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 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.
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.
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.