Preface
Introduction to the course
Using these notes
A note on notation
1
Two-body problem
Problem setup
Three conserved quantities
Orbits, effective potential
Scattering
2
Lagrange’s Equations
Covariant formulation
Covariance: introduction
Euler-Lagrange Equations
Covariance of Euler-Lagrange Equations
Constraints
Extremization formulation
Representation perspective
Separability of quadratic Lagrangians
3
Noether’s theorem
4
Hamiltonian Mechanics
Legendre transform
Convex functions
Properties of the Legendre transform
Hamilton’s equations
Differential geometry perspective
Algebra of Poisson brackets
5
Spacetime geometry
Matrix representation of spacetime
The Lorentz group
Boosts and rotations
6
Perturbation Theory
Dyson’s formula
Example: Fourier transform
Bibliography
Physics 151 F24 Notes
Bibliography