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| equation definition math example: In Pursuit of the Unknown Ian Stewart, 2012-03-13 The seventeen equations that form the basis for life as we know it. Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives. Using seventeen of our most crucial equations -- including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time -- Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries. An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world. |
| equation definition math example: Introductory Business Statistics 2e Alexander Holmes, Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| equation definition math example: Prealgebra 2e Lynn Marecek, Maryanne Anthony-Smith, Andrea Honeycutt Mathis, 2020-03-11 The images in this book are in color. For a less-expensive grayscale paperback version, see ISBN 9781680923254. Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi. |
| equation definition math example: Head First Algebra Tracey Pilone, Dan Pilone, 2009 Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, the book uses a visually rich format designed for the way your brain works, not a text-heavy approach that puts you to sleep.--Publisher's note. |
| equation definition math example: Five Equations That Changed the World Dr. Michael Guillen, 2012-06-05 A Publishers Weekly best book of 1995! Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as a wholly accessible, beautifully written exploration of the potent mathematical imagination, and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. |
| equation definition math example: Math with Bad Drawings Ben Orlin, 2018-09-18 A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark bad drawings, which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike. |
| equation definition math example: Linear Ordinary Differential Equations Earl A. Coddington, Robert Carlson, 1997-01-01 Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions. |
| equation definition math example: The Fundamental Theorem of Algebra Benjamin Fine, Gerhard Rosenberger, 2012-12-06 The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal capstone course in mathematics. |
| equation definition math example: A First Course in Differential Equations with Modeling Applications Dennis G. Zill, 1997 |
| equation definition math example: R Markdown Yihui Xie, J.J. Allaire, Garrett Grolemund, 2018-07-27 R Markdown: The Definitive Guide is the first official book authored by the core R Markdown developers that provides a comprehensive and accurate reference to the R Markdown ecosystem. With R Markdown, you can easily create reproducible data analysis reports, presentations, dashboards, interactive applications, books, dissertations, websites, and journal articles, while enjoying the simplicity of Markdown and the great power of R and other languages. In this book, you will learn Basics: Syntax of Markdown and R code chunks, how to generate figures and tables, and how to use other computing languages Built-in output formats of R Markdown: PDF/HTML/Word/RTF/Markdown documents and ioslides/Slidy/Beamer/PowerPoint presentations Extensions and applications: Dashboards, Tufte handouts, xaringan/reveal.js presentations, websites, books, journal articles, and interactive tutorials Advanced topics: Parameterized reports, HTML widgets, document templates, custom output formats, and Shiny documents. Yihui Xie is a software engineer at RStudio. He has authored and co-authored several R packages, including knitr, rmarkdown, bookdown, blogdown, shiny, xaringan, and animation. He has published three other books, Dynamic Documents with R and knitr, bookdown: Authoring Books and Technical Documents with R Markdown, and blogdown: Creating Websites with R Markdown. J.J. Allaire is the founder of RStudio and the creator of the RStudio IDE. He is an author of several packages in the R Markdown ecosystem including rmarkdown, flexdashboard, learnr, and radix. Garrett Grolemund is the co-author of R for Data Science and author of Hands-On Programming with R. He wrote the lubridate R package and works for RStudio as an advocate who trains engineers to do data science with R and the Tidyverse. |
| equation definition math example: Bad Boy Ballmer Fredric Alan Maxwell, 2002-09-17 The life of Steve Ballmer is an incredible story of tremendous ambition, genius, arrogance, and charisma, an up-by-the-bootstraps saga of how the child of immigrants growing up in suburban Michigan became the only American billionaire to acquire his wealth working for someone else. In the tradition of The New New Thing and The Silicon Boys, Bad Boy Ballmer will tell this story of a man so shamelessly arrogant that he told reporters to heck with Janet Reno, so intense and aggressive that he ripped his vocal cords by talking to loudly. In this revealing biography -- based on in-depth study and interviews with Microsoft insiders -- Fredric Alan Maxwell provides the complete, controversial narrative of one of the technology industry's most influential, talked-about figures: Steven Anthony Ballmer, the awkward Detroit Country Day School valedictorian who rose to become Microsoft's president, and in the past two years, its CEO. Together with Bill Gates, Ballmer leads the company he and Gates took from less than 30 employees to some 50,000, and annual revenues from $12 million to more than $20 billion and rising. A balanced