Mathematical Physics and Special Theory of Relativity

B.Sc. pt II course

Dates and timings: Monday and Tuesday, 08:00 AM – 09:00 AM

Starting date: Revision of pre-requisites from July 27, new course material from August 10, 2015

Course started in July 2015 and ended in January 2016. Now this page is archived.

  • No student was present: 27 and 28 July 2015
  • Revision Lecture 0.1, 0.2: Relation of physics and mathematics: 3 and 4 August 2015
  • Lecture 1: Introduction to co-ordinate system: 10 August 2015
  • References: Arfken-Weber vol 6, Page 1-4
  • Lecture 2: Orthogonal co-ordinate system: 11 August 2015
  • References: Hassani, second edition, Chapter 1
  • Lecture 3: Curvilinear co-ordinate system: 17 August 2015
  • Lecture 4: Orthogonal Curvilinear co-ordinate system, Scale factors: 18 August 2015
  • Lecture 5: Introduction to Cartesian, circular, cylindrical and spherical polar co-ordinate: 24 August 2015
  • Students Election: : 25 August 2015
  • Lecture 6: Gradient in curvilinear coordinates: 31 August 2015
  • Lecture 7: Divergence in curvilinear coordinates: 1 September 2015
  • Lecture 8: Curl in in curvilinear coordinates: 7 September 2015
  • Lecture 9: Gradient, divergence and curl in Cartesian, cylindrical and spherical coordinates: 8 September 2015
  • Lecture 10: Co-ordinate transformation from one type to another: 14 September 2015
  • Lecture 11: Jacobian: 15 September 2015
  • Special Lecture: Introduction to Fourier series: 19 September 2015
  • Lecture 12: Introduction to Tensors: 21 September 2015
  • Lecture 13: Covariant, Contravariant and Mixed Tensors: 22 September 2015
  • Lecture 14: Addition, Multiplication and Contraction of Tensors: 28 September 2015
  • Lecture 15: Metric tensor and its use in transformation of tensors: 29 September 2015
  • Lecture 16: Simple uses of tensors: 5 October 2015
  • Lecture 17: Dirac Delta Function and its properties: 6 October 2015
  • Lecture 18: Introduction to special relativity: 12 October 2015
  • Holiday : 13 October 2015
  • Lecture 19: Rotation in space-like and time like vectors: 19 October 2015
  • Lecture 20: World line, macro-causality: 20 October 2015
  • Lecture 21: Four vector formation, Energy momentum four vector, Relativistic equation of motion: 26 October 2015
  • Lecture 22: Invariance of rest mass, orthogonality of four force and four velocity: 27 October 2015
  • Holiday :2 November 2015
  • Holiday :3 November 2015
  • Holiday :9 November 2015
  • Holiday :10 November 2015
  • Lecture 23: Lorentz force as an example of four force, transformation of four frequency vector, Longitudinal and transverse Doppler's effect.: 16 November 2015
  • Lecture 24: Transformation between laboratory and center of mass system and it's applications.: 17 November 2015
  • One leave: 23 November 2015
  • Lecture 25: Problems of CM-frame and Lab-frame.: 24 November 2015
  • Lecture 26: Electromagnetic potential: 30 November 2015
  • Lecture 27: Transformation of electric and magnetic fields between two inertial frames.: 1 December 2015
  • Special Lecture: Introduction to differential equations: 3 December 2015
  • Lecture 28: The second order linear differential equation with variable coefficient and singular points, series solution method and its application to the Hermite's. Legendre's and Laguerre's differential equations: 7 December 2015
  • Lecture 29: Basic properties like orthogonality, recurrence relation, graphical represntation and generating function of Hermite, Lagendre, Leguerre and Associated Legendre: 8 December 2015
  • One leave: 14 December 2015
  • Lecture 30: Simple applications of Hermite, Lagendre, Leguerre functions: 15 December 2015
  • Lecture 31, 32: Solution of partial differential equations, Laplace equation in 3D with application: 21 December 2015
  • Lecture 33, 34: Helmholtz equation with it's applications, Diffusion equation in 2D with it's applications: 22 December 2015
  • Holiday :28 December 2015
  • Holiday :29 December 2015
  • Lecture 35: Laplace equation in spherical coordinate system with applications: 4 January 2016
  • Lecture 36: Laplace equation in cylindrical coordinate system with applications: 5 January 2016
  • Lecture 37: Revision class: 11 January 2016
  • Lecture 38: Revision class: 12 January 2016

Unit I

Orthogonal Curvilinear co-ordinate system. Scale factors, expression for gradient, divergence and curl and their applications to Cartesian, circular, cylindrical and spherical polar co-ordinate.

Co-ordinate transformation and Jacobian. Transformation of Covariant, Contravariant and Mixed Tensors. Addition, Multiplication and Contraction of Tensors. Metric tensor and its use in transformation of tensors.

Dirac Delta Function and its properties.

Unit II

Lorentz transformation and rotation in space-time like and space like vector, world line, macro-causality.

Four vector formulation, energy momentum four vector, relativistic equation of motion, invariance of rest mass, orthogonality of four force and four velocity. Lorentz force as an example of four force, transformation of four frequency vector, longitudinal and transverse Doppler's effect.

Transformation between laboratory and center of mass system, four momentum conservation, kinematics of decay products of unstable particles and reaction thresholds: Pair production, inelastic collision of two particles, Compton effect.

Unit III

(A) Transformation of electric and magnetic fields between two inertial frames.

(B) The second order linear differential equation with variable coefficient and singular points, series solution method and its application to the Hermite's. Legendre's and Laguerre's differential equations; Basic properties like orthogonality, recurrence relation, graphical represntation and generating function of Hermite, Lagendre, Leguerre and Associated Legendre function (simple applications).

Unit IV

Techniques of separation of variables and its application to following boundary value problems. (i) Laplace equation in three dimensional Cartesian coordinate system-line charge between two earthed parallel plates. (ii) Helmholtz equation in circular cylindrical coordinates-cylindrical resonant cavity, (iii) Wave wquation in spherical polar coordinates the vibrations of a circular membrane, (iv) Diffusion equation in two dimensional Cartesian coordinate system, heat conduction in thin rectangular plate, (v) Laplace equation in spherical coordinate system- electric potential around a spherical surface.


Reference books

  1. Mathematical Methods by Potter and Glodberg (Prentice Hall of India Pvt. Ltd.) (I followed.)
  2. Applied Mathematics for Engineers and Physicists by Pipes and Harvill (McGraw Hill Book Co.)
  3. Mathematical Methods for Physicists (6ed) by George B. Arfken and Hans J. Weber.
  4. Mathematical Methods for Students of Physics and Related Fields by Sadri Hassani