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.

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

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