portrait, this book reveals the good boy Ballmer -- the dedicated son who once took three months off to care for his ailing parents, and the bad boy Ballmer -- the ruthless businessman who at the same time devised and led a scorched earth policy against other software developers, a policy that earned him the nickname The Em-balmer. Bad Boy Ballmer is also the definitive story of the Bill Gates/Steve Ballmer relationship, from their 1974 meeting at a Harvard dorm to the present. Providing fresh insights into the longstanding bond between this odd couple, who describe their relationship as a marriage, the book will show how Ballmer and Gates work together to form Microsoft's ego and id. Or, as former competitor, Novell's Ray Noorda calls them, the Pearly Gates and the Emballmer: one promises you heaven, the other prepares you for the grave. One half of the new economy's most powerful partnership, Ballmer's greatest accomplishment, Bad Boy Ballmer shows, may be putting up with Gates for over two decades. Eye-opening and thorough, Bad Boy Ballmer is a shocking look at one of the masterminds of the technological age. |
| equation definition math example: Intermediate Algebra 2e Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, 2020-05-06 |
| equation definition math example: Linear Algebra As An Introduction To Abstract Mathematics Bruno Nachtergaele, Anne Schilling, Isaiah Lankham, 2015-11-30 This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises. |
| equation definition math example: Technical Mathematics Paul A. Calter, Michael A. Calter, 2011-03-22 This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed. The authors continue to provide real-world, technical applications that promote intuitive reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computer-assisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications. |
| equation definition math example: bookdown Yihui Xie, 2016-12-12 bookdown: Authoring Books and Technical Documents with R Markdown presents a much easier way to write books and technical publications than traditional tools such as LaTeX and Word. The bookdown package inherits the simplicity of syntax and flexibility for data analysis from R Markdown, and extends R Markdown for technical writing, so that you can make better use of document elements such as figures, tables, equations, theorems, citations, and references. Similar to LaTeX, you can number and cross-reference these elements with bookdown. Your document can even include live examples so readers can interact with them while reading the book. The book can be rendered to multiple output formats, including LaTeX/PDF, HTML, EPUB, and Word, thus making it easy to put your documents online. The style and theme of these output formats can be customized. We used books and R primarily for examples in this book, but bookdown is not only for books or R. Most features introduced in this book also apply to other types of publications: journal papers, reports, dissertations, course handouts, study notes, and even novels. You do not have to use R, either. Other choices of computing languages include Python, C, C++, SQL, Bash, Stan, JavaScript, and so on, although R is best supported. You can also leave out computing, for example, to write a fiction. This book itself is an example of publishing with bookdown and R Markdown, and its source is fully available on GitHub. |
| equation definition math example: Introductory Algebra Elayn Martin-Gay, K. Elayn Martin-Gay, 2012 Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Introductory Algebra, Fourth Edition was written to provide students with a solid foundation in algebra and to help students make the transition to intermediate algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success. Note: This is the standalone book, if you want the book/access card order the ISBN below: 0321760123 / 9780321760128 Introductory Algebra plus MyMathLab/MyStatLab -- Access Card Package Package consists of: 0321431308 / 9780321431301 MyMathLab/MyStatLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321726383 / 9780321726384 Introductory Algebra |
| equation definition math example: Engineering Mathematics John Bird, 2017-07-14 Now in its eighth edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for a range of Level 2 and 3 engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae and multiple choice tests. |
| equation definition math example: Principia Mathematica Alfred North Whitehead, Bertrand Russell, 1910 |
| equation definition math example: Prealgebra Lynn Marecek, MaryAnne Anthony-Smith, 2015-09-25 Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Prealgebra follows a nontraditional approach in its presentation of content. The beginning, in particular, is presented as a sequence of small steps so that students gain confidence in their ability to succeed in the course. The order of topics was carefully planned to emphasize the logical progression throughout the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics.--BC Campus website. |
| equation definition math example: Ordinary Differential Equations with Applications Carmen Chicone, 2008-04-08 Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions. |
| equation definition math example: Discrete Mathematics Oscar Levin, 2016-08-16 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| equation definition math example: Basic Algebra Anthony W. Knapp, 2007-07-28 Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems. |
