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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
57Pages
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
76Pages
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
NAPages
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.
Author(s): Joseph A. Minahan
86Pages
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
95Pages
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
NAPages
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
263Pages
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
177Pages
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.
Author(s): Eric L. Michelsen
273Pages
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.
Author(s): Klaus Hef
279Pages
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
90Pages
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
224Pages
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
57Pages
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.
Author(s): Dr. R. L. Herman
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