Sal Khan - Khan Academy


Insertion Sort Algorithm

Insertion Sort Algorithm

Topic: Algorithms and Data Structures
Teacher: Sal Khan
Concepts In This Lecture:
Insertion Sort in Python

Insertion Sort in Python

Topic: Algorithms and Data Structures
Teacher: Sal Khan
Concepts In This Lecture:
Introduction to Programs Data Types and Variables

Introduction to Programs Data Types and Variables

Topic: Intro to Computer Science and Programming Languages
Teacher: Sal Khan
Concepts In This Lecture:
For Loops in Python

For Loops in Python

Topic: Intro to Computer Science and Programming Languages
Teacher: Sal Khan
Concepts In This Lecture:
While Loops in Python

While Loops in Python

Topic: Intro to Computer Science and Programming Languages
Teacher: Sal Khan
Concepts In This Lecture:
Comparing Iterative and Recursive Factorial Functions

Comparing Iterative and Recursive Factorial Functions

Topic: Intro to Computer Science and Programming Languages
Teacher: Sal Khan
Concepts In This Lecture:
Introduction to Limits (HD)

Introduction to Limits (HD)

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Squeeze Theorem

Squeeze Theorem

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Calculus: Derivatives 1 (new HD version)

Calculus: Derivatives 1 (new HD version)

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Calculus: Derivatives 2 (new HD version)

Calculus: Derivatives 2 (new HD version)

Topic: Calculus
Teacher: Sal Khan
Calculus: Derivatives 3

Calculus: Derivatives 3

Topic: Calculus
Teacher: Sal Khan
The Chain Rule

The Chain Rule

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Product Rule

Product Rule

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Quotient Rule

Quotient Rule

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Implicit Differentiation

Implicit Differentiation

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Implicit Differentiation (part 2)

Implicit Differentiation (part 2)

Topic: Calculus
Teacher: Sal Khan
More implicit differentiation

More implicit differentiation

Topic: Calculus
Teacher: Sal Khan
Introduction to L'Hopital's Rule

Introduction to L'Hopital's Rule

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Inflection Points and Concavity Intuition

Inflection Points and Concavity Intuition

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Maxima Minima Slope Intuition

Maxima Minima Slope Intuition

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Monotonicity Theorem

Monotonicity Theorem

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Calculus: Graphing Using Derivatives

Calculus: Graphing Using Derivatives

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Graphing with Calculus

Graphing with Calculus

Topic: Calculus
Teacher: Sal Khan
Optimization with Calculus 1

Optimization with Calculus 1

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Optimization with Calculus 2

Optimization with Calculus 2

Topic: Calculus
Teacher: Sal Khan
Optimization with Calculus 3

Optimization with Calculus 3

Topic: Calculus
Teacher: Sal Khan
Optimization  Example 4

Optimization Example 4

Topic: Calculus
Teacher: Sal Khan
Equation of a tangent line

Equation of a tangent line

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Ladder rate-of-change problem

Ladder rate-of-change problem

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Mean Value Theorem

Mean Value Theorem

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
The Indefinite Integral or Anti-derivative

The Indefinite Integral or Anti-derivative

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Integration by Parts (part 6 of Indefinite Integration)

Integration by Parts (part 6 of Indefinite Integration)

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Indefinite Integration (part 7)

Indefinite Integration (part 7)

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Another u-subsitution example

Another u-subsitution example

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Introduction to definite integrals

Introduction to definite integrals

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Definite integrals (part II)

Definite integrals (part II)

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Definite Integrals (area under a curve) (part III)

Definite Integrals (area under a curve) (part III)

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Definite integral with substitution

Definite integral with substitution

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Integrals: Trig Substitution 1

Integrals: Trig Substitution 1

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Periodic Definite Integral

Periodic Definite Integral

Topic: Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Introduction to matrices

Introduction to matrices

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Matrix multiplication (part 1)

Matrix multiplication (part 1)

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Inverse Matrix (part 1)

Inverse Matrix (part 1)

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Inverting Matrices (part 3)

Inverting Matrices (part 3)

