### 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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