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This text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many practical applications in engineering analysis, approximation, and curve-plotting problems. Because of its usefulness for computing, the algebraic approach is the main theme, but a brief discussion of the synthetic approach is also presented as a way of gaining additional insight before proceeding with the algebraic manipulation. Professionals, students, and researchers in applied mathematics, solid modeling, graphics, robotics, and engineering design and analysis will find this a useful reference.
Turning to the Gospels, James Bryan Smith invites you to compare your ideas about God with what Jesus himself reveals about his Father. In this Good and Beautiful Series book, Smith leads you through a process of spiritual formation that includes activities aimed at making these new narratives real in your body and soul as well as your mind.
Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.
Planned, developed and written by practising classroom teachers with a wide variety of experience in schools, this maths course has been designed to be enjoyable and motivating for pupils and teachers. The course is open and accessible to pupils of all abilities and backgrounds, and is differentiated to provide material which is appropriate for all pupils. It provides spiral coverage of the curriculum ehich involves regular revisiting of key concepts to promote familiarity through practice. This book, designed for the higher level of the GCSE, adheres to the Edexcel specification.
Fascinating patient stories and dynamic exercises help you connect to healing emotions, ease anxiety and depression, and discover your authentic self. Sara suffered a debilitating fear of asserting herself. Spencer experienced crippling social anxiety. Bonnie was shut down, disconnected from her feelings. These patients all came to psychotherapist Hilary Jacobs Hendel seeking treatment for depression, but in fact none of them were chemically depressed. Rather, Jacobs Hendel found that they’d all experienced traumas in their youth that caused them to put up emotional defenses that masqueraded as symptoms of depression. Jacobs Hendel led these patients and others toward lives newly capable of joy and fulfillment through an empathic and effective therapeutic approach that draws on the latest science about the healing power of our emotions. Whereas conventional therapy encourages patients to talk through past events that may trigger anxiety and depression, accelerated experiential dynamic psychotherapy (AEDP), the method practiced by Jacobs Hendel and pioneered by Diana Fosha, PhD, teaches us to identify the defenses and inhibitory emotions (shame, guilt, and anxiety) that block core emotions (anger, sadness, fear, disgust, joy, excitement, and sexual excitement). Fully experiencing core emotions allows us to enter an openhearted state where we are calm, curious, connected, compassionate, confident, courageous, and clear. In It’s Not Always Depression, Jacobs Hendel shares a unique and pragmatic tool called the Change Triangle—a guide to carry you from a place of disconnection back to your true self. In these pages, she teaches lay readers and helping professionals alike • why all emotions—even the most painful—have value. • how to identify emotions and the defenses we put up against them. • how to get to the root of anxiety—the most common mental illness of our time. • how to have compassion for the child you were and the adult you are. Jacobs Hendel provides navigational tools, body and thought exercises, candid personal anecdotes, and profound insights gleaned from her patients’ remarkable breakthroughs. She shows us how to work the Change Triangle in our everyday lives and chart a deeply personal, powerful, and hopeful course to psychological well-being and emotional engagement.
Presents a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. This work introduces the notions of a transformation group and of an abstract group. It gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.
The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?
This textbook illustrates one-component phase diagrams, binary equilibrium phase diagrams and ternary phase diagrams for ceramics, polymers and alloys by presenting case studies on preparation processes, and provides up-to-date information on nano-crystal materials, non-crystal materials and functional materials. As second volume in the set, it is an extension of the first volume on physical aspect of materials.