By Vladimir G Ivancevic

This graduate-level monographic textbook treats utilized differential geometry from a contemporary medical standpoint. Co-authored via the originator of the world's prime human movement simulator - "Human Biodynamics Engine", a fancy, 264-mechanical procedure, modeled via differential-geometric instruments - this is often the 1st booklet that mixes glossy differential geometry with a large spectrum of purposes, from sleek mechanics and physics, through nonlinear keep an eye on, to biology and human sciences. The publication is designed for a two-semester direction, which provides mathematicians various purposes for his or her conception and physicists, in addition to different scientists and engineers, a robust idea underlying their types.

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**Extra info for Applied Differential Geometry: A Modern Introduction**

**Example text**

7 Topological Strings and Black Hole Attractors . 8 Application: Advanced Geometry and Topology of String Theory . . . . . . . . . . . . 1 Noncommutative Gauge Theory . 2 Open Strings in the Presence of Constant B−Field . . . . . 2 K−Theory Classification of Strings . . . . . . 1232 1232 1233 . . 1235 1241 Bibliography 1253 Index 1295 April 19, 2007 16:57 WSPC/Book Trim Size for 9in x 6in ApplDifGeom Chapter 1 Introduction In this introductory chapter we will firstly give a soft, ‘plain English’ introduction into manifolds and related differential–geometric terms, with intention to make this book accessible to the wider scientific and engineering community.

2 Topological manifolds with boundary Generally speaking, it is possible to allow a topological manifold to have a boundary. The prototypical example of a topological manifold with boundary is the Euclidean closed half–space. Most points in Euclidean closed half–space, those not on the boundary, have a neighborhood homeomorphic to Euclidean space in addition to having a neighborhood homeomorphic to Euclidean closed half–space, but the points on the boundary only have neighborhoods homeomorphic to Euclidean closed half–space and not to Euclidean space.

9 Residues . . . . . . . . . . . 1 Topological Invariance . . . . . 2 Vanishing Theorems . . . . . 3 Computation on K¨ahler Manifolds . 11 SW Theory and Integrable Systems . . . . 1 SU (N ) Elliptic CM System . . . 3 Twisted CM–Systems Defined by Lie Algebras . . . . . . . 4 Scaling Limits of CM–Systems . . 5 Lax Pairs for CM–Systems . . . 6 CM and SW Theory for SU (N ) . . 7 CM and SW Theory for General Lie Algebra . . . . . . . . 12 SW Theory and WDVV Equations .