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Matrices to solve a system of equations

Matrices to solve a system of equations

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Matrices to solve a vector combination problem

Matrices to solve a vector combination problem

Topic: Linear Algebra
Teacher: Sal Khan
Singular Matrices

Singular Matrices

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
3-variable linear equations (part 1)

3-variable linear equations (part 1)

Topic: Linear Algebra
Teacher: Sal Khan
Solving 3 Equations with 3 Unknowns

Solving 3 Equations with 3 Unknowns

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Introduction to Vectors

Linear Algebra: Introduction to Vectors

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Vector Examples

Linear Algebra: Vector Examples

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Parametric Representations of Lines

Linear Algebra: Parametric Representations of Lines

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Combinations and Span

Linear Combinations and Span

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Introduction to Linear Independence

Linear Algebra: Introduction to Linear Independence

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
More on linear independence

More on linear independence

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Span and Linear Independence Example

Span and Linear Independence Example

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Subspaces

Linear Subspaces

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Basis of a Subspace

Linear Algebra: Basis of a Subspace

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Vector Dot Product and Vector Length

Vector Dot Product and Vector Length

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Proving Vector Dot Product Properties

Proving Vector Dot Product Properties

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Proof of the Cauchy-Schwarz Inequality

Proof of the Cauchy-Schwarz Inequality

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Vector Triangle Inequality

Linear Algebra: Vector Triangle Inequality

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Defining the angle between vectors

Defining the angle between vectors

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Dot and Cross Product Comparison/Intuition

Dot and Cross Product Comparison/Intuition

Topic: Multivariable Calculus
Teacher: Sal Khan
Matrices: Reduced Row Echelon Form 3

Matrices: Reduced Row Echelon Form 3

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Introduction to the Null Space of a Matrix

Introduction to the Null Space of a Matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Proof: Any subspace basis has same number of elements

Proof: Any subspace basis has same number of elements

Topic: Linear Algebra
Teacher: Sal Khan
Dimension of the Null Space or Nullity

Dimension of the Null Space or Nullity

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
A more formal understanding of functions

A more formal understanding of functions

Topic: Linear Algebra
Teacher: Sal Khan
im(T):  Image of a Transformation

im(T): Image of a Transformation

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Preimage of a set

Preimage of a set

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Preimage and Kernel Example

Preimage and Kernel Example

Topic: Linear Algebra
Teacher: Sal Khan
Linear Transformation Examples: Rotations in R2

Linear Transformation Examples: Rotations in R2

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Unit Vectors

Unit Vectors

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Introduction to Projections

Introduction to Projections

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Introduction to Orthonormal Bases

Linear Algebra: Introduction to Orthonormal Bases

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Lin Alg: Projections onto subspaces with orthonormal bases

Lin Alg: Projections onto subspaces with orthonormal bases

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Defining a plane in R3 with a point and normal vector

Defining a plane in R3 with a point and normal vector

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Cross Product Introduction

Linear Algebra: Cross Product Introduction

Topic: Multivariable Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Proof: Relationship between cross product and sin of angle

Proof: Relationship between cross product and sin of angle

Topic: Multivariable Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Matrices: Reduced Row Echelon Form 1

Matrices: Reduced Row Echelon Form 1

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Matrices: Reduced Row Echelon Form 2

Matrices: Reduced Row Echelon Form 2

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Matrix Vector Products

Matrix Vector Products

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Null Space 2: Calculating the null space of a matrix

Null Space 2: Calculating the null space of a matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Null Space 3: Relation to Linear Independence

Null Space 3: Relation to Linear Independence

Topic: Linear Algebra
Teacher: Sal Khan
Column Space of a Matrix

Column Space of a Matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Null Space and Column Space Basis

Null Space and Column Space Basis

Topic: Linear Algebra
Teacher: Sal Khan
Visualizing a Column Space as a Plane in R3

Visualizing a Column Space as a Plane in R3

Topic: Linear Algebra
Teacher: Sal Khan
Dimension of the Column Space or Rank

Dimension of the Column Space or Rank

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Showing relation between basis cols and pivot cols

