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.
This note covers Laws of
nature and mathematical beauty, Gaussian Integrals and related functions,
Basic gaussian integrals, Stirling formula error functions, Real numbers,
Complex numbers, Scalars, Vectors, Tensors and spinor, Fourier
transformation, Curvilinear coordinates, Partial differential equations,
Solving partial differential equation by separation of variables, Solving
laplace equation in spherical polar coordinates, Spherical harmonics and
legendre functions, Bessel function, Spherical bessel function and
matrices.
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
This is a lecture
note on Mathematical methods in physics. It covers the following topics: Group
Theory and Lie Algebras,Path Integrals, Topology, Differential Geometry,
Yang-Mills.
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.
The purpose of the
“Funky” series of documents is to help develop an accurate physical, conceptual,geometric, and pictorial understanding of important physics topics. We focus on
areas that don’t seem to be covered well in most texts. Topics covered includes: Vectors, Green’s
Functions, Complex Analytic Function, Conceptual Linear Algebra, Probability,
Statistics, and Data Analysis, Practical Considerations for Data Analysis,
Numerical Analysis, Fourier Transforms and Digital Signal Processing, Tensors,
Without the Tension, Differential Geometry.
This note
covers the following topics: Measuring: Measured Value and Measuring Unit, Signs
and Numbers and Their Linkages, Sequences and Series and Their Limits,
Functions, Differentiation, Taylor Series, Integration, Complex Numbers,
Vectors.
This note describes the following topics: Notation for scalar product, Linear
vector spaces, Operators, Eigenvectors and Eigenvalues, Green’s functions,
Integral Equations, Variational calculus.
This note covers the following topics: Prologue, Free Fall and Harmonic Oscillators, ODEs and SHM, Linear Algebra,
Harmonics - Fourier Series, Function Spaces, Complex Representations, Transform
Techniques, Vector Analysis and EM Waves, Oscillations in Higher Dimensions.