Introduction to Mathematical Physics & Classical Mechanics B.Sc First Sem Bihar

Syllabus

Introduction to Mathematical Physics & Classical Mechanics

Major Course I (MJC-1)

MJC-1: 4 Credit

Unit 1: Concept of Differentiation & Integration                                     01 Credit (15 hrs)

Differential calculus: Geometric Meaning of derivative; Maxima & Minima; Approximation of derivative; Partial Differentiation. Approximation using Taylor and Binomial series.

Integral Calculus: Geometric Meaning of integration, order and degree of differential equation. Solution of First order (homogeneous & Non-homogeneous), Integrating Factor. Exact and Inexact Differentials. D-operator & Solution of Second order Differential Equation.

Unit  II: Vector Algebra &Vector Calculus                                               01 Credit (15 hra)

Vector Triple Products & their significance: concept of scalar & vector fields, Gradient of scalar. Divergence & Curl of vectors and their physical applications in Physics
(e.g. Equation of continuity,  Euler’s equation of motion, Bernoulli’s theorem, Fourier heat flow, Poisson’s and Laplace's equation in a gravitational field, Gauss’s law of in Electrostatic, etc.).

Unit 111: Fundamentals of Dynamics                                                         01 Credit (15 hrs)

Inertial and Non-Inertial Frame of Reference, Rotating frame of Referenc,. Centrifugal and Coriolis Forces with their applications (Effect on value of ‘g’. On path of freely falling body, Geo-physical effect); Foucault pendulum, Direct proof of rotation of Earth.

Unit IV: Centre -of- Mass Frame and Central Forces                            01 Credit (15 hrs)

Lab frame & Centre of Mass frame, Two dimensional collision in physical problems. Relation connecting Scattering angle, Recoil angle. final velocities in C-frame &
L-frame, Cross section & Rutherford scattering. Central forces and their equations,; General Equation of central orbit. Kepler’s law of Planetary motion, Artificial satellite.

Minor Course I (MIC-1)

MIC-1: 2 Credit

Unit I: Introduction to Calculus & Vector                                                  01 Credit (15 hrs)

Differential Calculus: Geometric Meaning of derivative; Maxima & Minima; Approximation of derivative; Partial Differentiation.

Integral Calculus: Geometric Meaning of integration, order and degree of differential equation, Solution of First order (homogeneous & Non-homogeneous), Integrating Factor, Exact and Inexact Differentials. Recapitulation of Vectors, Vector Algebra involving two and three vectors, Introduction to Gradient, Divergence, Curl of Vectors with their physical significance.

Unit II: Fundamentals of Dynamics                                                             01 Credit (15 hrs)

Inertial and Non-Inertial Frame of Reference. Rotating frame, Fictitious Forces-Centrifugal and Coriolis Forces with their applications (Effect on value of ‘g’, On path of freely falling body) Introduction to special theory of relativity & its postulates.