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A compendium of mathematical definitions, formulas, figures, tabulations, and references. Intended for a broad spectrum of readers with a wide range of mathematical backgrounds and interests. The text and all the equations and figures are searchable. The entries are extensively cross-linked and cross-referenced, some with external Web links. Standard mathematical references are given at the end of most entries to facilitate additional reading. The work also contains a large number of explicit formulas and derivations. Because of the alphabetical listing of entries in the encyclopedia, neither table of contents nor index are included. Most articles are followed by a "see also" list of related entries for quick navigation.
Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis - providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. It covers exponential function, and the development of trigonometric functions from the integral. The text is designed for a one-semester advanced calculus course for advanced undergraduates or graduate students.
Techniques, methods, and applications of calculus using real-world examples from business and economics as well as the life and social sciences. An introduction to differential and integral calculus, Fundamentals of Calculus presents key topics suited for a variety of readers in fields ranging from entrepreneurship and economics to environmental and social sciences. Practical examples from a variety of subject areas are featured throughout each chapter and step-by-step explanations for the solutions are presented. Specific techniques are also applied to highlight important information in each section, including symbols interspersed throughout to further reader comprehension. In addition, the book illustrates the elements of finite calculus with the varied formulas for power, quotient, and product rules that correlate markedly with traditional calculus.
Why do students find learning mathematics difficult? Can anything be done about this? What can we learn from mathematics lessons in which students are motivated to struggle with difficult mathematical ideas? How can teachers make sense of the research which is available, and use it to improve practice in real classrooms? This book explores the factors that influence young people's learning of mathematics. It uses a holistic, socio-culturally informed approach to show how all young people can be encouraged to engage with and learn mathematics. Rich examples from classroom practice are used to connect theory and practice. The role of mathematical tools, including information and communications technologies, is discussed. A key focus of the book is the link between teaching and learning, including different ways in which teachers can design and orchestrate mathematical learning environments.
This book aims to support and develop teachers' understanding of the key primary mathematics topics. It takes an innovative approach by defining exactly what is meant by 'understanding' and uses this model to examine and explain various mathematical topics. The authors emphasize the importance of the different representations that can be used for mathematical concepts and inform the reasoning process. By focusing on understanding, the book also draws attention to common misconceptions that teachers may encounter in the classroom. Key features: Specific focus on 'understanding' to offer new insights in to how to teach the topics, case studies to demonstrate how to communicate mathematical topics in the classroom, end of chapter questions to stimulate discussion. The authors integrate research and theory throughout, to highlight core issues. This theoretical background is also linked directly to classroom practice and informs suggestions for how topics can be communicated in the classroom. This offers valuable guidance to trainee teachers on how to teach the topics and presents experienced teachers with the opportunity to develop their subject and pedagogical knowledge.
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
The author's primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of mathematical "apparatus" work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques.