07:17

Factorization of the Quantum Harmonic Oscillator

17:33

Real = difficult, Complex = easy

10:20

Integral of exponential times sine or cosine

06:42

Fourier Transform of a Gaussian

12:02

Dirichlet integral by Laplace transform

13:00

Airy function - basic properties

10:20

Poisson kernel using complex numbers

11:36

Ricci scalar for conformally flat metrics - example

11:50

Square wave - Fourier series by elementary methods

07:36

Cosmological equation for constant density universe

12:28

Properties of Wirtinger derivatives

11:41

Schwarzian derivative of a Mobius transformation is zero

16:04

Holomorphic functions are harmonic

16:19

Solutions to Laplace's equation - average of nearby points

10:40

Square root of a complex number in cartesian form

13:05

A definite trig integral using complex numbers

15:34

Arctangent at infinity using complex numbers

18:04

Product of a sum of 2 squares using complex numbers

11:48

Alternating binomial sum of reciprocals

11:50

Trig identities using complex numbers

10:57

Energy is conserved for the Harmonic Oscillator

18:14

Generalized Fresnel Integrals

11:46

Sign change of the Schwarzschild metric at the horizon

13:06

Painleve-Gullstrand metric

13:40

Complex valued arcsin function

17:44

Arctangent of a complex number

14:14

An interesting integration formula by parity

13:24

Ricci Tensor for Birkoff's theorem

12:06

Christoffel Symbols for Birkhoff's Theorem

06:19

Integral of an odd function over a symmetric domain vanishes

13:04

General telescoping series

13:28

A deceptively simple Electrodynamics integral

19:41

Ricci Tensor for the Kasner metric

16:56

Christoffel symbols for the Kasner metric

16:06

The Wallis product formula for pi in two easy ways!

08:05

Indefinite Integral of the Gaussian?!?!

15:03

Trigonometric integral representation of the Beta function.

11:11

Generalized alternating harmonic series integral

13:40

Unusual Telescoping series - trig and hyperbolic functions

08:20

Harmonic Series diverges - Euler's integral

10:53

Derivative of the sine function by Laplace Transform

08:54

Infinite Sum of Zeta functions!

21:00

Leibniz rule for derivatives - proof, binomial theorem connection

29:49

General Leibniz formula for derivatives - examples

19:16

Zeta regularized product of the positive integers

21:37

Derivative of the Zeta function evaluated at zero

21:22

100th subscriber special! - sum of cubes

28:43

Infinite order differential equations

12:56

String action in light cone coordinates

10:44

Unusual fourth order trig identity (QED)

16:48

Frullani Integral Formula

03:19

Arctan(x)+arctan(1/x)=pi/2

19:44

Derivative of Sin(x) is Cos(x) in four ways!

06:34

The limit does not exist! (Mean Girls)

22:40

Matrix magic trick!

12:27

Infinitude of the Primes Part III: Irrationality of Pi

15:11

Infinitude of the Primes Part II: Euler Zeta function and the Harmonic series

11:28

Infinitude of the Primes Part I: Euclid's proof

23:18

Fresnel-Gaussian Integral???

23:04

Surface area of the d-Sphere