This document provides an overview of various mathematical methods in physics, listing over 200 topics ranging from curl and divergence to Fourier series to group theory to Laplace transforms. Each topic includes brief definitions and examples of applying the concept to physics problems. The examples demonstrate computing divergence and curl of vector fields, using properties of Laplace transforms, and solving differential equations related to orthogonal functions.

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Mathematical Methods in Physics

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168 Curl
169 DEL Operator
170 Delta Function
Example
Solution
Example

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Example
Show that
Solution
Hence the result.

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Mathematical Methods in Physics
171 De Moivre’s Theorem
172 Determinants, trace theorem, relation between determinants and traces
173 Differential operators, gradient, divergence, curl
174 Divergence
Divergence
Example
Solution
Example

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Example

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Example
Solution
Example
Curl of a Vector Function

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Example
Solution

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Example
Solution
Now, as per

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Example
Solution

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Example

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Example
Solution

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Example
Compute the divergence of the following vector fields.
Solution
Example
Solution

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Example
Find the curl of each of the following vector fields.
Solution
Example

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Solution

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DIVERGENCE OF COORDINATE VECTOR
Example

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Example
Example
Example

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The curl of a is given by
Example
Mathematical Methods in Physics
175 Eigenvalue problems, Completeness of Eigen Functions
176 Euler’s Formula
177 Euler-Maclaurin Formula
178 Fourier series, properties of Fourier series, Fourier transform, properties of Fourier transforms, Fourier
convolution theorem, Discrete Fourier transform, Fourier Analysis, Fourier cosine and sine series, Fourier
integral, Complex form of Fourier series, Fourier transform of derivatives
179 Frobenius' Method
180 Gamma Function, Digamma and Polygamma Functions

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Mathematical Methods in Physics
181 Gauss’s divergence theorem, Gauss' Law
182 Generating Function
183 Geodesics
184 Gibbs phenomenon
185 Gradient
The Divergence Theorem

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The Divergence Theorem
Mathematical Methods in Physics
186 Gram-Schmidt orthognonalization
187 Green’s Functions, Green’s function for one-dimensional problem, Eigenfunction expansion of Green’s
function, Green’s function in terms of Eigen-Function, Green’s function for Dirac Delta functions

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188 Green’s Theorem
189 Group Theory, subgroup, cyclic groups and permutation groups, isomorphism, Cayley’s theorem,
properties of isomorphism, automorphism, cosets, properties of cosets, conjugate classes and invariant
subgroups, group representations, some special groups, the symmetry group D2,D3, one dimensional
unitary group U(1), orthogonal groups SO(2) and SO(3), the SU(n) groups, Homogeneous Lorentz group
190 Hankel Functions

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Mathematical Methods in Physics
191 Harmonic Functions
192 Hermite equation as Schrodinger equation of quantum harmonic oscillator
193 Hermite Functions
194 Hermitian operators
195 Hilbert Space

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196 Initial boundary value problem
197 Kronecker Product
198 Laguerre functions and associated Laguerre functions
Mathematical Methods in Physics
199 Laplace transforms, properties of Laplace transforms, Laplace transform of derivatives, Laplace
Convolution theorem, inverse Laplace transform
200 Laplacian in orthogonal curvilinear coordinates
201 Legendre Equation, Associated Legendre Equation
202 Legendre Functions, Legendre functions of the second kind
203 Legendre Polynomials
The Laplace transform
Example

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Solution
As per
Example