Yves Talpaert 
Mechanics in Differential Geometry [PDF ebook] 

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