## Yvonne Choquet-Bruhat, Cecile Dewitt-Morette, and Margaret Dillard-Bleick

### Analysis, Manifolds, and Physics: Part I

Originally published by North-Holland, Amsterdam, 1977

**Summary (Math Reviews)**

"The authors belong, respectively, to departments of mechanics, astronomy, and radiology. The book does not appear to suffer in the quality of its mathematical exposition from this fact, but it gains immensely in the form of a wide variety of physical examples. These are contained in problems and exercises whose solutions are often outlined. Some samples are: Clifford algebras, the Feynman-Green function, the strain tensor, wormholes, time-dependent Hamiltonians, and electromagnetic shock waves."

**Content**

- Review of fundamental notions of analysis
- Differential calculus on Banach spaces
- Differentiable manifolds, finite dimensional case
- Integration on manifolds
- Riemannian manifolds, Kahlerian manifolds
- Connections on a principle fibre bundle
- Distributions
- Differentiable manifolds, infinite dimensional case

### Analysis, Manifolds, and Physics: Part II

North-Holland Publishing Co., Amsterdam, 1989

**Summary (Math Reviews)**

"This companion volume extends the applications to a more detailed discussion and to more sophisticated and interesting ones as well. To illustrate, here is a topic from each chapter: the Fierz identity, the stress-energy tensor, Stiefel manifolds, the Weyl Heisenberg group, Calabi-Yau spaces, Chern-Simons classes, and Wightman and Schwinger functions."