Канал: Nicholas Kozenieski

Some concrete examples of derivatives and integrals as linear transformations

Some concrete examples of derivatives and integrals as linear transformations

Proof that every triangle is equilateral

Proof that every triangle is equilateral

100pi Subscriber Special (ft. Robert St. Pierre)

100pi Subscriber Special (ft. Robert St. Pierre)

Deriving the Gaussian curve equation

Deriving the Gaussian curve equation

Complex differentiabilty and the Cauchy-Riemann equations

Complex differentiabilty and the Cauchy-Riemann equations

Cauchy integral theorem intuition and proof

Cauchy integral theorem intuition and proof

Greens Theorem intuition

Greens Theorem intuition

300 subscriber special- Water bottle review (ft. Matthew Boutot)

300 subscriber special- Water bottle review (ft. Matthew Boutot)

A triggy integral

A triggy integral

Stokes’ theorem over manifolds and what the derivative really is

Stokes’ theorem over manifolds and what the derivative really is

Tetrahedrons area vectors sum to the zero vector

Tetrahedrons area vectors sum to the zero vector

Infinities and circles

Infinities and circles

Multivariable implicit differentiation theorems

Multivariable implicit differentiation theorems

The true n-dimensional second derivative test

The true n-dimensional second derivative test

Multivariable Taylor series and quadratic forms for the 2nd derivative test

Multivariable Taylor series and quadratic forms for the 2nd derivative test

What actually is the derivative?

What actually is the derivative?

The quickest proof ever of the Jacobian Matrix, not clickbait :)

The quickest proof ever of the Jacobian Matrix, not clickbait :)

But what actually is a matrix?

But what actually is a matrix?

Using rotational symmetry for 3D graphs

Using rotational symmetry for 3D graphs

An e-pic integral

An e-pic integral

Vector dot and cross product proofs

Vector dot and cross product proofs

The Poisson distribution

The Poisson distribution

The gamma function - i! Do you factorial?

The gamma function - i! Do you factorial?

Euclidean algorithm via matrices: Bezóuts identity proof, general/particular solutions to ax+by=c

Euclidean algorithm via matrices: Bezóuts identity proof, general/particular solutions to ax+by=c

Proving that the Fibonacci sequence is a strongly divisible sequence

Proving that the Fibonacci sequence is a strongly divisible sequence

The Euclidean Algorithm for finding the greatest common divisor of two numbers: Proof+example

The Euclidean Algorithm for finding the greatest common divisor of two numbers: Proof+example

Infinitely many primes via the Fibonacci Numbers

Infinitely many primes via the Fibonacci Numbers

Infinitely many primes, but no prime generating function exists, but chains of composites exists

Infinitely many primes, but no prime generating function exists, but chains of composites exists

Two minute proof on reducing the modulos mod phi(n)

Two minute proof on reducing the modulos mod phi(n)

Viva Voce: Giving living breath to generalizing the Shoelace Theorem

Viva Voce: Giving living breath to generalizing the Shoelace Theorem

Generating all possible primitive Pythagorean triples

Generating all possible primitive Pythagorean triples

Japanese multiplication and why it works

Japanese multiplication and why it works

Using complex numbers to get to the meaning of the real valued radius of convergence

Using complex numbers to get to the meaning of the real valued radius of convergence

Sum of (squares) of sines and cosines where the angles form an arithmetic progression

Sum of (squares) of sines and cosines where the angles form an arithmetic progression

Euler’s Totient theorem: Statement, examples, proof, and consequences

Euler’s Totient theorem: Statement, examples, proof, and consequences

Freshman’s dream product and quotient rules

Freshman’s dream product and quotient rules

Some binary puzzle fun

Some binary puzzle fun

The method of stars and bars

The method of stars and bars

Properties of the Klein bottle

Properties of the Klein bottle

History music video

History music video

History music video trailer

History music video trailer

Overkill: finding the area of a unit circle with multivariable calculus

Overkill: finding the area of a unit circle with multivariable calculus

The magnitude of the determinant of a matrix is the volume of the parallelpiped in n-space - Proof!

The magnitude of the determinant of a matrix is the volume of the parallelpiped in n-space - Proof!

Quick and dirty proofs of the law of sines and cosines (plus a fun end problem!)

Quick and dirty proofs of the law of sines and cosines (plus a fun end problem!)

