Physical Applications of Geometric Algebra

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 Method of Physics by Njah

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

57 Pages

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

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

Mathematical Methods for Physics

This note describes the following topics: Notation for scalar product, Linear vector spaces, Operators, Eigenvectors and Eigenvalues, Green’s functions, Integral Equations, Variational calculus.

Author(s): Niels Walet

90 Pages

An introduction to mathematical physics

This book  is intended primarily as a class-book for mathematical students and as an introduction to the advanced treatises dealing with the subjects of the different chapters, but since the analysis is kept as simple as possible, It will be useful for chemists and others who wish to learn the principles of these subjects.

Author(s): Robert Alexander Houstoun

224 Pages

Lecture Notes Methods of Mathematical Physics I

This note covers the following topics: Linear Algebra, Functional Analysis, Special Functions, Integral Transform and Fourier Series.

Author(s): Dr. A. N. Njah, University of Agriculture, Abeokuta

57 Pages

Differential Geometry and Physics

Currently this section contains no detailed description for the page, will update this page soon.

Author(s): NA

NA Pages

Basic Bundle Theory and K Cohomology Invariants [PDF 356p]

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Author(s): NA

NA Pages

Lecture notes for Engineering Mathematics

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Author(s): NA

NA Pages

Topology and Geometry for Physics

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Author(s): NA

NA Pages

COMPLEX GEOMETRY OF NATURE AND GENERAL RELATIVITY [PDF 229p]

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Author(s): NA

NA Pages

Lectures on Orientifolds and Duality [PDF 64p]

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Author(s): NA

NA Pages