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  • The Learning and Teaching of Calculus : Ideas, Insights and Activities
    The Learning and Teaching of Calculus : Ideas, Insights and Activities

    This book is for people who teach calculus – and especially for people who teach student teachers, who will in turn teach calculus.The calculus considered is elementary calculus of a single variable.The book interweaves ideas for teaching with calculus content and provides a reader-friendly overview of research on learning and teaching calculus along with questions on educational and mathematical discussion topics. Written by a group of international authors with extensive experience in teaching and research on learning/teaching calculus both at the school and university levels, the book offers a variety of approaches to the teaching of calculus so that you can decide the approach for you.Topics covered includeA history of calculus and how calculus differs over countries todayMaking sense of limits and continuity, differentiation, integration and the fundamental theorem of calculus (chapters on these areas form the bulk of the book)The ordering of calculus concepts (should limits come first?)Applications of calculus (including differential equations)The final chapter looks beyond elementary calculus.Recurring themes across chapters include whether to take a limit or a differential/infinitesimal approach to calculus and the use of digital technology in the learning and teaching of calculus.This book is essential reading for mathematics teacher trainers everywhere.

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  • Teaching, Tutoring and Training in the Lifelong Learning Sector
    Teaching, Tutoring and Training in the Lifelong Learning Sector

    This core text provides comprehensive support for pre-service and in-service trainee teachers in the Lifelong Learning Sector covering all they need to know to achieve QTLS status. Supporting trainees through all stages of their professional development, the text takes the reader through the theoretical background underpinning teaching and learning and offers practical guidance on day-to-day challenges. This fourth edition has been fully revised and updated and includes a new chapter on teaching practice with notes on observation and lesson planning.New information on behaviour management has been added to support trainees in an aspect of teaching that many find challenging.

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  • Quick Calculus : A Self-Teaching Guide
    Quick Calculus : A Self-Teaching Guide

    Discover an accessible and easy-to-use guide to calculus fundamentals In Quick Calculus: A Self-Teaching Guide, 3rd Edition, a team of expert MIT educators delivers a hands-on and practical handbook to essential calculus concepts and terms.The author explores calculus techniques and applications, showing readers how to immediately implement the concepts discussed within to help solve real-world problems.In the book, readers will find: An accessible introduction to the basics of differential and integral calculusAn interactive self-teaching guide that offers frequent questions and practice problems with solutions. A format that enables them to monitor their progress and gauge their knowledge This latest edition provides new sections, rewritten introductions, and worked examples that demonstrate how to apply calculus concepts to problems in physics, health sciences, engineering, statistics, and other core sciences.Quick Calculus: A Self-Teaching Guide, 3rd Edition is an invaluable resource for students and lifelong learners hoping to strengthen their foundations in calculus.

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  • Pre-Calculus, Calculus, and Beyond
    Pre-Calculus, Calculus, and Beyond

    This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and grade-level appropriate.The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject. This volume distinguishes itself from others of the same genre in getting the mathematics right.In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles.It also provides details for extending the domain of definition of sine and cosine to all real numbers.It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians. In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs.An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator.This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture. This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.

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  • What is the difference between calculus and advanced calculus?

    Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities. It includes topics such as limits, derivatives, and integrals. Advanced calculus, on the other hand, delves deeper into these concepts and explores more advanced topics such as multivariable calculus, vector calculus, and differential equations. Advanced calculus typically requires a stronger mathematical background and is more theoretical and abstract compared to basic calculus.

  • Struggling with calculus?

    If you are struggling with calculus, don't worry, you are not alone. Many students find calculus to be a challenging subject due to its complex concepts and problem-solving techniques. It's important to seek help from your teacher, classmates, or a tutor to clarify any doubts and practice regularly to improve your understanding and skills in calculus. Remember, with dedication and perseverance, you can overcome the challenges and succeed in mastering calculus.

  • What is calculus?

    Calculus is a branch of mathematics that deals with the study of rates of change and accumulation. It is divided into two main branches: differential calculus, which focuses on the concept of the derivative and rates of change, and integral calculus, which deals with the concept of the integral and accumulation of quantities. Calculus is widely used in various fields such as physics, engineering, economics, and computer science to solve problems involving continuous change and motion.

  • Is calculus difficult?

    Calculus can be difficult for some people, as it involves complex concepts and requires a strong understanding of algebra and trigonometry. However, with dedication and practice, many students are able to grasp the concepts and excel in calculus. It is important to seek help from teachers, tutors, or online resources if you are struggling with calculus, as it is a foundational subject for many fields of study, including engineering, physics, and economics.

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  • Calculus
    Calculus

    Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis.His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote.Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort.Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

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  • Calculus
    Calculus

    Calculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role.The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition.The author has restructured the subject matter in the book by using Tarski's version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity.The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem.Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.

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  • Honors Calculus
    Honors Calculus

    This is the first modern calculus book to be organized axiomatically and to survey the subject's applicability to science and engineering.A challenging exposition of calculus in the European style, it is an excellent text for a first-year university honors course or for a third-year analysis course.The calculus is built carefully from the axioms with all the standard results deduced from these axioms.The concise construction, by design, provides maximal flexibility for the instructor and allows the student to see the overall flow of the development.At the same time, the book reveals the origins of the calculus in celestial mechanics and number theory.The book introduces many topics often left to the appendixes in standard calculus textbooks and develops their connections with physics, engineering, and statistics.The author uses applications of derivatives and integrals to show how calculus is applied in these disciplines.Solutions to all exercises (even those involving proofs) are available to instructors upon request, making this book unique among texts in the field. * Focuses on single variable calculus * Provides a balance of precision and intuition * Offers both routine and demanding exercises

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  • Essential Calculus
    Essential Calculus

    This book is for instructors who think that most calculus textbooks are too long.In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers?ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems.The book is only 900 pages--two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics.The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com.Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books.ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

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  • Why does calculus work?

    Calculus works because it provides a precise and systematic way to analyze and understand change. By using concepts such as limits, derivatives, and integrals, calculus allows us to model and solve real-world problems involving rates of change, accumulation, and optimization. Its rigorous mathematical framework enables us to make accurate predictions and calculations in various fields such as physics, engineering, economics, and biology.

  • What is vector calculus?

    Vector calculus is a branch of mathematics that deals with vector fields and their derivatives. It involves studying functions that have both a magnitude and a direction, such as velocity and force. Vector calculus is used in various fields such as physics, engineering, and computer science to analyze and solve problems involving quantities that have both magnitude and direction. It includes operations like gradient, divergence, curl, and line integrals, which help in understanding the behavior of vector fields in three-dimensional space.

  • What is integral calculus?

    Integral calculus is a branch of calculus that deals with the concept of integration, which is essentially the reverse process of differentiation. It involves finding the integral of a function, which represents the area under the curve of the function. This area can be used to calculate quantities such as displacement, velocity, and acceleration. Integral calculus is widely used in various fields such as physics, engineering, economics, and statistics to solve problems involving continuous quantities.

  • What is differential calculus?

    Differential calculus is a branch of mathematics that deals with the study of rates at which quantities change. It involves the concept of derivatives, which represent the rate of change of a function at a given point. Differential calculus is used to solve problems involving motion, optimization, and many other real-world applications where understanding how quantities change over time is important. It is a fundamental tool in mathematics and is essential in fields such as physics, engineering, economics, and biology.

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