Advanced methods of mathematical physics
In an introductory style with many examples, Advanced Methods of Mathematical Physics presents, some of the concepts, methods, and tools that form the core of mathematical physics. The material covers two main broad categories of topics: 1) abstract topics, such as groups, topology, integral equations, and stochasticity, and 2) the methods of nonlinear dynamics.
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Rudiments of Topology and Differential Geometry
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arbitrary constant bifurcation point called coefficients consider continuous coordinates corresponding coset critical point curve defined Definition Let denoted dependent variables derivatives determined differentiable manifold differential equation dimensional discussed distribution function dynamical system eigenfunctions eigenvalues equivalent Example exists fact finite Fredholm Fredholm integral equation Further given group G Hamiltonian Hence homomorphism implies independent infinite infinitesimal integral equation interval invariant inverse KdV equation kernel Liapunov function Lie group limit cycle limit point linear system mathematical matrix method modes NLDE node non-empty nonlinear system normal subgroup Note obtained open set operator OPLGTs orbits oscillator parameter PDEs permutation phase plane phase portrait physical problem properties random variables result Riccati Riccati equation satisfies Show shown in Fig stable stochastic processes subgroup of G subset subspace theorem theory topological space topology trajectories transformation unstable zero solution