This book by M. do Carmo, winner of the 1992 Mathematics Price of the Third World Academy of Sciences, gives an introduction to the theory of differentiable forms. Since it only assumes elementary calculus and elementary linear algebra, it is suitable for second year undergraduate and graduate students in mathematics and physics.
M.P. Do Carmo
Differential Forms and Applications
"This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. Each chapter is followed by interesting exercises. Thus, this is an ideal book for a one-semester course."--ACTA SCIENTIARUM MATHEMATICARUM
1. Differential Forms in Rn.- 2. Line Integrals.- 3. Differentiable Manifolds.- 4. Integration on Manifolds; Stokes Theorem and Poincare's Lemma.- 1. Integration of Differential Forms.- 2. Stokes Theorem.- 3. Poincare's Lemma.- 5. Differential Geometry of Surfaces.- 1. The Structure Equations of Rn.- 2. Surfaces in R3.- 3. Intrinsic Geometry of Surfaces.- 6. The Theorem of Gauss-Bonnet and the Theorem of Morse.- 1. The Theorem of Gauss-Bonnet.- 2. The Theorem of Morse.- References.
Number Of Pages: 118
Published: September 1994
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.06 x 16.1
Weight (kg): 0.21