Канал: Christopher Thomas

relationship graphs

relationship graphs

camping graph

camping graph

Kim's house graph

Kim's house graph

Graphs about driving home

Graphs about driving home

Info from Graphs Vocabulary

Info from Graphs Vocabulary

How I make videos

How I make videos

A few common mistakes

A few common mistakes

Another example of an improper integral

Another example of an improper integral

An example of an improper integral

An example of an improper integral

Definition of an improper integral

Definition of an improper integral

the Mandlebrot set

the Mandlebrot set

other versions of the golden ratio

other versions of the golden ratio

calculating the golden ratio

calculating the golden ratio

the golden ratio

the golden ratio

Sierpinski's triangle

Sierpinski's triangle

Fractals

Fractals

logarithmic differentiation

logarithmic differentiation

using logarithms to solve limits

using logarithms to solve limits

rerarraing for L'Hopital

rerarraing for L'Hopital

L'Hopital with natural logarithms

L'Hopital with natural logarithms

a second L'Hopital's example

a second L'Hopital's example

A cautionary tale

A cautionary tale

first L'Hopital's example

first L'Hopital's example

L'Hopital's Rule

L'Hopital's Rule

using the quadratic formula

using the quadratic formula

the quadratic formula

the quadratic formula

more on completing the square

more on completing the square

how Babylonians would complete a square

how Babylonians would complete a square

babylonians loved squares

babylonians loved squares

Euclid's fifth postulate

Euclid's fifth postulate

Euclid's first four postulates

Euclid's first four postulates

definitions of addition and multiplication

definitions of addition and multiplication

peano postulates

peano postulates

axioms

axioms

$third example of partial fractions$

third example of partial fractions

$second example of partial fractions$

second example of partial fractions

$first full example of partial fractions$

first full example of partial fractions

$partial fractional decomposition$

partial fractional decomposition

polynomial long division

polynomial long division

$the strategy for partial fractions$

the strategy for partial fractions

$motivation for partial fractions$

motivation for partial fractions

an example of advanced trigonometic substitution

an example of advanced trigonometic substitution

advanced trigonometric substitution

advanced trigonometric substitution

consequences of the square root of two

consequences of the square root of two

root 2 is irrational

root 2 is irrational

the square root of 2

the square root of 2

proof by contradiction

proof by contradiction

direct proofs

direct proofs

kinds of math statements

kinds of math statements

consequences of Russell's paradox

consequences of Russell's paradox

Russell's paradox

Russell's paradox

venn diagrams

venn diagrams

complements of sets

complements of sets

third example of trigonometric substitution

third example of trigonometric substitution

second example of trigonometric substitution

second example of trigonometric substitution

first example of trigonometric substitution

first example of trigonometric substitution

the concept of trigonometric substitution

the concept of trigonometric substitution

the integral of secant cubed

the integral of secant cubed

the integral of secant

the integral of secant

main trick for secants and tangents

main trick for secants and tangents

$repeating decimals into fractions$

repeating decimals into fractions

$finite decimals to fractions$

finite decimals to fractions

$fractions to decimals$

fractions to decimals

sets of numbers

sets of numbers

set operations

set operations

set notation

set notation

a tangent and secant paradox

a tangent and secant paradox

u substitution with tangents and secants

u substitution with tangents and secants

the convert-to-sines-and-cosines trick

the convert-to-sines-and-cosines trick

strategies for sines and cosines to even powers

strategies for sines and cosines to even powers

half angle formulas

half angle formulas

strategies for sines and cosines

strategies for sines and cosines

depicting a four dimensional box

depicting a four dimensional box

explaining boxes to lower-dim creatures

explaining boxes to lower-dim creatures

patterns among the low dimensions

patterns among the low dimensions

three dimensional containers

three dimensional containers

two dimensional containers

two dimensional containers

one dimensional containers

one dimensional containers

zero dimensional containers

zero dimensional containers

flatland

flatland

why we consider containers

why we consider containers

a zen interlude

a zen interlude

A clever trick with integration by parts

A clever trick with integration by parts

The integral of the arcsine of x.

