This Open Access textbook presents Carnot-Carathéodory spaces from the perspective of Lie groups. Its main objective is to illustrate how these non-smooth geometries manifest in various mathematical domains, including metric geometry and geometric group theory. In contrast to other sources, this book utilizes the formalism of Lie groups to showcase how this theory facilitates the development of geometry and analysis on the non-smooth structure of Carnot-Carathéodory spaces. Major results are presented with rigorous mathematical proofs, and references for further exploration are provided. Open problems in these areas are discussed, offering insights into recent developments and avenues for future research. Prerequisite topics such as differential geometry, measure theory, and group theory are incorporated in the main flow of the chapters, ensuring a comprehensive understanding. Junior researchers seeking an introduction to the field of sub-Riemannian geometry will find this an invaluable introductory companion. The book is also suitable for those entering research subjects on the interplay between geometry, analysis, and group theory.
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【簡介】 Welcome to the International Metric Version of Essential Calculus. For this metric version, the units of measurement used in most of the examples and exercises have been changed from U.S. Customary units to metric units. We did not update problems that are U.S. Customary units such as dimensions of a baseball field or U.S. postal rates. We excited to offer you a new edition with more resources then ever that will help you understand and master calculus. This text includes features and resources that continue to make Essential Calculus a valuable learning tool for students and a trustworthy teaching tool for instructors. Essential Calculus provides the clear instruction, precise mathematics, and thorough coverage that you expect for your course. 【目錄】 1. Limits and Their Properties 2. Differentiation 3. Applications of Differentiation 4. Integration 5. Logarithmic, Exponential, and Other Transcendental Functions 6. Applications of Integration 7. Integration Techniques and Improper Integrals 8. Infinite Series 9. Parametric Equations and Polar Coordinates 10. Vectores and the Geometry of Space 11. Functions of Several Variables 12. Multiple Integration 13. Vector Analysis Appendix A. Proofs of Selected Theorems (Online)* Appendix B. Integration Tables B1 Appendix C. Precalculus Reviews (Online)* Appendix D. Rotation and the General Second-Degree Equation (Online)* Appendix E. Complex Numberss (Online)* Appendix F. Business and Economic Applications (Online)* Appendix G. Fitting Models to Data (Online)* Answers to Selected Exercises Index
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【簡介】 【目錄】 1. FUNCTIONS AND LIMITS. 2. DERIVATIVES. 3. APPLICATIONS OF DIFFERENTIATION. 4. INTEGRALS. 5. APPLICATIONS OF INTEGRATION. 6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. 7. TECHNIQUES OF INTEGRATION. 8. FURTHER APPLICATIONS OF INTEGRATION. 9. DIFFERENTIAL EQUATIONS. 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. 11. SEQUENCES, SERIES, AND POWER SERIES. 12. VECTORS AND THE GEOMETRY OF SPACE. 13. VECTOR FUNCTIONS. 14. PARTIAL DERIVATIVES. 15. MULTIPLE INTEGRALS. 16. VECTOR CALCULUS. APPENDIXES. A Numbers, Inequalities, and Absolute Values. B Coordinate Geometry and Lines. C Graphs of Second-Degree Equations. D Trigonometry. E Sigma Notation. F Proofs of Theorems. G Answers to Odd-Numbered Exercises.
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【簡介】 Calculus：Early Transcendentals, Metric Edition ISBN13：9780357113516 出版社：Cengage Learning; Inc 作者：James Stewart (McMaster University);Saleem (California State University Watson Long Beach);Daniel K. Clegg (Palomar College) 【目錄】 Preface. To the Student. Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus. 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Discovery Project: Families of Implicit Curves. Derivatives of Logarithmic Functions and Inverse Trigonometric Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Approximations and Differentials. Discovery Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. What Derivatives Tell Us about the Shape of a Graph. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Technology. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton's Method. Antiderivatives. Review. Problems Plus. 5. INTEGRALS. The Area and Distance Problems. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus. 6. APPLICATIONS OF INTEGRATION. Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Applied Project: Where to Sit at the Movies. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Technology. Discovery Project: Patterns in Integrals. Approxi
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【簡介】 微積分是大學數學的基礎學科，內容包括單變數與多變數函數、極限、微分、積分等。其發展與應用幾乎囊括所有非文史哲領域，如物理、化學、醫學、電資、工程、管理科學、建築、航太、經濟與人工智慧等，都是以微積分為基本工具。本書內容包括微積分的基本主題、相關的範例與解題步驟、重要定義與定理等，並強調應用層面，新版更新許多實際生活資料與應用問題，還有豐富的精美圖形幫助學生進行理解，並適時地介紹數學家的故事及微積分的歷史發展，內容相當充實完備，可為學生在各個領域建立深厚紮實的基礎，延伸到專業領域的應用。 【目錄】 第 1章 極限及其性質 第 2 章 微分 第 3 章 微分的應用 第 4 章 積分 第 5 章 積分技巧 第 6 章 積分的應用 第 7 章 無窮級數 第 8 章 多變數函數 第 9 章 多重積分 附錄 附錄 A 極坐標、空間坐標和向量 附錄 B 積分表
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【簡介】 Description Welcome to the International Metric Version of Essential Calculus: Early Transcendental Functions. For this metric version, the units of measurement used in most of the examples and exercises have been changed from U.S. Customary units to metric units. We did not convert problems that are specific to the U.S. Customary units, such as dimensions of a baseball field or U.S. postal rates. We are excited to offer you a new edition with more resources then ever that will help you understand and master calculus. This text includes features and resources that continue to make Essential Calculus: Early Transcendental Functions a valuable learning tool for students and a trustworthy teaching tool for instructors. Essential Calculus: Early Transcendental Functions provides the clear instruction, precise mathematics, and thorough coverage that you expect for your course. 【目錄】 Table of Contents 1. Limits and Their Properties 2. Differentiation 3. Applications of Differentiation 4. Integration 5. Applications of Integration 6. Integration Techniques and Improper Integrals 7. Infinite Series 8. Parametric Equations, and Polar Coordinates 9. Vectores and the Geometry of Space 10. Vector-Valued Functions 11. Functions of Several Variables 12. Multiple Integration 13. Vector Analysis Appendix A. Proofs of Selected Theorems (Online)* Appendix B. Integration Tables Appendix C. Precalculus Reviews (Online)* Appendix D. Rotation and the General Second-Degree Equation (Online)* Appendix E. Complex Numberss (Online)* Appendix F. Business and Economic Applications (Online)* Answers to Selected Exercises Index
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