Frontmatter -- Contents -- Preface -- 1. Introduction -- 2. Calculus of Vector Functions -- 3. Tangent Spaces and 1-forms -- 4. Line Integrals -- 5. Differential Calculus of Mappings -- 6. Applications of Differential Calculus -- 7. Double and Triple Integrals -- 8. Wedge Products and Exterior Derivatives -- 9. Integration of Forms -- 10. Stokes' Theorem and Applications -- Bibliography -- Index.
Summary
This textbook offers a high-level introduction to multi-variable differential calculus. By introducing differential forms early as a basic concept, the structures behind Stokes' and Gauss' theorems become much clearer. Furthermore, it offers a natural route to differential geometry.
Local Note
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