| equation definition math example: Problem Solving with Python 3. 7 Edition Peter D. Kazarinoff, 2019-09-15 Get started solving problems with the Python programming language!This book introduces some of the most famous scientific libraries for Python: * Python's math and statistics module to do calculations * Matplotlib to build 2D and 3D plots * NumPy to complete calculations on arrays * Jupiter Notebooks to share results with a team * SymPy to solve equations * PySerial to control an Arduino with Python * MicroPython to control an LEDThis book is great for budding engineers and data scientists. The text starts with the basics but finishes with topics rarely included in other engineering and data science programming books like SymPy and PySerial and MicroPython. |
| equation definition math example: 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 |
| equation definition math example: What is Mathematics? Richard Courant, Herbert Robbins, 1978 |
| equation definition math example: Solving Transcendental Equations John P. Boyd, 2014-09-23 Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute--not always needed, but indispensible when it is. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. |
| equation definition math example: 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. |
| equation definition math example: Euler's Pioneering Equation Robin Wilson, 2018-02-22 In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence. What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula. |
| equation definition math example: The Rhind Mathematical Papyrus Arnold Buffum Chace, |
| equation definition math example: Calculus: Functions and models James Stewart, 2012 |
| equation definition math example: CLEP. , 2012 REA's CLEP test preps are perfect for adults returning to college or attending for the first time, military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit. /Our review covers all the College Algebra topics found on the official exam: sets, number systems and operations, exponents and radicals, equations, inequalities, ratio and proportion, and more. /Students start their study by taking our half-length diagnostic practice test online. This timed test includes automatic scoring and diagnostic feedback, so students can pinpoint their strengths and weaknesses. The book includes 2 full-length practice tests that mirror the actual exam, allowing test-takers to become familiar with the test format before taking the CLEP. Each practice test comes with detailed explanations of answers, so students can identify areas in need of improvement and be prepared on test day. |
| equation definition math example: Calculus: Early Transcendentals James Stewart, Daniel K. Clegg, Saleem Watson, 2020-01-23 James Stewart's Calculus series is the top-seller in the world because of its problem-solving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, Daniel Clegg and Saleem Watson continue his legacy of providing students with the strongest foundation for a STEM future. Their careful refinements retain Stewart’s clarity of exposition and make the 9th Edition even more useful as a teaching tool for instructors and as a learning tool for students. Showing that Calculus is both practical and beautiful, the Stewart approach enhances understanding and builds confidence for millions of students worldwide. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| equation definition math example: Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being George Lakoff, Rafael E. Nunez, 2000-11-02 A study of the cognitive science of mathematical ideas. |
| equation definition math example: A First Course in Linear Algebra Kenneth Kuttler, Ilijas Farah, 2020 A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook.--BCcampus website. |
| equation definition math example: The Problem with Math Is English Concepcion Molina, 2012-09-04 Teaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism. |
| equation definition math example: APEX Calculus Gregory Hartman, 2015 APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back). |
| equation definition math example: Basic Equations Kathy Kifer, S. Harold Collins, 1997-04 Word Problems used to solve everyday problems: Equations & Number Relationships; Variables; Basic Linear Equations; Formulae. |
| equation definition math example: Notes on Diffy Qs Jiri Lebl, 2019-11-13 Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions. |
| equation definition math example: Practical Discrete Mathematics Ryan T. White, Archana Tikayat Ray, 2021-02-22 A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning. What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book. |
| equation definition math example: Solving Math Problems Field Stone Publishers, 2008 |
What is the difference between equation and formula?
An equation is a statement that connects two expressions with an $=$ sign and asserts their equality. An identity is an equation that holds for every variable tuple for which the equation is …
What is the equation for a 3D line? - Mathematics Stack Exchange
May 28, 2013 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
在理工科中，Formula, Equation 和 Function 这三个词有什么异 …
Dec 31, 2014 · Equation常指方程,用方程来求解未知数,或者解出多个未知数间的对应关系. equation作为等式用的情况我感觉不常见,可能是某些常用的方便计算的式子,或者某些先决条 …
Find the Vector Equation of a line perpendicular to the plane.
