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.
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.
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.
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,
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.