دانلود کتاب Manifolds and Differential Forms

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Preface
Chapter 1. Introduction
1.1. Manifolds
1.2. Equations
1.3. Parametrizations
1.4. Configuration spaces
Exercises
Chapter 2. Differential forms on Euclidean space
2.1. Elementary properties
2.2. The exterior derivative
2.3. Closed and exact forms
2.4. The Hodge star operator
2.5. div, grad and curl
Exercises
Chapter 3. Pulling back forms
3.1. Determinants
3.2. Pulling back forms
Exercises
Chapter 4. Integration of 1-forms
4.1. Definition and elementary properties of the integral
4.2. Integration of exact 1-forms
4.3. Angle functions and the winding number
Exercises
Chapter 5. Integration and Stokes\' theorem
5.1. Integration of forms over chains
5.2. The boundary of a chain
5.3. Cycles and boundaries
5.4. Stokes\' theorem
Exercises
Chapter 6. Manifolds
6.1. The definition
6.2. The regular value theorem
Exercises
Chapter 7. Differential forms on manifolds
7.1. First definition
7.2. Second definition
Exercises
Chapter 8. Volume forms
8.1. n-Dimensional volume in RN
8.2. Orientations
8.3. Volume forms
Exercises
Chapter 9. Integration and Stokes\' theorem for manifolds
9.1. Manifolds with boundary
9.2. Integration over orientable manifolds
9.3. Gauss and Stokes
Exercises
Chapter 10. Applications to topology
10.1. Brouwer\'s fixed point theorem
10.2. Homotopy
10.3. Closed and exact forms re-examined
Exercises
Appendix A. Sets and functions
A.1. Glossary
A.2. General topology of Euclidean space
Exercises
Appendix B. Calculus review
B.1. The fundamental theorem of calculus
B.2. Derivatives
B.3. The chain rule
B.4. The implicit function theorem
B.5. The substitution formula for integrals
Exercises
Appendix C. The Greek alphabet
Bibliography
Notation Index
Index