By Vladimir G Ivancevic
This graduate-level monographic textbook treats utilized differential geometry from a latest clinical point of view. Co-authored by means of the originator of the world's major human movement simulator - "Human Biodynamics Engine", a posh, 264-mechanical approach, modeled via differential-geometric instruments - this can be the 1st publication that mixes glossy differential geometry with a large spectrum of purposes, from sleek mechanics and physics, through nonlinear regulate, to biology and human sciences. The publication is designed for a two-semester direction, which supplies mathematicians various purposes for his or her conception and physicists, in addition to different scientists and engineers, a robust concept underlying their versions.
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Extra resources for Applied Differential Geometry: A Modern Introduction
10 Path Integrals via Jets: Perturbative Quantum Fields . . . . . . . . . . . . . 4 Sum over Geometries and Topologies . . . . . . 1 Simplicial Quantum Geometry . . . . . . 2 Discrete Gravitational Path Integrals . . . . 3 Regge Calculus . . . . . . . . . . 4 Lorentzian Path Integral . . . . . . . 5 Application: Topological Phase Transitions and Hamiltonian Chaos . . . . . . . . 1 Phase Transitions in Hamiltonian Systems . .
8 Transition Amplitude for a Single Point Particle . 9 Witten’s Open String Field Theory . . . . 1 Operator Formulation of String Field Theory . . . . . . . . . 2 Open Strings in Constant B−Field Background . . . . . . . . 3 Construction of Overlap Vertices . . 4 Transformation of String Fields . . . 6 Application: Dynamics of Strings and Branes . . . 1 A Relativistic Particle . . . . . . . . 2 A String . . . . . . . . . . . . 3 A Brane . .
797 . . . . . . . . . . . . . 12 Time–Dependent Lagrangian Dynamics . . . Time–Dependent Hamiltonian Dynamics . . . Time–Dependent Constraints . . . . . . Lagrangian Constraints . . . . . . . . Quadratic Degenerate Lagrangian Systems . . Time–Dependent Integrable Hamiltonian Systems Time–Dependent Action–Angle Coordinates . . Lyapunov Stability . . . . . . . . . First–Order Dynamical Equations . . . . . Lyapunov Tensor and Stability .