| Weeks | Topics |
| 1 |
Introduction, Concept of Topology, Manifold, Map, Atlas
|
| 2 |
Differential Manifold, Boundary, Diffeomorphism, Submanifold
|
| 3 |
Curve, Function, Tangent Vector, Coordinate Basis, Tangent Space, Vector
|
| 4 |
Cotangent Space, Covector, Tangent Bundle, Cotangent Bundle
|
| 5 |
Tensor, Some Operations on Tensors
|
| 6 |
Exterior Multiplication, Exterior Algebra, Differential Forms, Some Operations on Exterior Algerbra
|
| 7 |
Exact Form, Laplace-Beltrami Operator, Lie Derivative, Applications
|
| 8 |
Midterm
|
| 9 |
Integral, Stokes’s Theorem, Spacetime
|
| 10 |
Minkowski Metric Tensor, Light Cone, Minkowski Space, Current 1-form, Continuity Relation
|
| 11 |
Maxwell 2-form, Gauge Invariance, Lorenz Gauge Condition, Wave Equation, Energymomentum 3-forms
|
| 12 |
Net Electric Charge, Conservation of Electric Charge, Cartan Structure Equations
|
| 13 |
Riemann Spacetime, Some Curvature Calculations
|
| 14 |
Schwarzschild Solution to Einstein’s Equation
|