Semester I
MAJOR-I: PHYS1011: MATHEMATICAL PHYSICS-I (Credits: Theory-03, Practical - 01)
F.M. = 75 (Theory – 40, Practical – 20, Internal Assessment –15)
COURSE OBJECTIVE: The aim of this course is to equip the students with mathematical methods that are important prerequisites for physics courses.
Theory: 45 Lectures
Calculus:
Recapitulation: Limits, Continuity, Average and instantaneous quantities, Differentiation. Plotting functions. Intuitive ideas of continuous, differentiable etc. functions and plotting of curves. Approximation: Taylor and binomial series (statements only).
[Theory Notes 08/08/2024] [Theory Notes 2023]
(3 Lectures)
First Order and Second Order Differential equations: First Order Differential Equations and Integrating Factor. Homogeneous Equations with constant coefficients. Wronskian and general solution. Statement of the existence and the Uniqueness theorem for Initial Value Problems. Particular Integral. [Notes updated-2024] [Class Notes 2023] [Home Work Set - 2] [Solution of Home Work Set-2]
(9 Lectures)
Calculus of functions of more than one variable: Partial derivatives, Exact and inexact differentials. [Some Solved problems]
(6 Lectures)
Vector Calculus:
Recapitulation of vectors: Properties of vectors under rotations. Scalar product and its invariance under rotations. Vector product, Scalar triple product and their interpretation in terms of area and volume respectively. Scalar and Vector fields.
(5 Lectures)
Vector Differentiation: Directional derivatives and normal derivative. Gradient of a scalar field and its geometrical interpretation. Divergence and curl of a vector field. Del and Laplacian operators. Vector identities.
(6 Lectures)
Vector Integration: Ordinary integrals of vectors, Multiple integrals, Jacobian. Notion of an infinitesimal line, surface and volume elements. Line, surface and volume integrals of vector fields. Flux of a vector field, Gauss' divergence theorem. Green's and Stokes Theorems and their applications (no rigorous proofs).
(10 Lectures)
Orthogonal Curvilinear Coordinates:
Derivation of Gradient, Divergence, Curl and Laplacian in Cartesian, Spherical and Cylindrical Coordinate Systems. [Class Notes][Home Work Set-OCC]
(6 Lectures)
Class Test Question (18-February-2025)
Netaji Mahavidyalaya Internal Assessment Question 2024
BU Question Paper 2023 [Also click here for the model Solution (restricted)]
Internal Assessment Question 2023 (Physics Minor)[Exam on 09-04-2024]
Solution of Internal Assessment Question 2023 (Physics Minor) [uploaded on 10-04-2024]