A Visual Introduction to Differential Forms and Calculus on ManifoldsSpringer, 3 de nov. de 2018 - 468 páginas 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. |
Conteúdo
1 | |
2 An Introduction to Differential Forms | 31 |
3 The Wedgeproduct | 69 |
4 Exterior Differentiation | 107 |
5 Visualizing One Two and ThreeForms | 151 |
6 PushForwards and PullBacks | 189 |
7 Changes of Variables and Integration of Forms | 229 |
8 Poincaré Lemma | 258 |
10 Manifolds and Forms on Manifolds | 309 |
11 Generalized Stokes Theorem | 337 |
Electromagnetism | 369 |
A Introduction to Tensors | 394 |
B Some Applications of Differential Forms | 435 |
463 | |
465 | |
9 Vector Calculus and Differential Forms | 277 |
Outras edições - Ver todos
A Visual Introduction to Differential Forms and Calculus on Manifolds Jon Pierre Fortney Prévia não disponível - 2018 |
Termos e frases comuns
actually axis base point basis elements change of coordinates computations consider coordinate functions curl F defined definition denoted differential forms directional derivative dt A dx dual dual space dx A dy dx dy dy A dz Einstein summation notation electric field equations Euclidian exact example exterior derivative exterior differentiation function f geometric given gives global formula hand side identity inner product Jacobian k-form Lie derivative linear functional magnetic field manifold R2 mapping mathematical matrix metric notation one-form parallelepiped parallelepiped spanned parameterized picture plane Poincaré lemma point x0 positive orientation pull-back push-forward Question simply ſº Stokes Suppose surface tangent bundle tangent space theorem three-form Tºp transformation two-form unit vector vector calculus vector field vector space vector vp volume form wedgeproduct write zero-form