CORE COURSE (HONOURS IN PHYSICS)
SEMESTER I
PHYSICS-C I: MATHEMATICAL PHYSICS-I
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type: 4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Calculus:
First Order Differential Equations and Integrating Factor. Second Order Differential equations: Homogeneous Equations with constant coefficients.. Statement of existence and Uniqueness Theorem for Initial Value Problems. Particular Integral for typical source terms like polynomials, exponential, sine, cosine etc. Calculus of multivariable functions: Partial derivatives, exact differentials. Integrating factor, with simple illustration.
Vector Calculus:
Recapitulation of vectors: Properties of vectors under rotations. Scalar product and its invariance under rotations. Vector product, Scalar triple product and their geometrical interpretation. Scalar and Vector fields. Vector Differentiation: Gradient of a scalar field and its geometrical interpretation. Divergence and curl of a vector field. Del and Laplacian operators. Vector identities. Vector Integration: Line, surface and volume integrals of Vector fields. Flux of a vector field. Gauss' divergence theorem, Green's and Stokes Theorems and their applications. Dirac Delta function and its properties:
Orthogonal Curvilinear Coordinates:
Orthogonal Curvilinear Coordinates. Expression for Gradient, Divergence, Curl and Laplacian in orthogonal curvilinear co-ordinates. Derivation of Gradient, Divergence, Curl and Laplacian in Cartesian, Spherical and Cylindrical Coordinate Systems.
Reference Books:
• Mathematical Methods for Physicists, G.B. Arfken, H.J. Weber, F.E. Harris, 2013, 7th Edn., Elsevier. • An introduction to ordinary differential equations, E.A. Coddington, 2009, PHI learning
• Differential Equations, George F. Simmons, 2007, McGraw Hill.
• Mathematical Tools for Physics, James Nearing, 2010, Dover Publications.
• Mathematical methods for Scientists and Engineers, D.A. McQuarrie, 2003, Viva Book
Also attempt some problems on differential equations like:
1. Solve the coupled first order differential equations
dx/dt= y+x-(x^2)/3
dy/dt= -x
for four initial conditions x(0) = 0, y(0) = -1, -2, -3, -4. Plot x vs y for each of the four initial conditions on the same screen for 0 ≤ t ≤ 15.
2. The ordinary differential equation describing the motion of a pendulum is 𝜗" = −sin (𝜗) The pendulum is released from rest at an angular displacement α i.e. 𝜗 (0) = α, 𝜗′(0) = 0. Use the RK4 method to solve the equation for α = 0.1, 0.5 and 1.0 and plot 𝜗 as a function of time in the range 0 ≤ t ≤ 8π. Also, plot the analytic solution valid in the small 𝜗 (𝑠𝑖𝑛 𝜗 ≈ 𝜗).
3. Solve the differential equation:
PHYSICS-C II: MECHANICS
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type: 4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Fundamentals of Dynamics:
Reference frames. Inertial frames; Review of Newton’s Laws of Motion. Dynamics of a system of particles. Centre of Mass. Principle of conservation of momentum. Impulse. Momentum of variable-mass system: motion of rocket.
Rotational Dynamics:
Angular momentum of a particle and system of particles. Torque. Principle of conservation of angular momentum. Moment of Inertia. Calculation of moment of inertia for rectangular, cylindrical and spherical bodies. Kinetic energy of rotation. Motion involving both translation and rotation.
Elasticity:
Elastic constants and interrelation between them. Twisting torque on a Cylinder or Wire and twisting couple.
Flexure of beam:
Bending of beam, Cantilever.
Surface Tension:
Ripples and Gravity waves, Determination of Surface Tension by Jaeger’s and Quinke’s methods. Temperature dependance of Surface Tension.
Fluid Motion:
Poiseuille’s Equation for Flow of a Liquid through a Capillary Tube and the corrections. Central Force Motion: Motion of a particle under a central force field. Two-body problem and its reduction to one-body problem and its solution.. Kepler’s Laws.. Weightlessness.
Reference Books:
• An introduction to mechanics, D. Kleppner, R.J. Kolenkow, 1973, McGraw-Hill.
• Mechanics, Berkeley Physics, vol.1, C.Kittel, W.Knight, et.al. 2007, Tata McGraw-Hill.
• Physics, Resnick, Halliday and Walker 8/e. 2008, Wiley.
• Analytical Mechanics, G.R. Fowles and G.L. Cassiday. 2005, Cengage Learning.
• Feynman Lectures, Vol. I, R.P.Feynman, R.B.Leighton, M.Sands, 2008, Pearson Education
• Introduction to Special Relativity, R. Resnick, 2005, John Wiley and Sons.
PHYSICS LAB- LAB C II (2 Credits) FM: 25
1. Measurements of length (or diameter) using vernier caliper, 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 g and velocity for a freely falling body using Digital Timing Technique
6. To determine Coefficient of Viscosity of water by Capillary Flow Method (Poiseuille’s method).
7. To determine the Modulus of Rigidity of a bar by method of bending.
8. To determine the elastic Constants of a wire by Searle’s method.
9. To determine the value of g using Bar Pendulum.
10. To determine the value of g using Kater’s Pendulum.
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