This text presents a graduate-level introduction to differential geometry for mathematics & physics students The exposition follows the historical development of the concepts of connection & curvature with the goal of explaining the Chern-Weil theory of characteristic classes on a principal bundle Along the way we encounter some of the high points in the history of differential geometry for example Gauss' Theorema Egregium & the Gauss-Bonnet theorem Exercises throughout the book test the reader's understanding of the material & sometimes illustrate extensions of the theory Initially the prerequisites for the reader include a passing familiarity with manifolds After the first chapter it becomes necessary to understand & manipulate differential forms A knowledge of de Rham cohomology is required for the last third of the text Prerequisite material is contained in author's text An Introduction to Manifolds & can be learned in one semester For the benefit of the reader & to establish common notations Appendix A recalls the basics of manifold theory in addition in an attempt to make the exposition more self-contained sections on algebraic constructions such as the tensor product & the exterior power are included Differential geometry as its name implies is the study of geometry using differential calculus It dates back to Newton & Leibniz in the seventeenth century but it was not until the nineteenth century with the work of Gauss on surfaces & Riemann on the curvature tensor that differential geometry flourished & its modern foundation was laid Over the past one hundred years differential geometry has proven indispensable to an understanding of the physical world in Einstein's general theory of relativity in the theory of gravitation in gauge theory & now in string theory Differential geometry is also useful in topology several complex variables algebraic geometry complex manifolds & dynamical systems among other fields The field has even found applications to group theory as in Gromov's work & to probability theory as in Diaconis's work It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal ...

This is a textbook on differential geometry well-suited to a variety of courses on this topic For readers seeking an elementary text the prerequisites are minimal & include plenty of examples & intermediate steps within proofs while providing an invitation to more excursive applications & advanced topics For readers bound for graduate school in math or physics this is a clear concise rigorous development of the topic including the deep global theorems For the benefit of all readers the author employs various techniques to render the difficult abstract ideas herein more understandable & engaging Over 300 color illustrations bring the mathematics to life instantly clarifying concepts in ways that grayscale could not Green-boxed definitions & violet-boxed theorems help to visually organize the mathematical content Color is even used within the text to highlight logical relationships Applications abound! The study of conformal & equiareal functions is grounded in its application to cartography Evolutes involutes & cycloids are introduced through Christiaan Huygens' fascinating story in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock he invented mathematics that would later be applied to optics & gears Clairaut's Theorem is presented as a conservation law for angular momentum Green's Theorem makes possible a drafting tool called a planimeter Foucault's Pendulum helps one visualize a parallel vector field along a latitude of the earth Even better a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface In truth the most profound application of differential geometry is to modern physics which is beyond the scope of this book The GPS in any car wouldn't work without general relativity formalized through the language of differential geometry Throughout this book applications metaphors & visualizations are tools that motivate & clarify the rigorous mathematical content but never replace it ...

In this new edition of a bestseller author Deborah Blaz helps you differentiate lessons for your world language students based on their learning styles interests prior knowledge & comfort zones This practical book uses brain-based teaching strategies to help students of all ability levels thrive in a rigorous differentiated learning environment Each chapter provides classroom-tested activities & tiered lesson plans to help you teach vocabulary speaking listening reading & writing in world language classes in ways that are interactive engaging & effective for all learners Features new to this edition
Includes:ample thematic units to make your lessons more authentic & immersive New strategies for using technology to differentiate world language instruction Additional checklists rubrics & feedback forms to help you organize your lesson plans & track students' progress New connections to the Common Core State Standards the ACTFL Standards Webb's Depth of Knowledge & Bloom's Taxonomy You'll also learn how to differentiate assessment effectively to help all students show their full potential Classroom-ready tools & templates can be downloaded as free e Resources from our website (wwwroutledgecom 9781138906181) for immediate use
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We've all been there We know we must talk to a colleague our boss or event a friend about something we know will be at least uncomfortable & at worst explosive So we repeatedly mull it over until we can no longer put it off & then finally stumble through a confrontation when we could have had a conversation Difficult Conversations is the definitive work on handling these unpleasant exchanges based on 15 years of research at the Harvard Negotiation Project It teaches us to work through them by understand that we're not engaging in one dialogue but three the "what happened" conversation (what do we believe was said & done) the "feelings" conversation (the emotional impact on everyone involved) & the "identity" conversation (what does this mean for everyone's opinion of themselves) In a world where asking for a pay rise saying 'no' to your boss asking a favour or apologizing for a mistake can be a horrendous nightmare Difficult Conversations deserves its position as a business classic ...

What is a difficult conversation? Asking for a pay rise saying 'no' to your boss or spouse confronting a friend or neighbor asking a difficult favor apologizing This book helps you to turn your difficult conversations into positive problem-solving experiences 272 pages Patton Bruce ...

This is 15 Dice Set & is Approx. 20 bigger than standard dice Each set contains 3x D4 4x D6 2x D8 D10 D12 3x D20 & Percentile Dice Role 4 Initiative are large High-Visibility Polyhedral Dice & are over 20 bigger than standard polyhedral dice They have bigger bolder numbers ...

This is 15 Dice Set & is Approx. 20 bigger than standard dice Each set contains 3x D4 4x D6 2x D8 D10 D12 3x D20 & Percentile Dice Role 4 Initiative are large High-Visibility Polyhedral Dice & are over 20 bigger than standard polyhedral dice They have bigger bolder numbers ...

This is 15 Dice Set & is Approx. 20 bigger than standard dice Each set contains 3x D4 4x D6 2x D8 D10 D12 3x D20 & Percentile Dice Role 4 Initiative are large High-Visibility Polyhedral Dice & are over 20 bigger than standard polyhedral dice They have bigger bolder numbers ...

This is 15 Dice Set & is Approx. 20 bigger than standard dice Each set contains 3x D4 4x D6 2x D8 D10 D12 3x D20 & Percentile Dice Role 4 Initiative are large High-Visibility Polyhedral Dice & are over 20 bigger than standard polyhedral dice They have bigger bolder numbers ...

This is 15 Dice Set & is Approx. 20 bigger than standard dice Each set contains 3x D4 4x D6 2x D8 D10 D12 3x D20 & Percentile Dice Role 4 Initiative are large High-Visibility Polyhedral Dice & are over 20 bigger than standard polyhedral dice They have bigger bolder numbers ...