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Part One. Vectors and Forms 1. Mathematical Preliminaries 2. Vector Fields 3. Exterior Forms 4. Exterior Derivatives, Lie Derivatives, and Integration 5. Antiexact Differential Forms and Homotopy Operators Part Two. Applications to Mathematics 6. Isovector Methods for Second-Order Partial Differential Equations 7. Calculus of Variations Part Three. Applications to Physics 8. Modern Thermodynamics 9. Electrodynamics with Electric and Magnetic Charges 10. Gauge Theories Appendix Index
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