Yves Talpaert

Mechanics in Differential Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

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Produktdetails

• Verlag: Walter de Gruyter
• Seitenzahl: 588
• Erscheinungstermin: 20. März 2012
• Englisch
• ISBN-13: 9783110917796
• Artikelnr.: 54168103

Inhaltsangabe

i-vi -- CONTENTS -- PREFACE -- CHAPTER ?. INTRODUCTION TO TENSORS -- 1. WELL KNOWN CONCEPTS -- 2. OPERATIONS ON TENSORS -- CHAPTER 1. FOUNDATIONS OF DIFFERENTIAL GEOMETRY -- 1. MANIFOLDS -- 2. TANGENT VECTOR SPACE -- 3. TANGENT BUNDLE, VECTOR FIELD, AND LIE ALGEBRA -- 4. COTANGENT BUNDLE AND COVECTOR FIELDS -- 5. TENSOR ALGEBRA AND TENSOR FIELDS -- 6. EXTERIOR DIFFERENTIAL FORMS -- 7. LIE DERIVATIVE, LIE GROUP, AND LIE ALGEBRA -- 8. INTEGRATION OF FORMS -- 9. RIEMANNIAN GEOMETRY -- EXERCISES -- CHAPTER 2. SYMPLECTIC GEOMETRY -- 1. PRELIMINARIES -- 2. SYMPLECTIC GEOMETRY -- CHAPTER 3. A MODERN EXPOSITION OF MECHANICS -- 1. LAGRANGIAN MECHANICS -- 2. HAMILTONIAN MECHANICS -- 3. COMPARISON OF THE LAGRANGIAN AND HAMILTONIAN FORMULATIONS -- 4. HAMILTON-JACOBI MECHANICS -- 5. INTRODUCTION TO PERTURBATIONS -- EXERCISES -- CHAPTER 4. THE N-BODY PROBLEM; AN ORIGINAL METHOD FOR LARGE ? -- 1. N-BODY PROBLEM, EQUATIONS AND INTEGRALS -- 2. THE N-BODY PROBLEM IN STATISTICAL MECHANICS -- BIBLIOGRAPHY -- GLOSSARY OF SYMBOLS -- INDEX