Mathematical Physics I by Rajesh Verma and P.K. Gangwar is a comprehensive textbook designed for B.Sc. 1st semester students pursuing major or minor in Physics under the FYUGP NEP syllabus of Gauhati University and other Indian universities. The book provides a strong mathematical foundation crucial for understanding core concepts in physics.

It covers essential topics such as vector algebra, vector calculus, partial differentiation, multiple integrals, and their physical applications. The content is structured to build problem-solving skills and deepen analytical understanding, making it ideal for undergraduate learners. Each chapter includes step-by-step explanations, solved problems, and practice exercises to enhance learning outcomes.

This textbook serves as a vital academic resource for students aiming to develop precision and confidence in applying mathematical techniques to physics problems.

? Course Content:

Unit 1: Calculus

• Recapitulation: Limits, continuity, average and instantaneous quantities, differentiation.

• Plotting functions, intuitive ideas of continuous, differentiable functions.

• Curve plotting, approximation: Taylor and Binomial Series (statements only).

• First & Second Order Differential Equations: Integrating factor, homogeneous equations with constant coefficients.
  (Total: 9 Lectures)

Unit 2: Calculus of Functions of More Than One Variable

• Partial derivatives, exact and inexact differentials

• Integrating factor with illustration

• Probability Concepts:

  • Independent random variables, probability distributions (Binomial, Gaussian, Poisson)

  • Mean, variance

  • Dependent events: Conditional probability

  • Bayes’ Theorem, Hypothesis testing
    (4 Lectures)

Unit 3: Vector Calculus – I

• Recapitulation of Vectors:

  • Scalar product and its invariance under rotation

  • Vector product, scalar triple product and their physical interpretations

  • Scalar and vector fields
    (4 Lectures)

Unit 4: Vector Integration

• Notion of infinitesimal line, surface, and volume elements

• Line, surface, and volume integrals of vector fields

• Flux of a vector field

• Theorems: Gauss' Divergence, Green’s, and Stokes’
  (10 Lectures)

Unit 5: Orthogonal Curvilinear Coordinates & Dirac Delta Function

• Curvilinear Coordinates: Cartesian, spherical, and cylindrical systems

• Gradient, Divergence, Curl & Laplacian in curvilinear coordinates

• Dirac Delta Function:

  • Definition, representation as a limit of a Gaussian and rectangular function

  • Properties
    (2 Lectures)