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.
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 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
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.
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.
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
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.
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.