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Polar equation of a circle - Mathematics Stack Exchange
For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation …
simple geometry question- equation of cylinder
The equation of an object is a way of telling whether a point is part of an object -- if you substitute the coordinates of the point into the equation and the equation is true, then the point is on the …
Equation of a rectangle - Mathematics Stack Exchange
Oct 2, 2011 · If the equations of the diagonals of the rectangle are Ax + By + C = 0 and Dx + Ey + F = 0 then an equation for the rectangle is: M|Ax + By + C| + N|Dx + Ey + F| = 1. M and N can …
General formula for solving quartic (degree $4$) equations
Jul 28, 2010 · Also of note, Wolfram sells a poster that discusses the solvability of polynomial equations, focusing particularly on techniques to solve a quintic (5th degree polynomial) …
Compute the characteristic equation of a $3 \\times 3$ matrix
May 1, 2025 · The characteristic equation is used to find the eigenvalues of a square matrix A. First: Know that an eigenvector of some square matrix A is a non-zero vector x such that Ax = …
Ellipse in polar coordinates - Mathematics Stack Exchange
To derive the polar coordinates of an ellipse, I believe it is simpler to start from a geometric perspective rather than an algebraic one. If you begin with the equation $$ …
Math 951 Lecture Notes Chapter 6 { Introduction to …
It follows that, as with the previous example, the operator eAt converges uniformly on L p (R n ), i.e. in L(L p (R n )), to the identity operator as t!0. Example: Given a2L 1 (R n ), de ne the …
Chapter 8Chapter 8 Slutsky Equation - Lancaster University
Pure Substitution EffectPure Substitution Effect Slutsky isolated the change in demand due only to the change indemand due only to the change in relative prices by asking “What is the change …
5.11 Stiff Differential Equation - University of Notre Dame
Example. The initialvalue problem 𝑦𝑦′= −30𝑦𝑦, 0 ≤𝑡𝑡 ≤ - 1.5, 𝑦𝑦(0) = 1 3 has exact solution 𝑦𝑦(𝑡𝑡) = 1 3 𝑒𝑒−30𝑡𝑡. Use Euler’s method and 4-stage Runge-Kutta method to solve with step size ℎ= 0.1 respectively. …
An array is a way to represent multiplication and division …
A Parent's Guide to the "NEW" Math ****Module 1 Topics**** Here are some things I think might be useful to you if your child is struggling with the current math topics. I hope they are helpful. …
Notes, Examples, and practice (with solutions) - Math Plane
Important: Check your answers! Sometimes, math techniques produce extraneous solutions Example: Cross Multiply 4: 3X + 3 Check solutions: (substitute in the original equation) x = -1 …
3 Congruences and Congruence Equations - University of …
Definition 3.1. For each n ∈N, the set Zn = {0,1,. . .,n −1}comprises the residues modulo n. Integers a,b are said to be congruent modulo n if they have the same residue: we write a ≡b …
Recursive Sequences - University of Kentucky
quence in Example 1 is called a first-order difference equation because an depends on just the preceding term an1, whereas the Fibonacci sequence is a second-order difference equation …
11.2 Circles & Ellipses - Snow College
• Find an equation of a circle given the center and the ... • The definition of a circle is the set of all ... circle is called the circumference. Circles in Nature • Circles can also be seen all around us …
Definitions - MathCity.org
An equation is said to be a reciprocal equation if it remain unchanged, when x is replace by 1 x for example 1 x 2 x Exponential equation: An equation in which variable occurs in exponent is …
Lesson 6: Literal Equations, Inequalities, and Absolute Value
Example 4: Solve the following equation for x: y = mx + b. ... DEFINITION: An algebraic inequality is a mathematical sentence connecting an expression to a value, variable, or another …
Formulas, Symbols, Math - Appraisal Institute
equation is: I = R × V. Using equation solving techniques, the formula can be rewritten to solve for value with V = I R as the result. The rules of equation solving are quite simple and are as …
LATEX Math Mode - MIT
1. Text math mode (\begin{math}...\end{math}): the formula appears in the middle of running text (e.g. x2 + y2). 2. Display math mode (\begin{displaymath}... \end{displaymath}): the formula is …
Mathematical Statistics, Lecture 5 Prediction - MIT …
Prediction Example Example 1.4.1 Assembly line operating at varying capacity, month-by-month. Every day, the assembly line is susceptible to shutdowns due to mechanical failure. Z = …
