematical Modeling in Economics and Finance is designed as a textbook for an upper-division course on modeling in the economic sciences. The emphasis throughout is on the modeling process including post-modeling analysis and criticism. It is a textbook on modeling that happens to focus on financial instruments for the management of economic risk. The book combines a study of mathematical modeling with exposure to the tools of probability theory, difference and differential equations, numerical simulation, data analysis, and mathematical analysis. Students taking a course from Mathematical Modeling in Economics and Finance will come to understand some basic stochastic processes and the solutions to stochastic differential equations. They will understand how to use those tools to model the management of financial risk. They will gain a deep appreciation for the modeling process and learn methods of testing and evaluation driven by data. The reader of this book will be successfully positioned for an entry-level position in the financial services industry or for beginning graduate study in finance, economics, or actuarial science. The exposition in Mathematical Modeling in Economics and Finance is crystal clear and very student-friendly. The many exercises are extremely well designed. Steven Dunbar is Professor Emeritus of Mathematics at the University of Nebraska and he has won both university-wide and MAA prizes for extraordinary teaching. Dunbar served as Director of the MAA's American Mathematics Competitions from 2004 until 2015. His ability to communicate mathematics is on full display in this approachable, innovative text. |
| functions and modeling math: Precalculus Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Melonie Rasmussen, Rick Norwood, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2014-10-23 Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses.--Preface. |
| functions and modeling math: Mathematical Modelling Simon Serovajsky, 2021-11-24 Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented. Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc. |
| functions and modeling math: RFID in Logistics Erick C. Jones, Christopher A. Chung, 2007-12-03 Radio Frequency Identification (RFID) tagging is now mandated by the department of defense and many of the world's largest retailers including Wal-Mart. In order to stay competitive, more than 200,000 manufacturers and suppliers must develop strategies for integrating RFID technologies into their supply chains. RFID in Logistics: A Practical Introd |
| functions and modeling math: Functions in Mathematics Mark Daniels, Efraim P. Armendariz, 2011-06 When discussing the mathematical knowledge of elementary school teachers, the National Council of Teachers of Mathematics concludes that teachers must have a deep understanding of mathematics and be able to easily draw on that knowledge with flexibility in their teaching tasks. Mathematics teachers must understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected endeavor. This inquiry and exploration-based workbook has been designed as a tool for pre-service and in-service mathematics teachers to use as a guidebook for doing mathematics and exploring mathematics topics in depth. The lessons chosen for this text serve as a function-based approach that connects important topics in the secondary mathematics curriculum and act as a bridge to university-level mathematics. Whether used as a course text or for individual professional development purposes, this book should be approached from the standpoint of discovery and reflection about the significance of the selected topics. It is the authors' hope that the explorations contained within serve as vehicles for classroom discussion and presentation of mathematics topics, or as starting points for further investigation. Efraim P. Armendariz is a professor of mathematics at the University of Texas at Austin. His mathematical interests include noncommutative ring theory, development of educational programs addressing accessibility issues, and development of secondary mathematics teachers. He received a Ph.D. in Mathematics from the University of Nebraska-Lincoln in 1966. Mark L. Daniels is a clinical associate professor of mathematics and UTeach Natural Sciences at the University of Texas at Austin. His research interests involve the preparation of pre-service teachers and the incorporation of instructional methodology in mathematics courses taken by students seeking certification. |
| functions and modeling math: Differential Equations Robert L. Borrelli, Courtney S. Coleman, 2004-01-02 This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs. |
| functions and modeling math: An Invitation to Arithmetic Geometry Dino Lorenzini, 2021-12-23 Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject. |
| functions and modeling math: Calculus for the Life Sciences James L. Cornette, Ralph A. Ackerman, 2015-12-30 Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text. The students should have studied algebra, geometry, and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. |
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Inverse functions and transformations: Matrix transformations Finding inverses and determinants: Matrix transformations More determinant depth: Matrix transformations Transpose of a matrix: …
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Jun 5, 2025 · Read this article in another language: 🇦🇲 Հայերեն 🇮🇩 Bahasa Indonesia 🇧🇬 български 🇫🇷 Français 🇲🇽 Español 🇮🇳 हिन्दी (इंडिया) 🇧🇷 Português (Brasil) ------- Welcome ...
Free, fun educational app for young kids | Khan Academy Kids
Inspire a lifetime of learning with our educational app for kids ages 2-7. Kids can learn reading, writing, math, counting, ABCs, addition, subtraction, social-emotional skills, & more. 100% free …
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Apprenez gratuitement les Mathématiques, l'Art, la Programmation, l'Economie, la Physique, la Chimie, la Biologie, la Médecine, la Finance, l'Histoire et plus encore. Khan Academy est une …
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Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point …
Input validation 2nd step in 2nd unit of Intro to computer science ...
Feb 25, 2025 · If you have more difficulty with figuring out Python Challenges, I encourage you to use the Questions or Help Requests functions provided in the website. I think you will get a …
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Learn about functions, their properties, and how to work with them in algebra on Khan Academy.
Free Math Worksheets - Khan Academy Blog
Mar 15, 2021 · Differentiation: composite, implicit, and inverse functions; Contextual applications of differentiation; Applying derivatives to analyze functions; Integration and accumulation of …
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Analyze polynomials in order to sketch their graph.
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Inverse functions and transformations: Matrix transformations Finding inverses and determinants: Matrix transformations More determinant depth: Matrix transformations Transpose of a matrix: …
Khan Academy for Parents: Quick Start Guide
Jun 5, 2025 · Read this article in another language: 🇦🇲 Հայերեն 🇮🇩 Bahasa Indonesia 🇧🇬 български 🇫🇷 Français 🇲🇽 Español 🇮🇳 हिन्दी (इंडिया) 🇧🇷 Português (Brasil) ------- Welcome ...
Free, fun educational app for young kids | Khan Academy Kids
Inspire a lifetime of learning with our educational app for kids ages 2-7. Kids can learn reading, writing, math, counting, ABCs, addition, subtraction, social-emotional skills, & more. 100% free …
Khan Academy
Apprenez gratuitement les Mathématiques, l'Art, la Programmation, l'Economie, la Physique, la Chimie, la Biologie, la Médecine, la Finance, l'Histoire et plus encore. Khan Academy est une …
Khan Academy
Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point …
Input validation 2nd step in 2nd unit of Intro to computer science ...
Feb 25, 2025 · If you have more difficulty with figuring out Python Challenges, I encourage you to use the Questions or Help Requests functions provided in the website. I think you will get a …
