COURSE I (THEORY) – 4 credits Course Code: PHYC101

MATHEMATICAL METHODS IN PHYSICS – 3 credits

(i) DIFFERENTIAL EQUATIONS: Differential equations of first- and second- order and first degree (homogeneous and inhomogeneous with constant coefficients) and their solutions. Gamma and Beta functions. [10 classes]

(ii) VECTOR CALCULUS:

a) Scalar and vector fields, Differentiation of vectors, gradient, divergence, curl and Laplacian operators. [8 classes]

b) Vector relations in orthogonal curvilinear co-ordinates, Expressions for gradient, divergence, curl and Laplacian operator in spherical polar and cylindrical polar co- ordinates.[8 classes]

c) Gauss’s, Stoke’s and Green’s theorems.[5 classes]

d) INTEGRAL TRANSFORMS:

a) LAPLACE TRANSFORMS: Laplace transform and its basic properties, Transformation of elementary functions, Transform of derivatives and integrals, Inverse transformation, Convolution theorem, Applications to simple problems described by first and second order differential equations. [8 classes]

b) FOURIER SERIES: Fourier’s theorem and its applications in the analysis of square and saw-tooth waves, Fourier integrals and transformations, applications to simple problems. [12 classes]

e) THEORY OF ERRORS: Standard and probable errors, Propagation of errors, Principle of least square fitting of data (linear case). [3 classes]

[Total: 54 classes]

A SET OF TWO ASSIGNMENTS- 1 credit (unguided learning process)

REFERENCE BOOKS:

1. Mathematical Physics by Butkov.

2. Mathematical Methods for Physicists by Weber & Arfken.

3. Mathematical Physics by Ghatak, Goyal & Chua

4. Mathematical Physics by Rajput. B.S.

5. Mathematical Physics by Gupta, B.D.

6. Mathematical Methods in Physical Sciences by M. Boas

7. Schaum series on Laplace transform

8. Schaum series on Vector Calculus

9. Mathematical Physics by H. K. Das

10. Higher Engineering Mathematics by B. S. Grewal

COURSE II (THEORY) – 4 credits Course Code: PHYC102

GENERAL PHYSICS – 1.5 credits

(i) ELASTICITY: Relations between different elastic constants, Torsional rigidity of cylinder, torsional oscillations, Searle’s method of determination of elastic constants of a material. [10 classes]

(ii) FLEXURE OF BEAM: Cantilever and supported beam. [4 classes]

(iii) SURFACE TENSION: Ripple and gravity waves, Determination of surface tension by Quinke’s method, Surface tension and evaporation. [6 classes]

(iv) VISCOSITY: Poiseuille’s formula for flow of fluid through capillary tubes, Determination of coefficient of viscosity – Rankine’s method. [4 classes]

(v) HYDRODYNAMICS: Equation of continuity, Euler’s equation of motion, Bernoulli’s theorem from Euler’s equation. [6 classes]

ACOUSTICS - 1.5 credits

(i) Vibration of material bodies: Free vibrations: Analytical treatment, energy expression, Damped vibrations: Analytical treatment, energy expression, decrement and logarithmic decrement, relaxation time, Forced Vibrations: Analytical treatment, mechanical impedance, amplitude resonance, energy resonance, sharpness of resonance, Phases of forced vibrations, effect of damping factor on amplitude, energy and phase of forced vibration.[7 classes]

(ii) Vibration of strings and Rods: Speed of transverse wave along a stretched string, One dimensional wave equation and its solution, Analysis of vibration of a plucked string using Fourier's Theorem, Young's law, Transverse vibration of rod, Vibration of tuning fork.[7 classes]

(iii) Longitudinal waves: Group velocity and phase velocity of a wave in a dispersive medium, Speed of longitudinal wave in an elastic fluid medium, Energy density and energy transmission (intensity) in waves, Intensity measurement by Rayleigh's disc method, Loudness, intensity level, Bel and Phon.[ 4 classes]

(iv) Acoustics of Buildings: Reverberation and time of reverberation. Standard reverberation time, Sabine's formula and its limitations, Measurement of absorption coefficient.[4 classes]

[Total: 52 classes]

A SET OF TWO ASSIGNMENTS- 1 credit (unguided learning process)

REFERENCE BOOKS:

1. Textbook of Sound by Kinsler & Frey.

2. Waves and Acoustics by Chakraborty & Choudhury.

3. Sound by Wood A.

4. A Textbook of Sound by Khanna & Bedi.

5. General Properties of Matter by Newmann & Searle.

6. General Properties of Matter by Mathur, D.S.

7. A Treatise on General Properties of Matter by Chatterjee & Sengupta.

COURSE IX (LAB SESSION) - 2 credits Course Code: PHYC103

LIST OF EXPERIMENTS

(i) Determination of Young’s modulus by bending of beam method.

(ii) Determination of elastic constants by Searle’s apparatus.

(iii) Determination of acceleration due to gravity by Kater’s pendulum.

(iv) Determination of viscosity of liquid by Poiseuille’s method.

(v) Determination of speed of sound using Kundt’s tube apparatus.

(vi) Laws of transverse vibration by sonometer.