UNIT 1
Classical Mechanics - I
Constraints and Degrees of Freedom – Generalized coordinates – Generalized displacement –
Velocity – Acceleration – Momentum – Force – Potential Energy – D’Alembert’s Principle –
Lagrangians equation from D’Alembert’s principle – Application of Lagrange’s equation of
motion to Linear Harmonic Oscillator, Simple Pendulum and Compound Pendulum.
UNIT 2
Classical Mechanics – II
Phase Space – Hamiltonian function – Hamiltonian Principle – Hamilton’s canonical
equations of motion- Physical significance of H – Applications of Hamiltonian equations of
motion to Simple Pendulum, Compound Pendulum and Linear Harmonic Oscillator.
UNIT 3
Special Functions
Definition – The Beta function – Gamma function – Evaluation of Beta function – Other
forms of Beta function – Evaluation of Gamma function – Other forms of Gamma function -
Relation between Beta and Gamma functions – Problems.
UNIT4
Matrices
Introduction – special types of Matrices – Transpose of a Matrix – The Conjugate of a Matrix
– Conjugate Transpose of a Matrix – Symmetric and Anti symmetric – Hermitian and skew
Hermitian – Orthogonal and Unitary Matrices – Properties – Characteristics equation – Roots
and characteristics vector – Diagonalization of matrices – Cayley – Hamilton theorem –
Problems
Anx.22 D - B.Sc. Physics (SDE) 2007-08 Page 6 of 21
UNIT 5
Vector Calculus
Ñ Operator – Divergence – Second derivative of Vector functions or fields – The Laplacian
Operator – Curl of a Vector – Line Integral – Line Integral of a Vector field around an
infinitesimal rectangle – Curl of Conservative field – Surface Integral – Volume Integral
(without problem) – Gauss’s Divergence theorem and it’s proof in the simple problems –
Stoke’s and its proof with simple problems.

## BSc Subjects