Showing relation between basis cols and pivot cols

Topic: Linear Algebra
Teacher: Sal Khan
Showing that the candidate basis does span C(A)

Showing that the candidate basis does span C(A)

Topic: Linear Algebra
Teacher: Sal Khan
Vector Transformations

Vector Transformations

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Transformations

Linear Transformations

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Matrix Vector Products as Linear Transformations

Matrix Vector Products as Linear Transformations

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Transformations as Matrix Vector Products

Linear Transformations as Matrix Vector Products

Topic: Linear Algebra
Teacher: Sal Khan
Image of a subset under a transformation

Image of a subset under a transformation

Topic: Linear Algebra
Teacher: Sal Khan
Sums and Scalar Multiples of Linear Transformations

Sums and Scalar Multiples of Linear Transformations

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
More on Matrix Addition and Scalar Multiplication

More on Matrix Addition and Scalar Multiplication

Topic: Linear Algebra
Teacher: Sal Khan
Linear Transformation Examples: Scaling and Reflections

Linear Transformation Examples: Scaling and Reflections

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Expressing a Projection on to a line as a Matrix Vector prod

Expressing a Projection on to a line as a Matrix Vector prod

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Compositions of Linear Transformations 1

Compositions of Linear Transformations 1

Topic: Linear Algebra
Teacher: Sal Khan
Surjective (onto) and Injective (one-to-one) functions

Surjective (onto) and Injective (one-to-one) functions

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Example of Finding Matrix Inverse

Linear Algebra: Example of Finding Matrix Inverse

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Rule of Sarrus of Determinants

Linear Algebra: Rule of Sarrus of Determinants

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Determinant as Scaling Factor

Linear Algebra: Determinant as Scaling Factor

Topic: Linear Algebra
Teacher: Sal Khan
Linear Algebra: Transpose of a Matrix

Linear Algebra: Transpose of a Matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra:  Determinant of Transpose

Linear Algebra: Determinant of Transpose

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Rowspace and Left Nullspace

Linear Algebra: Rowspace and Left Nullspace

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Orthogonal Complements

Linear Algebra: Orthogonal Complements

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Lin Alg:  Orthogonal Complement of the Orthogonal Complement

Lin Alg: Orthogonal Complement of the Orthogonal Complement

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Lin Alg: Orthogonal Complement of the Nullspace

Lin Alg: Orthogonal Complement of the Nullspace

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Lin Alg: Showing that A-transpose x A is invertible

Lin Alg: Showing that A-transpose x A is invertible

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Least Squares Approximation

Linear Algebra: Least Squares Approximation

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Least Squares Examples

Linear Algebra: Least Squares Examples

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Change of Basis Matrix

Linear Algebra: Change of Basis Matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Lin Alg: Invertible Change of Basis Matrix

Lin Alg: Invertible Change of Basis Matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix

Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: The Gram-Schmidt Process

Linear Algebra: The Gram-Schmidt Process

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Introduction to Eigenvalues and Eigenvectors

Linear Algebra: Introduction to Eigenvalues and Eigenvectors

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra:  Finding Eigenvectors and Eigenspaces example

Linear Algebra: Finding Eigenvectors and Eigenspaces example

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Vector Triple Product Expansion (very optional)

Vector Triple Product Expansion (very optional)

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix

Linear Algebra: Example solving for the eigenvalues of a 2x2 matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Linear Algebra:  Eigenvectors and Eigenspaces for a 3x3 matrix

Linear Algebra: Eigenvectors and Eigenspaces for a 3x3 matrix

Topic: Linear Algebra
Teacher: Sal Khan
Concepts In This Lecture:
Normal vector from plane equation

Normal vector from plane equation

Topic: Multivariable Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Point distance to plane

Point distance to plane

Topic: Multivariable Calculus
Teacher: Sal Khan
Concepts In This Lecture:
Distance Between Planes

Distance Between Planes

Topic: Multivariable Calculus
Teacher: Sal Khan
Concepts In This Lecture:

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