A Visual Introduction to Differential Forms and Calculus on Manifolds

1. Front Matter

   Pages i-xii

   PDF

2. Background Material

   • Jon Pierre Fortney

   Pages 1-30

3. An Introduction to Differential Forms

   • Jon Pierre Fortney

   Pages 31-67

4. The Wedgeproduct

   • Jon Pierre Fortney

   Pages 69-105

5. Exterior Differentiation

   • Jon Pierre Fortney

   Pages 107-149

6. Visualizing One-, Two-, and Three-Forms

   • Jon Pierre Fortney

   Pages 151-188

7. Push-Forwards and Pull-Backs

   • Jon Pierre Fortney

   Pages 189-228

8. Changes of Variables and Integration of Forms

   • Jon Pierre Fortney

   Pages 229-257

9. Poincaré Lemma

   • Jon Pierre Fortney

   Pages 259-275

10. Vector Calculus and Differential Forms

    • Jon Pierre Fortney

    Pages 277-308

11. Manifolds and Forms on Manifolds

    • Jon Pierre Fortney

    Pages 309-335

12. Generalized Stokes’ Theorem

    • Jon Pierre Fortney

    Pages 337-367

13. An Example: Electromagnetism

    • Jon Pierre Fortney

    Pages 369-393

14. Back Matter

    Pages 395-468

    PDF

This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.

• differential forms
• wedgeproduct
• visualization of differential forms
• calculus on manifolds
• integration of differential forms
• exterior differentiation
• tangent bundle
• cotangent bundle
• pull-backs of differential forms
• manifolds
• vector calculus
• Stokes’ theorem
• electromagnetism

 “The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book.” (Hirokazu Nishimura, zbMath 1419.58001, 2019)  

• Department of Mathematics and Statistics, Zayed University, Dubai, United Arab Emirates

  Jon Pierre Fortney

Jon Pierre Fortney, Zayed University, Dubai, United Arab Emirates.  

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