Clifford Taubes

"Given that a college-level life science student will take only one additional calculus course after learning the very basics of differentiation and integration, what material should such a course cover? This book answers that question. It is based on a very successful one-semester course taught at Harvard and aims to teach students in the life sciences how to use differential equations to facilitate their research. It requires only a semester's background in calculus. Notions from linear algebra and partial differential equations that are most useful to the life sciences are introduced as and when needed, and in the context of life science applications are drawn from real published papers. In addition, the course is designed to teach students how to recognize when differential equations can help focus research. A course taught with this book can replace a standard course in multivariable calculus that is typically taught to engineers and physicists."--Jacket.

In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.