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.
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.
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.
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
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.
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.
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.