Where does the Jacobian Matrix come from? 2 different answers/perspectives

Where does the Jacobian Matrix come from? 2 different answers/perspectives

Deriving the complex valued Fourier Series for e^x + an open problem I’ve found

Deriving the complex valued Fourier Series for e^x + an open problem I’ve found

Deriving the real valued Fourier Series for e^x + a bonus summation

Deriving the real valued Fourier Series for e^x + a bonus summation

Deriving the complex valued Fourier Series!

Deriving the complex valued Fourier Series!

Deriving the real valued Fourier Series!

Deriving the real valued Fourier Series!

2020 AP Calc. BC Mock Exam Q2 (15 min.)

2020 AP Calc. BC Mock Exam Q2 (15 min.)

2020 AP Calc. BC Mock Exam Q1 (25 min.)

2020 AP Calc. BC Mock Exam Q1 (25 min.)

Calc. I #8 - Proving quadratic limits using limit definitions!

Calc. I #8 - Proving quadratic limits using limit definitions!

Calc. 1 #7 - Proving linear limits using epsilon delta definitions!

Calc. 1 #7 - Proving linear limits using epsilon delta definitions!

Math for fun: Proving pi is irrational!

Math for fun: Proving pi is irrational!

Calc. 3 #21- Multivariable extreme value theorem (EVT) and examples

Calc. 3 #21- Multivariable extreme value theorem (EVT) and examples

Calc.3 #20 - Rigorous proof of second partial derivatives test!

Calc.3 #20 - Rigorous proof of second partial derivatives test!

Calc. 3 #19 - Finding local max/min of surfaces using 2nd Derivative Test

Calc. 3 #19 - Finding local max/min of surfaces using 2nd Derivative Test

Calc. 3 #18 - Tangent to planes to level curves of functions in 3D (4D functions!)

Calc. 3 #18 - Tangent to planes to level curves of functions in 3D (4D functions!)

Calc. 3 #17 - Measuring change in any direction to a surface? Directional Derivatives!

Calc. 3 #17 - Measuring change in any direction to a surface? Directional Derivatives!

Calc. 3 #16 - Deriving and using the Multivariable Chain Rule

Calc. 3 #16 - Deriving and using the Multivariable Chain Rule

Calc. 3 #15 - Deriving the equation of a tangent plane and normal line to a function

Calc. 3 #15 - Deriving the equation of a tangent plane and normal line to a function

Calc. 3 #14 - Clairaut’s Theorem: Meaning, examples, and proof

Calc. 3 #14 - Clairaut’s Theorem: Meaning, examples, and proof

Calc. 3 #13 - Motivation, definition, and meaning of the partial derivative

Calc. 3 #13 - Motivation, definition, and meaning of the partial derivative

Calc. 3 #3 - Derivatives of dot product, cross product, constant magnitude vector functions

Calc. 3 #3 - Derivatives of dot product, cross product, constant magnitude vector functions

Calc. 3 #5 - Curvature Part 1: Intuition, deriving the formula, and an example

Calc. 3 #5 - Curvature Part 1: Intuition, deriving the formula, and an example

Calc. 3 #6 - Curvature Part 2: Deriving the alternate formula for vector function curvature

Calc. 3 #6 - Curvature Part 2: Deriving the alternate formula for vector function curvature

Calc. 3 #4 - Derivatives of vector functions and equations of tangent lines

Calc. 3 #4 - Derivatives of vector functions and equations of tangent lines

Calc. 3 #9 - Unit Tangent, Normal, and Binormal vectors associated with a vector function

Calc. 3 #9 - Unit Tangent, Normal, and Binormal vectors associated with a vector function

Calc. 3 #10 - Deriving the Normal and Osculating Planes that define a vector function

Calc. 3 #10 - Deriving the Normal and Osculating Planes that define a vector function

Calc. 3 #11 - Multivariable Domains

Calc. 3 #11 - Multivariable Domains

Calc. 3 #12 - Multivariable Limits (and a shortcut with Polar Coordinates!)

Calc. 3 #12 - Multivariable Limits (and a shortcut with Polar Coordinates!)

