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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
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
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
Mathematical Physics Lecture Notes
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
NA Pages
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Author(s): NA
NA Pages
Physical Applications of Geometric Algebra
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Author(s): NA
NA Pages
Algebraic Quantum Field Theory [PDF 202p]
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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
Holomorphic Methods in Mathematical Physics [PDF 59p]
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Author(s): NA
NA Pages
Homological Methods in Equations of Mathematical Physics[PDF 150p]
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NA Pages
An Introduction to Noncommutative Geometry [PDF 18p]
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