MATH 3336 Discrete Mathematics Recurrence Relations …
Example: Find an explicit formula for the Fibonacci numbers. Step 1: Write the characteristic equation of a recurrence relation (CERR). If = 1 −1+ 2 −2, then 2− 1 − 2=0 is the characteristic …
Fractional Change - University at Albany
For example, suppose that the length of the time period is one quarter year, ∆ t =. 25. And suppose that the fractional change in the variable is. 02. Then the growth rate is. 02. 25 =. 08, …
Definition: The solution set for an equation is the set of all …
MATH 19000 section 1.1 Linear and Quadratic Equations in One Variable Page 1 of 6 Definition: The solution set for an equation is the set of all numbers that, when used in place of the …
Conic Sections: Hyperbolas
Example 2 Find the coordinates of the center, foci, and vertices, and the equations of the asymptotes of the graph (y - 2)2 64 - (x + 1)2 36 = 1. Then graph the equation. Since the y …
Solving Quadratic Equations - MATH 101 College Algebra
Review Theorem (Zero-Factor Property) If a product equals 0, then at least one of the factors must be 0. For real numbers a and b, if a ·b = 0 then a = 0 or b = 0 or both. Definition …
Math 13 — An Introduction to Abstract Mathematics
tegers you choose. It is not good enough to simply select, for example, 4 and 16, then write 4 +16 = 20. This is an example, or test, of the theorem, not a mathematical proof. According to the …
Mathematical induction & Recursion - University of Pittsburgh
4 CS 441 Discrete mathematics for CS M. Hauskrecht Mathematical induction Example: Prove n3 - n is divisible by 3 for all positive integers. • P(n): n3 - n is divisible by 3 Basis Step: P(1): 13 - …
Math Grade 8: Unit 7 Systems of Equations - Atlanta Public …
Mar 20, 2014 · solutions to a linear equation with two variables. ... In the example below, the solution is (-2, 1). 2) The lines are parallel so there are : no solutions : ... books contain several …
The Mathematics of Causal Relations - University of …
as Y(x,u) or Z(x,y). The expression Yx(u), for example, stands for the value that outcome Y would take in individual u, had treatment X been at level x. If u is chosen at random, Yx is a random …
7 Calculus of Variations - Stanford University
can be written as a partial differential equation. In particular, the Lagrangian associated with I is L(p;z;x) = (1+ jpj2)1=2: The associated Euler-Lagrange equation is Xn i=1 µ ux i (1+ jruj2)1=2 ¶ …
5.7 Literal Equations - Jon Blakely
b. Again, to solve this equation, we want to get the b on one side, and everything else on the other. The difference here is that we are going to want to clear the fraction from the equation …
Math 3321 - Homogeneous Equations with Constant …
Definition A second order linear homogeneous differential equation with constant coefficientsis an equation which can be written in the form y′′+ ay′+ by= 0. (1) Where aand bare real numbers. …
Introduction to Relations - Florida State University
Definition 1.4.1. Let Rbe a relation from Ato B. Then R 1 = f(b;a)j(a;b) 2 ... Give an example of a relation that does not satisfy any property given in Section 1.5. ... We may use the rst equation …
Streamlines and Stream Functions - Rose–Hulman Institute …
equation that describes the streamline in any flow is called a stream function. To develop the equation for a streamline we must first describe the direction of the velocity at any point in the …
Math 3321 - Introduction to Second Order Linear ODEs - UH
Definition A second order linear differential equationis an equation which can be written in the form y′′+ p(x)y′+ q(x)y= f(x) (1) where p, q, and fare continuous functions on some interval I. …
feynman diagrams 1
Schrodinger’s equation, and is written as f M i=fMi=ψ f ∫*(x)Mψ(x)d3x, where ψ f(x) is the final state wavefunction and ψ i(x) is the initial state wavefunction. In scattering theory the initial …
7.4 Solving Two-Step Equations - Big Ideas Learning
In the equation 5x + 2x = 16 − 2, 5x, 2x, 16, and 2 are called terms. 5x and 2x are called like terms. 16 and 2 are also like terms. 5x + 2x = 16 − 2 To solve, use the Distributive Property to …
Basic Linear Equations - Rochester Institute of Technology
a. Definition: A linear equation in one unknown is an equation in which the only exponent on the unknown is 1. b. The General Form of a basic linear equation is: ax b c. c. To Solve: the goal …
Chapter 5: Graphing Linear Equations - Math Mammoth
Chapter 5: Graphing Linear Equations Introduction This chapter focuses on how to graph linear equations, and in particular, on the concept of slope in that context.
