# 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.

*Friday,*, (5 PM - 7 PM)**18 Oct 2019**- 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)

*Tuesday,*, (4:45 PM - 6:45 PM)**22 Oct 2019**- Functional differentiation examples
- Principle of least action
- Derivation of Euler Lagrange equation using functional calculus

*Tuesday,*, (3:15 PM - 4:45 PM)**29 Oct 2019**- Understanding Lagrangians
- Two stick problem (PDF)
- Derivation of the Hamiltonian and the corresponding equations of motion.

*Tuesday,*, (5 PM - 7 PM)**5 Nov 2019**

Start of Special theory of relativity- Invariance of Maxwell’s equation with respect to Galilean transformation
- Inertial frames of reference
- Introduction to Spacetime diagrams

*Tuesday,*, (5 PM - 7 PM)**12 Nov 2019**- Relativity of simultaneity
- Derivation of the Lorentz boost factor using Spacetime diagrams
- General Lorentz transformations (Lorentz transformation for motion in more than 1 dimension)

*Tuesday,*, (5 PM - 7 PM)**19 Nov 2019**- Length contraction and time dilation
- Invariants in Special relativity
- Geometry of Euclidean space v/s Minkowski space

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

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

*Thursday,*, (5 PM - 7 PM) Part 1, Part 2**6 Dec 2019**- Vectors vs Co-vectors (Dual vectors)
- Metric tensors in general $g_{\mu\nu}$ and Minkowski metric $\eta_{\mu\nu}$
- Help for HW7

*Monday,*, (5 PM - 7 PM) Part 1, Part 2**10 Dec 2019**

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*Friday,*, (5 PM - 7 PM) Part 1, Part 2**31 Jan 2020**- 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 $

*Tuesday,*, (5 PM - 7 PM) Video**04 Feb 2020**- Finding a relation between $ \vec{E} $ and $\vec{B}$ using Maxwell’s equations and Wave equations.
- Different polarizations of the electromagnetic wave