Appendix: Problem Index
Chapter 1 Mathematical Physics
1.2.1 Vector Calculus
If ϕ = 1/r , ∇ϕ = r/r
3
1.1
Unit vector to the given surface at a point
1.2
Divergence of 1/r
2 is zero
1.3
If A and B are irrotational, A × B is solenoidal
1.4
(a) For central field F, Curl F = 0 (b) For a solenoidal field
function F(r ),
1.5
c A.dr between two points along the curve r, where A is defined
1.6
c A.dr around closed curve c defined by two equations where A is
defined
1.7
(a) Given field F is conservative (b) To find scalar potential
(c) Work done in moving a unit mass between two points
1.8
To verify Green’s theorem in the given plane, the bonded region
being defined by two equations
1.9
s A.ds, where S is sphere of radius R and A is defined.
1.10
A.dr around a circle in xy-plane where A is defined
1.11
(a) Curl of gradient is zero (b) divergence of curl is zero
1.12
Gradient and Laplacian of given function ϕ
1.13
(a) A unit vector normal to given surface at the given point
(b) Directional derivative at the given point in the given direction
1.14
The divergence of inverse square force is zero
1.15
Angle between two surfaces at given point
1.16
1.2.2 Fourier Series and Fourier Transforms
Fourier series expansion for saw-tooth wave
1.17
Fourier series expansion for square wave
1.18
To express π/4 as a series
1.19
Fourier transform of a square wave
1.20
To use Fourier integral to prove the given definite integral
1.21
Fourier transform of a Gaussian function is another Gaussian
function
1.22
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