Math Handbook of Formulas, Processes and Tricks
definitions, explanations and examples for elementary and advanced math topics. Mathguy.us – Developed specifically for math students from Middle School to College, based on the author's …
A Guide to Writing Mathematics - UC Davis
This is a math class! Why are we writing? There is a good chance that you have never written a paper in a math class before. So you might be wondering why writing is required in your math …
Slutsky equation - Social Science Computing Cooperative
Slutsky equation Thebasicconsumermodelis max x:p·x≤y U(x),whichissolvedbytheMarshalliandemandfunctionX(p,y ...
Introduction to functions - mathcentre.ac.uk
For example, we might have a function that added 3 to any number. So if we apply this function to the number 2, we get the number 5. If we apply this function to the number 8, we get the …
HIGHER ORDER DIFFERENTIAL EQUATIONS - University …
Note that for an nth order equation we can prescribe exactly n initial values. The proof of this theorem is di cult, and not part of math 320. 1.2. The general solution If you try to solve the di …
Chapter 11 Linear Differential Equations of Second and …
Example 37 Solve the differential equation: using method of variation of parameters. Solution: This is a Cauchy’s linear equation with variable coefficients.
Algebra 1 - Module 2 - Equations and Inequalities - NTN Math
• Explain a situation where it would be beneficial to rearrange a formula when solving an equation. Competencies • Students will create an equation from a situation and use that equation to …
1 Manifolds: definitions and examples - MIT Mathematics
examine this example later in the course. 4 The derivative of a map between vector spaces Let f : V → W be a smooth map between real vector spaces. Definition 4.1. Given x ∈ V we say that …
Mathematics/Grade 8 Unit 4: Functions - seymourschools.org
8.F.1 For example, the rule that takes x as input and gives x2+5x+4 as output is a function. Using y to stand for the output we can represent this function with the equation y = x2+5x+4, and the …
viii - UC Davis
4.2. VARIATIONAL FORMULATION 93 by replacing (a) in Definition 4.2 with the condition that u− w∈ H1 0(Ω).The definition is otherwise the same. The range of the trace map on H1(Ω) for …
PARTIAL DIFFERENTIAL EQUATIONS - UC Santa Barbara
The linear equation (1.9) is called homogeneous linear PDE, while the equation Lu= g(x;y) (1.11) is called inhomogeneous linear equation. Notice that if uh is a solution to the homogeneous …
Writing a Formal Mathematical Report - Kenyon College
this using LaTeX or Microsoft Word. (Word has an excellent equation editor that is easy to use. It can be found under “insert---object” in the menu. If you don’t know how to use it, this is a good …
MATHEMATICAL NOTES #1 - DEMAND AND SUPPLY …
additive term (the 3). So that's a quick way of finding slope & intercept in an equation. Downward-sloping If the slope is a positive number, the curve is upward-sloping. If the slope is a negative …
Lecture 27: Autonomous systems, 11/08/2021 - Harvard …
MATH 1B Lecture 27: Autonomous systems, 11/08/2021 Autonomous systems 27.1. A differential equation of the form y′ = f(y) is called an autonomous differential equation. An important …
Examples of contextualized problems - ICCB
Technical math example Use: lesson problem or assessment item Abbreviation definitions p.o. – medication is taken orally q.6.h. – frequency of medication taken (every 6 hours in this case) …
Transcendental Functions - Contemporary Calculus
nomial equation with integer coefficients. Any rational number is algebraic: for example, 5 7 is a solution of 7x −5 = 0. Any square root or cube root is an algebraic number: √ 3 is a solution of …
Matrices and Systems of Linear Equations - Purdue University
DEFINITION 2.1.1 An m×n (read “m by n”) matrix is a rectangular array of numbers arranged in m horizontal rows and n vertical columns. Matrices are usually denoted by uppercase letters, …
Lesson 7: Understanding Equations - Online Math Learning
term of the equation is in the same unit of measure. If one uses the other equation, what must be done to obtain the solution? If the other equation were used, then the given values of , , and …
