BS Physics Notes Series

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24. 630
Mathematical Methods in Physics

25. 631
168 Curl
169 DEL Operator
170 Delta Function
Example
Solution
Example

26. 632
Example
Show that
Solution
Hence the result.

27. 633
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

28. 634
Example

29. 635
Example
Solution
Example
Curl of a Vector Function

30. 636
Example
Solution

31. 637
Example
Solution
Now, as per

32. 638
Example
Solution

33. 639
Example

34. 640
Example
Solution

35. 641
Example
Compute the divergence of the following vector fields.
Solution
Example
Solution

36. 642
Example
Find the curl of each of the following vector fields.
Solution
Example

37. 643
Solution

38. 644
DIVERGENCE OF COORDINATE VECTOR
Example

39. 645
Example
Example
Example

40. 646
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

41. 647

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73. 679
Mathematical Methods in Physics
181 Gauss’s divergence theorem, Gauss' Law
182 Generating Function
183 Geodesics
184 Gibbs phenomenon
185 Gradient
The Divergence Theorem

74. 680
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

75. 681
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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98. 704
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

99. 705
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

100. 706
Solution
As per
Example