By Vladimir G Ivancevic
This graduate-level monographic textbook treats utilized differential geometry from a contemporary clinical standpoint. Co-authored through the originator of the area s prime human movement simulator Human Biodynamics Engine , a fancy, 264-DOF bio-mechanical method, modeled via differential-geometric instruments this can be the 1st booklet that mixes sleek 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 path, which supplies mathematicians a number of functions for his or her thought and physicists, in addition to different scientists and engineers, a robust thought underlying their versions.
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The notes from a suite of lectures writer added at nationwide Tsing-Hua collage in Hsinchu, Taiwan, within the spring of 1992. This notes is the a part of e-book "Thing Hua Lectures on Geometry and Analisys".
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Extra resources for Applied differential geometry. A modern introduction
6 Application: Force–Field Psychodynamics . . 1 Motivational Cognition in the Life Space Foam . . . . . . . . 5 Application: Witten’s TQFT, SW–Monopoles and Strings . . . . . . . . . . . . . . . 1 Topological Quantum Field Theory . . . . 2 Seiberg–Witten Theory and TQFT . . . . 2 Topological Lagrangian . . . . . 3 Quantum Field Theory . . . . . 1035 1036 1037 1038 1039 1043 1045 1047 1049 1050 1055 1057 1059 1061 1064 1069 1069 1072 1075 1079 1080 1097 1097 1103 1103 1105 1107 April 19, 2007 16:57 WSPC/Book Trim Size for 9in x 6in Contents Dimensional Reduction and 3D Field Theory .
2 Associated Bundles . . . . . . . . . 3 Classical Gauge Fields . . . . . . . . 4 Gauge Transformations . . . . . . . . 5 Lagrangian Gauge Theory . . . . . . . 6 Hamiltonian Gauge Theory . . . . . . . 7 Gauge Conservation Laws . . . . . . . 8 Topological Gauge Theories . . . . . . Application: Modern Geometrodynamics . . . . 1 Stress–Energy–Momentum Tensors . . . . 2 Gauge Systems of Gravity and Fermion Fields . 3 Hawking–Penrose Quantum Gravity and Black Holes .
2 General Covariance Condition . . . . . . Application: Jets and Hamiltonian Field Theory . . 1 Covariant Hamiltonian Field Systems . . . . 3 Evolution Operator . . . . . . . . . 4 Quadratic Degenerate Systems . . . . . . Application: Gauge Fields on Principal Connections . 1 Connection Strength . . . . . . . . 2 Associated Bundles . . . . . . . . . 3 Classical Gauge Fields . . . . . . . . 4 Gauge Transformations . . . . . . . . 5 Lagrangian Gauge Theory .