Maths for Physics

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 Physics by Indu Satija

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.

Author(s): Indu Satija

120 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

Maths for Physics

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