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Lecture Notes on Mathematical Statistical Physics
This note explains the following topics: classical statistical mechanics, Review of classical mechanics, Review of probability and measure, The Maxwellian distribution Probability spaces in classical mechanics, Review of thermodynamics Macro states, Macro variables, Thermal equilibrium and entropy, The Boltzmann equation, The thermodynamic arrow of time, Quantum statistical mechanics and thermodynamic ensembles.
Author(s): Roderich Tumulka
173 Pages
Mathematical Method of Physics by Njah
The PDF covers the following topics related to Mathematical Physics : Linear Algebra, Vector Space or Linear Space, Matrix Theory, Complex Matrices, Matrix Algebra, Consistency of Equations, Solution of Sets of Equations, Eigenvalues and Eigenvectors of a Matrix, Transformation, Bases and Dimension, Functional Analysis, Normed Spaces, Special Functions, the Gamma and Beta Functions, Bessel’s Functions, Legendre’s Polynomials, Hermite Polynomials, Laguerre Polynomials, Integral Transform and Fourier Series, Laplace Transform, the Dirac Delta Function &
Author(s): Dr. A. N. Njah, Department of Physics, University of Agriculture, Abeokuta
57 Pages
Mathematical Physics by Michael Aizenman
The PDF covers the following topics related to Mathematical Physics : Introduction to statistical mechanics, Canonical Ensembles for the Lattice Gas, Configurations and ensembles, The equivalence principle, Generalizing Ensemble Analysis to Harder Cases, Concavity and the Legendre transform, Basic concavity results, Concave properties of the Legendre transform, Basic setup for statistical mechanics, Gibbs equilibrium measure, Introduction to the Ising model, Entropy, energy, and free energy, Large deviation theory, Free energy, Basic Properties, Convexity of the pressure and its implications, Large deviation principle for van Hove sequences, 1-D Ising model, Transfer matrix method, Markov chains, 7 2-D Ising model, Ihara graph zeta function, Gibbs states in the infinite volume limit, Conditional expectation, Symmetry and symmetry breaking, Phase transitions, Random field models, Proof of symmetry-breaking of continuous symmetries, The spin-wave perspective, Infrared bound, Reflection positivity.
Author(s): Professor Michael Aizenman
76 Pages
An Introduction to Mathematical Physics Via Oscillation
The intent of this note is to introduce students to many of the mathematical techniques useful in their undergraduate physics education long before they are exposed to more focused topics in physics. Topics covered includes: ODEs and SHM, Linear Algebra, Harmonics - Fourier Series, Function Spaces, Complex Representations, Transform Techniques, Vector Analysis and EM Waves, Oscillations in Higher Dimensions.
Author(s): Dr. R. L. Herman
NA Pages
Mathematical Methods in Physics
The purpose of this note is to present standard and widely used mathematical methods in Physics, including functions of a complex variable, differential equations, linear algebra and special functions associated with eigenvalue problems of ordinary and partial differential operators.
Author(s): Eric D’Hoker
95 Pages
Mathematical Physics by Bergfinnur Durhuus and Jan Philip Solovej
The main focus of this note is on theoretical developments rather than elaborating on concrete physical systems, which the students are supposed to encounter in regular physics courses. Topics covered includes: Newtonian Mechanics, Lagrangian Mechanics, Hamiltonian Mechanics, Hilbert Spaces, Operators on Hilbert spaces and Quantum mechanics.
Author(s): Bergfinnur Durhuus and Jan Philip Solovej
177 Pages