The integral of the arcsine of x.

the antiderivative of ln x

the antiderivative of ln x

second integration by parts examples

second integration by parts examples

first integration by parts example

first integration by parts example

the procedure for using integration by parts

the procedure for using integration by parts

derivation of integration by parts

derivation of integration by parts

integration techniques undo derivative rules

integration techniques undo derivative rules

higher dimensional spaces

higher dimensional spaces

three dimensional space

three dimensional space

one and two dimensional spaces

one and two dimensional spaces

last inverse trig problem

last inverse trig problem

second inverse trigonometric example

second inverse trigonometric example

first inverse trig problem

first inverse trig problem

inverse trigonometric functions

inverse trigonometric functions

inverses

inverses

second trigonometric example

second trigonometric example

first trigonometric example

first trigonometric example

trigonometry in a nutshell

trigonometry in a nutshell

similar triangles

similar triangles

the concept of trigonometry

the concept of trigonometry

Eratosthenes measures the world part two

Eratosthenes measures the world part two

Eratosthenes measures the world part one

Eratosthenes measures the world part one

the itinerary of Alexander the Great

the itinerary of Alexander the Great

some results of Thales

some results of Thales

angles

angles

a brief history of the world

a brief history of the world

thales

thales

the forces of springs

the forces of springs

a snow example

a snow example

a spring example

a spring example

a work example

a work example

work as an integral

work as an integral

the units of work

the units of work

volumes of spheres

volumes of spheres

volumes of cones

volumes of cones

volumes of prisms

volumes of prisms

the Delian problem

the Delian problem

volumes and conversions

volumes and conversions

exponential decay example

exponential decay example

short cut for first example

short cut for first example

First example of exponential growth

First example of exponential growth

Solving the exponential growth equation

Solving the exponential growth equation

Exponential growth and decay

Exponential growth and decay

the converse to the Pythagorean Theorem

the converse to the Pythagorean Theorem

Pythagorean examples

Pythagorean examples

third and final proof

third and final proof

first proof of the Pythagorean theorem

first proof of the Pythagorean theorem

second proof of the Pythagorean Theorem

second proof of the Pythagorean Theorem

the cult of Pythagoras

the cult of Pythagoras

area and circumference examples

area and circumference examples

area of a circle

area of a circle

circumference examples

circumference examples

circles and circumference

circles and circumference

a diff eq with an initial condition

a diff eq with an initial condition

second example of a diff eq

second example of a diff eq

first example of a diff eq

first example of a diff eq

introduction to differential equations

introduction to differential equations

surface area example

surface area example

surface area

surface area

triangles and trapezoids

triangles and trapezoids

areas of rectangles and parallelograms

areas of rectangles and parallelograms

origins of geometry

origins of geometry

how to question a statistic

how to question a statistic

conducting surveys

conducting surveys

scientific method

scientific method

Difficult arclength examples

Difficult arclength examples

Easy arclength example

Easy arclength example

arclength formula

arclength formula

a complicated example of shells

a complicated example of shells

rotating around x = c

rotating around x = c

first example of shells

first example of shells

shells formula

shells formula

vertical rotation

vertical rotation

last z-score problems

last z-score problems

first z-score problems

first z-score problems

using a z-score table

using a z-score table

z scores

z scores

standard deviation on the bell curve

standard deviation on the bell curve

empirical rule

empirical rule

standard deviation

standard deviation

deviation

deviation

combining means

combining means

finding mean from a histogram

finding mean from a histogram

rotating around y = c

rotating around y = c

rotating the area between two curves

rotating the area between two curves

finding the volume of a cone

finding the volume of a cone

the disk method

the disk method

solids of rotation

solids of rotation

histograms

histograms

averages

averages

data

data

last example of areas between curves

last example of areas between curves

third example of areas between curves

third example of areas between curves

second example of areas between curves

second example of areas between curves

first area between curves example

first area between curves example

area between curves formula

area between curves formula

substitution with a definite integral

substitution with a definite integral

working with mortgages

working with mortgages

time to pay off a credit card

time to pay off a credit card

time to pay formula

time to pay formula

fourth substitution examples

fourth substitution examples

third substitution examples

third substitution examples

second substitution examples

second substitution examples

first substitution examples

first substitution examples

introduction to substitution

introduction to substitution

paying off a debt

paying off a debt

calculating payments formulas

calculating payments formulas

saving up for a goal

saving up for a goal

mount interest

mount interest

falling into debt

falling into debt

paying off a debt

paying off a debt

annuities

annuities

saving money

saving money

interest with payments formula

interest with payments formula

interest examples

interest examples

compound interest

compound interest

adding and subtracting percents

adding and subtracting percents