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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
Lecture Notes for Mathematical Methods of Physics
This note covers the following topics: Series of Functions, Binomial Theorem, Series Expansion of Functions, Vectors, Complex Functions, Derivatives, Intergrals, and the Delta Function, Determinants, Matrices, Vector Analysis, Vector Differentiation and Integration, Integral Theorems and Potential Theory, Curvilinear Coordinates, Tensor Analysis, Jacobians and Differential Forms, Vectors in Function Spaces, Gram-Schmidt Orthogonalization and Operators, Transformations, Invariants, and Matrix Eignevalue Problems, Hermitian and Normal Matrix Eigenvalue Paroblems, Ordinary Differential Equations, Second-Order Linear ODEs, Green's Functions.
Author(s): Gregory G. Howes
NA Pages
Mathematics is an integral component of all of the scientific disciplines, but for physics, it is a vital and essential skill that anyone who chooses to study this subject must master. Topics covered includes: Functions and Geometry, Complex Numbers, Matrices, Vectors, Limits, Differentiation, Partial Differentiation and Multivariable Differential Calculus, Integration, Multiple Integration, Differential Equations, Series and Expansions, Operators, Mechanics.
Author(s): Daniel Brett and Joseph Vovrosh
263 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
