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PHYSICS(HONOURS)
SEMESTER-I
C-I: MATHEMATICAL PHYSICS-I
(Credits: Theory-04, Practicals-02)
Marks:100 (Theory:70, Practical: 30)
Theory: 40 Classes (1 hr. duration)
The emphasis of course is on applications in solving problems of interest to physicists. The students
are to be examined entirely on the basis of problems, seen and unseen.
UNIT-I
Calculus: Calculus of functions of more than one variable: Partial derivatives, exact and inexact
differentials, Integrating factor, with simple illustration. Constrained Maximization using Lagrange
Multipliers. (4 Lectures)
Vector Calculus: Recapitulation of vectors: Properties of vectors under rotations. Scalar product
and its invariance under rotations. Vector product, Scalar triple product and their interpretation in
terms of area and volume respectively. Scalar and Vector fields. (5 Lectures)
UNIT-II
Orthogonal Curvilinear Coordinates: Orthogonal Curvilinear Coordinates, Derivation of Gra-
dient, Divergence, Curl and Laplacian in Cartesian, Spherical and Cylindrical Coordinate Systems.
Comparison of velocity and acceleration in cylindrical and spherical coordinate system. (7 Lectures)
Dirac Delta function and its properties: Definition of Dirac delta function. Representation
as limit of a Gaussian function and rectangular function. Properties of Dirac delta function. (3
Lectures)
UNIT-III
Vector Differentiation: Directional derivatives and normal derivative. Gradient of a scalar field
and its geometrical interpretation. Divergence and curl of a vector field. Del and Laplacian operators.
Vector identities, Gradient, divergence, curl and Laplacian in spherical and cylindrical coordinates.
(8 Lectures)
UNIT-IV
Vector Integration: Ordinary Integrals of Vectors. Multiple integrals, Jacobian. Notion of in-
finitesimal line, surface and volume elements. Line, surface and volume integrals of Vector fields.
Flux of a vector field. Gauss’ divergence theorem, Green’s and Stokes Theorems and their applica-
tions (no rigorous proofs). (13 Lectures)