Bentuk diferensial
Dalam matematika, bentuk diferensial menyediakan pendekatan terpadu untuk mendefinisikan integral pada kurva, permukaan, padatan, dan manifold berdimensi lebih tinggi. Gagasan modern tentang bentuk diferensial dipelopori oleh Élie Cartan. Gagasan ini memiliki banyak aplikasi, terutama dalam geometri, topologi, dan fisika.
Referensi
- Bachman, David (2006), A Geometric Approach to Differential Forms, Birkhäuser, ISBN 978-0-8176-4499-4
- Bachman, David (2003), A Geometric Approach to Differential Forms, arXiv:math/0306194v1, Bibcode:2003math......6194B
- Cartan, Henri (2006), Differential Forms, Dover, ISBN 0-486-45010-4—Translation of Formes différentielles (1967)
- Dieudonné, Jean (1972), Treatise on Analysis, vol. 3, New York-London: Academic Press, Inc., MR 0350769
- Edwards, Harold M. (1994), Advanced Calculus; A Differential Forms Approach, Modern Birkhäuser Classics, Boston, Basel, Berlin: Birkhäuser, doi:10.1007/978-0-8176-8412-9, ISBN 978-0-8176-8411-2
- Folland, Gerald B. (1999), Real Analysis: Modern Techniques and Their Applications (Edisi Second), John Wiley & Sons, ISBN 978-0-471-31716-6, provides a brief discussion of integration on manifolds from the point of view of measure theory in the last section.
- Flanders, Harley (1989) [1964], Differential forms with applications to the physical sciences, Mineola, New York: Dover Publications, ISBN 0-486-66169-5
- Fleming, Wendell H. (1965), "Chapter 6: Exterior algebra and differential calculus", Functions of Several Variables, Addison-Wesley, hlm. 205–238. This textbook in multivariate calculus introduces the exterior algebra of differential forms at the college calculus level.
- Morita, Shigeyuki (2001), Geometry of Differential Forms, AMS, ISBN 0-8218-1045-6
- Rudin, Walter (1976), Principles of Mathematical Analysis, New York: McGraw-Hill, ISBN 0-07-054235-X
- Spivak, Michael (1965), Calculus on Manifolds, Menlo Park, California: W. A. Benjamin, ISBN 0-8053-9021-9, standard introductory text.
- Tu, Loring W. (2008), An Introduction to Manifolds, Universitext, Springer, doi:10.1007/978-1-4419-7400-6, ISBN 978-0-387-48098-5
- Zorich, Vladimir A. (2004), Mathematical Analysis II, Springer, ISBN 3-540-40633-6
Pranala luar
- Weisstein, Eric W. "Bentuk diferensial". MathWorld.
- Sjamaar, Reyer (2006), Manifolds and differential forms lecture notes (PDF), a course taught at Cornell University.
- Bachman, David (2003), A Geometric Approach to Differential Forms, arXiv:math/0306194, Bibcode:2003math......6194B, an undergraduate text.
- Needham, Tristan. Visual differential geometry and forms: a mathematical drama in five acts. Princeton University Press, 2021.
Konten ini disalin dari wikipedia, mohon digunakan dengan bijak.
