Confirming Einstein’s General Theory of Relativity with Calculus: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on general relativity and the precession of Mercury’s orbit.

Part 1: Introduction

• Part 1a: Introduction
• Part 1b: Observed precession of Mercury
• Part 1c: Outline of argument

Part 2: Precession, polar coordinates, and conic sections

• Part 2a: Graphically exploring precession
• Part 2b: Polar coordinates and ellipses
• Part 2c: Polar coordinates, circles, and parabolas
• Part 2d: Polar coordinates and hyperbolas

Part 3: Method of successive approximations

Part 4: Principles from physics

• Part 4a: Angular momentum
• Part 4b: Acceleration in polar coordinates
• Part 4c: Newton’s Second Law and Newton’s Law of Gravitation

Part 5: Orbits under Newtonian mechanics

• Part 5a: Confirmation of solution
• Part 5b: Derivation with calculus
• Part 5c: Derivation with differential equations and the method of undetermined coefficients
• Part 5d: Derivation with differential equations and variation of parameters

Part 6: Orbits under general relativity

• Part 6a: New differential equation under general relativity
• Part 6b: Confirmation of solution
• Part 6c: Derivation with variation of parameters
• Parts 6d, 6e, 6f, 6g, 6h, 6i, 6j: Rationale for the method of undetermined coefficients
• Part 6k: Derivation with undetermined coefficients

Part 7: Computing precession

• Parts 7a, 7b, 7c, 7d: Predicting precession
• Part 7e: Computing precession

Part 8: Second- and third-order solutions with the method of successive approximations

Part 9: Pedagogical thoughts

Earlier this year, I presented these ideas for the UNT Math Department’s Undergraduate Mathematics Colloquium Series. The video of my lecture is below.