1000 Solved Problems in Modern Physics

Appendix: Problem Index...........................................

Chapter 1 Mathematical Physics

1.2.1 Vector Calculus

Ifφ= 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

IfAandBare irrotational,A×Bis solenoidal 1.4

(a) For central fieldF,CurlF=0 (b) For a solenoidal field

function F(r),

1.5

∫

∮cA.drbetween two points along the curver, whereAis defined 1.6

cA.draround closed curve c defined by two equations whereAis

defined

1.7

(a) Given fieldFis 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

∮

∫sA.ds, whereSis sphere of radiusRandAis defined. 1.10

A.draround a circle in xy-plane whereAis defined 1.11

(a) Curl of gradient is zero (b) divergence of curl is zero 1.12

Gradient and Laplacian of given functionφ 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 expressπ/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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