Calc. 3 #7 - General vector function arc length

Calc. 3 #7 - General vector function arc length

Calc. 3 #2 - Cross Product Motivation and Proof

Calc. 3 #2 - Cross Product Motivation and Proof

Calc. 3 #1 - Dot Product Motivation and Proof

Calc. 3 #1 - Dot Product Motivation and Proof

Calculus 1 #6 - Proofs of the product, chain, power, and quotient rules

Calculus 1 #6 - Proofs of the product, chain, power, and quotient rules

Calculus 1 #5 - Limit definition of derivative

Calculus 1 #5 - Limit definition of derivative

Calc. 3 #8 - Deriving the equation of a plane in 3D

Calc. 3 #8 - Deriving the equation of a plane in 3D

Calculus 1 #4 - The squeeze (sandwich) theorem!

Calculus 1 #4 - The squeeze (sandwich) theorem!

Calculus 1 #3 - Limits at infinity

Calculus 1 #3 - Limits at infinity

Calculus 1 #2 - Some limit algebra

Calculus 1 #2 - Some limit algebra

Calculus 1 #1 - Limit theory

Calculus 1 #1 - Limit theory

Clairaut Differential Equations

Clairaut Differential Equations

Diff. Eq #18 - What is the Laplace Transform? Motivation and definition

Diff. Eq #18 - What is the Laplace Transform? Motivation and definition

Diff. Eq #19 - Existence of the Laplace Transform and deriving “the big 4”

Diff. Eq #19 - Existence of the Laplace Transform and deriving “the big 4”

Diff Eq. #13 - Method of Undetermined Coefficients for order n=2

Diff Eq. #13 - Method of Undetermined Coefficients for order n=2

Deriving and using some basic properties of the Laplace Transform

Deriving and using some basic properties of the Laplace Transform

Diff. Eq #20 - Essential properties of Laplace transforms to derive other Laplace Transforms

Diff. Eq #20 - Essential properties of Laplace transforms to derive other Laplace Transforms

Diff. Eq #14 - Variation of Parameters for second order differential equations

Diff. Eq #14 - Variation of Parameters for second order differential equations

Diff. Eq #11 - Cauchy-Euler equation of order n=2

Diff. Eq #11 - Cauchy-Euler equation of order n=2

Diff. Eq #12 - Why multiply by ln(x) for repeated roots on a Cauchy-Euler equation?

Diff. Eq #12 - Why multiply by ln(x) for repeated roots on a Cauchy-Euler equation?

Diff. Eq #15 - The Wronskian Matrix and Linear Independence of fundamental solution sets

Diff. Eq #15 - The Wronskian Matrix and Linear Independence of fundamental solution sets

Diff. Eq #16 - The Annihilator Method (dun dun dun) and the D notation

Diff. Eq #16 - The Annihilator Method (dun dun dun) and the D notation

Diff. Eq #17 - Variation of parameters of order n

Diff. Eq #17 - Variation of parameters of order n

Diff. Eq #8 - First/Second order, linear, homogeneous diff. Eqs. with distinct real roots

Diff. Eq #8 - First/Second order, linear, homogeneous diff. Eqs. with distinct real roots

Diff. Eq #9 - Solving second order, linear, homogeneous diff eqs with repeated real roots

Diff. Eq #9 - Solving second order, linear, homogeneous diff eqs with repeated real roots

Diff. Eq #10 - Second order, linear, homogeneous diff eqs with complex auxiliary roots

Diff. Eq #10 - Second order, linear, homogeneous diff eqs with complex auxiliary roots

Diff. Eq #4 - Using “obvious” substitutions to transform diff. Eqs.

Diff. Eq #4 - Using “obvious” substitutions to transform diff. Eqs.

Diff. Eq #6 - Solving Exact Differential Equations

Diff. Eq #6 - Solving Exact Differential Equations

Diff. Eq #7 - Special integrating factors mu(x) and mu(y) for “almost” exact diff. Eqs.

Diff. Eq #7 - Special integrating factors mu(x) and mu(y) for “almost” exact diff. Eqs.

