KAZI NAZRUL UNIVERSITY(KNU) B.Sc PHYSICS HONOURS 1ST SEMESTER SYLLABUS

KAZI NAZRUL UNIVERSITY, ASANSOL

PHYSICS HONOURS SYLLABUS

1ST SEMESTER

Core Course-I :

MATHEMATICAL METHODS OF PHYSICS –I

[Credit: 6, Lecture : 60 hours, Marks : 50]

1. Calculus :

Infinite sequences and series; Conditional and Absolute Convergence; Tests for Convergence (proofs not required, only applications), Functions of several real variables – partial differentiation, Taylor's series, multiple integrals (5)

2. Vector Analysis :

Definition, Transformation properties, Differentiation and integration of vectors; Line integral, volume integral and surface integral involving vector fields; Gradient, divergence and curl of a vector field; Gauss' divergence theorem, Stokes' theorem, Green's theorem - application to simple problems; Orthogonal curvilinear co-ordinate systems, unit vectors in such systems, illustration by plane, spherical and cylindrical co-ordinate systems only. (15)

3. Determinant and Matrices :

Algebra of matrices – Equality, Addition, Multiplication; Transpose and conjugate transpose of a matrix, Singular and non-singular matrices; Adjoint and Inverse of a Matrix; rank of a matrix; Normal Forms; Solution of simultaneous equation of matrices by Cramer’s rule; Solution of systems of linear homogenous and inhomogeneous equations by matrix method; Cayley- Hamilton theorem; Characteristics equation of a square matrix and diagonalization; Properties of Eigenvalues and eigenvectors of matrices; Types of matrices - Symmetric, Skew- symmetric, Hermitian, Orthogonal and unitary matrices and their properties. (15)

4. Fourier Series:

Periodic functions. Orthogonality of sine and cosine functions, Dirichlet Conditions (Statement only). Expansion of periodic functions in a series of sine and cosine functions and determination of Fourier coefficients. Complex representation of Fourier series. Expansion of functions with arbitrary period. Expansion of non-periodic functions over an interval. Even and odd functions and their Fourier expansions. Application. Summing of Infinite Series. Term-by-Term differentiation and integration of Fourier Series. Parseval Identity. (15)

5. Partial Differential Equations

Functions of several variables; Partial Derivatives; Partial Differential Equations; Partial Differential Equations in Physics; Solutions by the method of separation of variables; Simple examples, Laplace's equation and its solution in Cartesian, spherical polar (axially symmetric problems), and cylindrical polar (`infinite cylinder' problems) coordinate systems; Diffusion equation. (10)

Core Course-II: MECHANICS (NEW)

[Credit:4, Theory Lecture: 45 hours, Marks:50]

1.Mechanics of a Single Particle

Velocity and acceleration of a particle in (i) plane polar coordinates - radial and cross-radial components (ii) spherical polar and (iii) cylindrical polar coordinate system; Time and path integral of force; work and energy; Conservative force and concept of potential; Conservation of energy; Dissipative forces; resistive motion and friction. Conservation of linear and angular momentum. (12 L)

2.Mechanics of a System of Particles

Linear momentum, angular momentum and energy - centre of mass decomposition; Equations of motion, conservation of linear and angular momenta. (8L)

3.Surface Tension:

Surface energy and surface tension, angle of contact, excess pressure on curved surface, capillary rise, equilibrium vapour pressure over curved surface. (6L)

4.Mechanics of Ideal Fluids and Viscosity

Definition of Newtonian and non-Newtonian fluids, Streamlines and turbulent flow. Stokes’ law-terminal velocity. Equation of continuity; Euler's equation of motion; Streamline motion -Bernoulli's equation and its applications. (7L)

5.Oscillations:

SHM: Simple Harmonic Oscillations. Differential equation of SHM and its solution. Kinetic energy, potential energy, total energy, and their time-average values. Damped oscillation. Forced oscillations: Transient and steady states; Resonance, sharpness of resonance; power dissipation and Quality Factor. Concept of different types of waves (plane, spherical, cylindrical), Group and phase velocity, Growth and decay of sound waves in hall, Sabine’s formula reverberation. (12)

MECHANICS LAB [Credit:2, Marks: 50]

1. Measurements of length (or diameter) using vernier calliper, screw gauge and travelling microscope.

2. To study the random error in observations.

3. To study the Motion of Spring and calculate (a) Spring constant, (b) g and (c) Modulus of rigidity.

4. To determine the Moment of Inertia of a Flywheel.

5. To determine the Coefficient of Viscosity of water by Capillary Flow Method (Poiseuille’s method).

6. To determine the Young's Modulus of a Wire by Optical Lever Method.

7. To determine the elastic Constants of a wire by Searle’s method.

8. To determine the value of g using Bar Pendulum.

9. Determination of surface tension of a liquid by Jaeger’s method.

10. Determination of Young’s modulus by flexure method.