Semester III tutorial for winter semester 2019/20

Literature

• Classical mechanics - Goldstein, Safko, Poole
• Analytical mechanics - Nolting
• Introduction to Electrodynamics - David Griffiths
• (Supplementary) Theoretical minimum : Special relativity and classical field theory - Leonard Susskind

Lectures

Some of the lectures have a link to videos. They were recorded by students for their own benefit with my consent.

1. Friday, 18 Oct 2019, (5 PM - 7 PM)

   • Functionals and Functional differentiation
   • Concept of a time average of a continuous function
   • A quick synopsis of the concept of a measure (For math III)
     
     

2. Tuesday, 22 Oct 2019, (4:45 PM - 6:45 PM)

   • Functional differentiation examples
   • Principle of least action
   • Derivation of Euler Lagrange equation using functional calculus
     
     

3. Tuesday, 29 Oct 2019, (3:15 PM - 4:45 PM)

   • Understanding Lagrangians
   • Two stick problem (PDF)
   • Derivation of the Hamiltonian and the corresponding equations of motion.
     
     

4. Tuesday, 5 Nov 2019, (5 PM - 7 PM)
   Start of Special theory of relativity

   • Invariance of Maxwell’s equation with respect to Galilean transformation
   • Inertial frames of reference
   • Introduction to Spacetime diagrams
     
     

5. Tuesday, 12 Nov 2019, (5 PM - 7 PM)

   • Relativity of simultaneity
   • Derivation of the Lorentz boost factor using Spacetime diagrams
   • General Lorentz transformations (Lorentz transformation for motion in more than 1 dimension)
     
     

6. Tuesday, 19 Nov 2019, (5 PM - 7 PM)

   • Length contraction and time dilation
   • Invariants in Special relativity
   • Geometry of Euclidean space v/s Minkowski space
     
     

7. Friday, 29 Nov 2019, (5 PM - 7 PM) Part 1, Part 2

   • Derivation of the Minkowski metric using a moving light(photon) clock
   • Light cone and causal structure in special relativity
   • Introduction to 4-vectors
   • Physical interpretation of proper time and spacetime interval (Invariants in SR)
   • Relativistic addition of velocities
   
   

8. Tuesday, 3 Dec 2019, (5 PM - 7 PM) Part 1, Part 2, Part 3

   • Repeating 4-vectors
   • 4-velocity vectors, deriving the $\gamma$ factor
   • Deriving the relativistic action $ S = -m \int_a^b \sqrt{1-\vec{v}^2} \mathrm{d}t $
   • 4-momentum tensor, derivation or relativistic energy
   
   

9. Thursday, 6 Dec 2019, (5 PM - 7 PM) Part 1, Part 2

   • Vectors vs Co-vectors (Dual vectors)
   • Metric tensors in general $g_{\mu\nu}$ and Minkowski metric $\eta_{\mu\nu}$
   • Help for HW7
   
   

10. Monday, 10 Dec 2019, (5 PM - 7 PM) Part 1, Part 2
    Start of some Classical field theory

    • Action principle for fields
    • Field theory : Lagrangian fields, Euler-Lagrange equation for fields
    • Wave equation in a classical field setting - Relativistic / 4-vector fields
    
    Data missing from 2-3 lectures in between
    
    

11. Friday, 31 Jan 2020, (5 PM - 7 PM) Part 1, Part 2

    • Defining 4-current : $ J^{\mu} = (\rho,J^{i}) $
    • Maxwell’s equations in tensor notation : $ \partial_\mu F^{\mu\nu} = \mu_0 J^\mu \quad $, $\partial_\lambda F_{\mu\nu}+\partial_\mu F_{\nu \lambda} + \partial_\nu F_{\lambda \mu} = 0 $
    
    

12. Tuesday, 04 Feb 2020, (5 PM - 7 PM) Video

    • Finding a relation between $ \vec{E} $ and $\vec{B}$ using Maxwell’s equations and Wave equations.
    • Different polarizations of the electromagnetic wave