Diff. Eq #5 - Solving differential equations of the form (ax+by+c)dx + (dx+ey+f)dy = 0

Diff. Eq #5 - Solving differential equations of the form (ax+by+c)dx + (dx+ey+f)dy = 0

Geometric proof of AM-GM inequality for 2 numbers

Geometric proof of AM-GM inequality for 2 numbers

Geometric meaning of the geometric mean

Geometric meaning of the geometric mean

Geometric proof of tangent half angle identity

Geometric proof of tangent half angle identity

Proof of Pythagorean Theorem using Geometric Means

Proof of Pythagorean Theorem using Geometric Means

Diff. Eq #1 - Homogeneous equations: derivation of substitutions and examples

Diff. Eq #1 - Homogeneous equations: derivation of substitutions and examples

Diff. Eq #3 - Bernoulli differential equations as an extension to linear differential equations

Diff. Eq #3 - Bernoulli differential equations as an extension to linear differential equations

Diff. Eq. #2 - Linear differential equations and Deriving mu(x) (InteGREATing factor!)

Diff. Eq. #2 - Linear differential equations and Deriving mu(x) (InteGREATing factor!)

Many math mistakes and more

Many math mistakes and more

The Fibonacci sequence and its relation to the golden ratio

The Fibonacci sequence and its relation to the golden ratio

Using multi variable chain rule to simplify single variable derivatives

Using multi variable chain rule to simplify single variable derivatives

Euler’s formula WITHOUT any Taylor Series!

Euler’s formula WITHOUT any Taylor Series!

Recursive and explicit formulas for volumes of n dimensional hyper spheres

Recursive and explicit formulas for volumes of n dimensional hyper spheres

Negative Sophomore’s Dream animated evaluation

Negative Sophomore’s Dream animated evaluation

Infinite nested radical representation of the imaginary unit

Infinite nested radical representation of the imaginary unit

An explanation of the Jacobian Matrix in terms of a correctional factor for integrals

An explanation of the Jacobian Matrix in terms of a correctional factor for integrals

A way to remember the product to sum/angle addition/subtraction/double/half angle identities

A way to remember the product to sum/angle addition/subtraction/double/half angle identities

Linear Algebra 1 - Matrices, Vectors, Systems of Linear Equations, and Basic Properties

Linear Algebra 1 - Matrices, Vectors, Systems of Linear Equations, and Basic Properties

Integration Strategies - Part 2

Integration Strategies - Part 2

Integration Strategies - Part 1

Integration Strategies - Part 1

AP Calc BC Review Chapter 5 Part 4 (final)

AP Calc BC Review Chapter 5 Part 4 (final)

AP Calc BC Review Chapter 5 Part 2

AP Calc BC Review Chapter 5 Part 2

AP Calc BC Review Chapter 5 Part 3

AP Calc BC Review Chapter 5 Part 3

AP Calc BC Review Chapter 5 Part 1

AP Calc BC Review Chapter 5 Part 1

Part 2 of 2 AP Calc BC Review

Part 2 of 2 AP Calc BC Review

Part 1 of 2 AP Calc BC Review

Part 1 of 2 AP Calc BC Review

AP Calc BC Exam Review

AP Calc BC Exam Review

AP Calc BC Review

AP Calc BC Review

AP Calc BC Review

AP Calc BC Review

Ap Calc BC Review

Ap Calc BC Review

Some tricky u substitution integrals for fun

Some tricky u substitution integrals for fun

$Calculus optimization to prove Snell's law of refraction$

Calculus optimization to prove Snell's law of refraction

Vieta's Formulas and Polynomial Roots

Vieta's Formulas and Polynomial Roots

Algebraic proof of Heron's formula

Algebraic proof of Heron's formula

A Brilliant (literally) Problem with floors and areas.

A Brilliant (literally) Problem with floors and areas.

Parameterization of a Cartesian curve, and undoing Parametric representations

Parameterization of a Cartesian curve, and undoing Parametric representations

Ramanujan summation of the natural numbers

Ramanujan summation of the natural numbers

Precalc. #4 Q's Part 2

Precalc. #4 Q's Part 2

Practice #4 Precalc. Q's

Practice #4 Precalc. Q's

Multinomial Theorem for Mu Alpha Theta Precalc.

Multinomial Theorem for Mu Alpha Theta Precalc.

A Complex (literally) Problem

A Complex (literally) Problem

Power rule proof, L'Hospitals rule, some limits

Power rule proof, L'Hospitals rule, some limits

AP Calc BC Review 2-Trig identities/formulas/graphs, limit techniques, definition of the derivative

AP Calc BC Review 2-Trig identities/formulas/graphs, limit techniques, definition of the derivative

AP Calc BC Review 1-Logs, functions, and certain exercises

AP Calc BC Review 1-Logs, functions, and certain exercises