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### CC-I: Mathematical Physics-I (32221101)

Unit 1
Calculus
Functions: Recapitulate the concept of functions. Plot and interpret graphs of functions
using the concepts of calculus.

First Order Differential Equations: First order differential Equations: Variable separable,
homogeneous, non-homogeneous, exact and inexact differential equations and Integrating
Factors. Application to physics problems

Second Order Differential Equations: Homogeneous Equations with constant
coefficients. Wronskian and general solution. Particular Integral with operator method,
method of undetermined coefficients and method of variation of parameters. Cauchy-Euler
differential equation and simultaneous differential equations of First and Second order.

Unit 2
Vector Analysis
Vector Algebra: Scalars and vectors, laws of vector algebra, scalar and vector product,
triple scalar product, interpretation in terms of area and volume, triple cross product,
product of four vectors. Scalar and vector fields.

Vector Differentiation: Ordinary derivative of a vector, the vector differential operator.
Directional derivatives and normal derivative. Gradient of a scalar field and its geometrical
interpretation. Divergence and curl of a vector field. Laplacian operators. Vector identities.

Vector Integration: Ordinary Integrals of Vectors. Double and Triple integrals, change of
order of integration, Jacobian. Notion of infinitesimal line, surface and volume elements.
Line, surface and volume integrals of Scalar and Vector fields. Flux of a vector field. Gauss’
divergence theorem, Green’s and Stokes Theorems and their verification (no rigorous
proofs).

Orthogonal Curvilinear Coordinates: Orthogonal Curvilinear Coordinates. Derivation of
Gradient, Divergence, Curl and Laplacian in Cartesian, Spherical and Cylindrical
Coordinate Systems.

Unit 3
Probability and statistics: Independent and dependent event, Conditional Probability.
Bayes’ Theorem, Independent random variables, Probability distribution functions, special
distributions: Binomial, Poisson and Normal. Sample mean and variance and their
confidence intervals for Normal distribution.

### Course Curriculum

 Function First Order Differential Equations Introduction to Differential Equations 00:25:00 Differential Equation of First order and First Degree 02:01:00 Second Order Differential Equations Differential Equation with Constant Coefficient 01:19:00 Differential Equation of Second Order 01:24:00 Vector Algebra Vector Differentiation Gradient 01:12:00 Tangent Plane and Normal 00:18:00 Problems on Gradient 00:07:00 Divergence and Curl 00:41:00 Vector Integration Line Integral 00:56:00 Greens Theorem 01:06:00 Surface Integral 01:19:00 Gauss Divergence Theorem 01:36:00 Stokes Theorem 00:56:00 Orthogonal Curvilinear Coordinates Probability and statistics

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