Problem Solving Methods and Strategies in High School Mathematical Competitions

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【簡介】 This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking. It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools. The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu. The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results. 【目錄】 Methods of Reduction Proofs by Contradiction Inductive Methods The Drawer Principle Inclusion–Exclusion Principle Extreme Principle Parity Area Methods Thinking Globally Proper Representations Combine Numbers and Figures Correspondence and Pairing Recurrence Colouring Assignment Methods Calculate in Two Ways Stepwise Adjustment Methods of Construction Invariants and Monovariants Graph Theory Method Solutions for the Exercises

Mathematical Methods and Physical Insights: An Integrated Approach (1版)

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Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension. Initial chapters review essential mathematical concepts and techniques that students need to know, helping students to fill gaps in their background knowledge and enabling instructors to focus on the main course material Each Part has sections designed to highlight and apply the techniques and concepts within, so that physics motivates the math, which deepens understanding of physics Boxed asides throughout the book called 'By the Ways' (BTWs) provide optional digressions into the math or physics, to help to lift motivated students to the next level Flexible paths through the text allow it to be used for both one- and two-semester courses, depending on the course goals and instructor's preference 本書目錄： Part I. Things You Just Gotta' Know: 1. Prelude: symbiosis 2. Coordinating coordinates 3. Complex numbers 4. Index algebra 5. Brandishing binomials 6. Infinite series 7. Interlude: orbits in a central potential 8. Ten integration techniques and tricks 9. The Dirac delta function 10. Coda: statistical mechanics Part II. The Calculus of Vector Fields: 11. Prelude: visualizing vector fields 12. grad, div & curl 13. Interlude: irrotational and incompressible 14. Integrating scalar & vector fields 15. The theorems of Gauss & Stokes 16. Mostly Maxwell 17. Coda: Simply connected regions Part III. Calculus in the Complex Plane: 18. Prelude: path independence in the complex plane 19. Series, singularities & branches 20. Interlude: conformal mapping 21. The calculus of residues 22. Coda: analyticity & causality Part IV. Linear Algebra: 23. Prelude: superposition 24. Vector space 25. The inner product 26. Interlude: rotations 27. The Eigenvalue problem 28. Coda: normal modes Entr'acte: Tensors 29. Cartesian tensors 30. Beyond cartesian Part V. Orthogonal Functions: 31. Prelude: 1 2 3 . . . infinity 32. Eponymous polynomials 33. Fourier series 34. Convergence and completeness 35. Interlude: beyond the straight & narrow 36. Fourier transforms 37. Coda: of time intervals and frequency bands Part VI. Differential Equations: 38. Prelude: first order first 39. Second-order ODEs 40. Interlude: the Sturm-Liouville Eigenvalue problem 41. Partial differential equations 42. Green's functions 43. Coda: quantum scattering Appendix A. Curvilinear coordinates Appendix B. Rotations in R3 Appendix C. The Bessel family of functions 會計 經濟 國際貿易 財務 企業管理 數學 機率與統計 資訊與資工 工業工程 社會與心理 醫務管理 物理 化學與化工 電子與電機 機械工程 航空工程 土木工程 環境工程 生命科學 護理 休閒觀光與餐飲 化妝品科學 其他 帳號 密碼 驗證碼

Chemical Analysis: Modern Instrumentation Methods and Techniques 3/e (3版)

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【簡介】 The third edition of Chemical Analysis: Modern Instrumentation Methods and Techniques provides an up-to-date overview of the common methods used for qualitative, quantitative, and structural chemical analysis. Assuming no background knowledge in the subject, this student-friendly textbook covers the fundamental principles and practical aspects of more than 20 separation and spectroscopic methods, as well as other important techniques such as elemental analysis, electrochemistry and isotopic labelling methods. Avoiding technical complexity and theoretical depth, clear and accessible chapters explain the basic concepts of each method and its corresponding instrumental techniques—supported by explanatory diagrams, illustrations, and photographs of commercial instruments. The new edition includes revised coverage of recent developments in supercritical fluid chromatography, capillary electrophoresis, miniaturized sensors, automatic analyzers, digitization and computing power, and more. 【目錄】 Chapter 1: General Aspects of Chromatography Chapter 2: Gas Chromatography Chapter 3: High-Performance Liquid Chromatography Chapter 4: Ion Chromatography Chapter 5: Thin-Layer Chromatography Chapter 6: Supercritical Fluid Chromatography Chapter 7: Size-Exclusion Chromatography Chapter 8: High-Performance Capillary Electrophoresis Chapter 9: Ultraviolet and Visible Absorption Spectroscopy Chapter 10: Infrared and Raman Spectroscopy Chapter 11: Fluorescence and Chemiluminescence Spectroscopy Chapter 12: X-Ray Fluorescence Spectroscopy Chapter 13: Atomic Absorption Spectroscopy Chapter 14: Atomic Emission Spectroscopy Chapter 15: Nuclear Magnetic Resonance Spectroscopy Chapter 16: Mass Spectrometry Chapter 17: Isotopic Analyses and Labelling Methods Chapter 18: Specific Analysers Chapter 19: Potentiometric and Ionometric Methods Chapter 20: Voltammetric Methods Chapter 21: Sample Preparation Chapter 22: Basic Statistical Parameters Appendix: Table of Some Useful Constants

Social Studies for the Twenty-First Century Methods and Materials for Teaching in Middle and Secondary Schools (1版)

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Now in its 5th edition, this popular text offers practical, interesting, exciting ways to teach social studies and a multitude of instructional and professional resources for teachers. Theory, curriculum, methods, and assessment are woven into a comprehensive model for setting objectives; planning lessons, units, and courses; choosing classroom strategies; and constructing tests for some of the field's most popular and enduring programs. The reflective and integrative framework emphasizes building imagination, insight, and critical thinking into everyday classrooms; encourages problem-solving attitudes and behavior; and provokes analysis, reflection, and debate. Throughout the text, all aspects of curriculum and instruction are viewed from a tripartite perspective that divides social studies instruction into didactic (factual), reflective (analytical), and affective (judgmental) components. These three components are seen as supporting one another, building the groundwork for taking stands on issues, past and present. At the center is the author's belief that the heart and soul of social studies instruction, perhaps all teaching, lies in stimulating the production of ideas; looking at knowledge from others' viewpoints; and formulating for oneself a set of goals, values, and beliefs that can be explained and justified in open discussion. This new edition is heavily revised and condensed to promote ease of use. "Build Your Own Lesson" additions to each chapter encourage improvisation and inquiry-based teaching and learning across subjects. A Companion Website offers additional activities, lessons, and resources for pre-service and practicing social studies teachers.