05:03

The Stirling Approximation: a 5-minute Derivation!

12:48

Jordan's Lemma Proof | Complex Variables

13:34

Introducing Bifurcations: The Saddle Node Bifurcation

08:46

Quantum Mechanics Example Problem: Heisenberg Uncertainty Principle

09:39

Einstein Notation: Proofs, Examples, and Kronecker Delta

08:56

Real Analysis Introduction: Sets and Set Operations

14:22

How to Solve a System of Linear Inequalities

09:00

Einstein Summation Convention: an Introduction

08:34

Stationary Action Problem 1: Sliding Block on Inclined Plane

10:47

Lagrange Equations: Multiple Particles and Constraints

07:53

Introduction to Tensors: Transformation Rules

12:30

The Faculty of Khan's 10,000 subscriber Q and A!

10:25

Introduction to Differential Geometry: Curves

11:15

Introduction to Tensors

10:52

Potentials and Impossibility of Oscillations | Nonlinear Dynamics

13:37

The Principle of Stationary Action

14:04

The Catenary Problem and Solution

11:08

Introducing Convolutions: Intuition + Convolution Theorem

12:59

Euler-Lagrange Equation: Constraints and Multiple Dependent Variables

12:40

The Heisenberg Uncertainty Principle: Proof/Explanation!

12:06

Position and Momentum from Wavefunctions | Quantum Mechanics

05:19

Introduction to Heat Transfer

12:03

Laplace Transforms for Partial Differential Equations (PDEs)

07:10

The Geodesic Problem on a Plane | Calculus of Variations

11:35

Introducing Green's Functions for Partial Differential Equations (PDEs)

11:45

Deriving Poiseuille's Law from the Navier-Stokes Equations

12:38

Introduction to Quantum Mechanics: Schrodinger Equation

13:02

The Generalized Uncertainty Principle | Proof/Derivation

10:48

Commutators and Eigenvalues/Eigenvectors of Operators

12:14

The Brachistochrone Problem and Solution | Calculus of Variations

04:21

Beltrami Identity Derivation | Calculus of Variations

09:40

Using Green's Functions to Solve Nonhomogeneous ODEs

13:41

Computing Improper Integrals using the Residue Theorem | Cauchy Principal Value

09:06

D'Alembert Solution to the Wave Equation

06:27

General Solution to the Wave Equation (via Change of Variables) | (2/2)

13:05

General Solution to the Wave Equation (via Transport Equation) | (1/2)

10:34

Introducing the Wave Equation: Derivation and Intuition

10:24

Linear Stability Analysis | Dynamical Systems 3

07:50

Derivation of the Euler-Lagrange Equation | Calculus of Variations

12:14

Computing Definite Integrals using the Residue Theorem

05:51

Bessel Function of the 2nd Kind | 2nd solution of Bessel's Equation

06:41

Introduction to Calculus of Variations

14:13

How to find the Residues of a Complex Function

07:43

Quantum Mechanics: Examples of Operators | Hermitian, Unitary etc.

10:12

Dynamical Systems: Definitions, Terminology, and Analysis

14:29

Bessel Functions of Half-Integer Order

10:51

Complex Integration: The ML Inequality Proof and Example

14:19

The Gamma Function, its Properties, and Application to Bessel Functions

07:13

Legendre's ODE III: Verifying/'Proving' Rodrigues' Formula

10:52

Legendre's ODE II: Deriving a formula for Legendre Polynomials

13:26

Problem 3: Thresholds, Inactivation, and Dendrite Length Constants

05:19

Old Channel Introduction

14:33

Bessel Functions and the Frobenius Method

12:25

Problem 2: Action Potentials, Channel Inactivation and Refractory Period

11:24

Problem 1: Membrane Input Resistance, Channel Currents, and Time Constants

03:35

Introduction to Operators in Quantum Mechanics

03:35

Dirac Notation: Properties and Neat Rules

03:26

Introduction to Dirac Notation

03:35

Introduction to Hilbert Spaces: Important Examples

05:17

An Introduction to Hilbert Spaces