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.

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.

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

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.

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.

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.

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