Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Why we got zero flux in divergence theorem example 1 | Multivariable Calculus | Khan Academy

Video vocabulary

become

Copy vocabulary

US / bɪ'kʌm /

UK / bɪˈkʌm /

A1
  • verb
  • To begin to be; grow to be; develop into
  • To be suitable for a particular job or role

final

Copy vocabulary

US / ˈfaɪnl /

UK / ˈfaɪnəl /

A1
  • adjecitve
  • That will not be changed; permanent
  • Being the last thing in a series
  • noun
  • Last game in a series in a competition

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

bound

Copy vocabulary

US / baʊnd /

UK / baʊnd /

A2
  • adjecitve
  • (Papers) being kept together or covered
  • Limited by a law, agreement, or contract
  • Forced to do something (through honor, duty, etc.)
  • Being closely connected to one or more people
  • noun
  • Held someone by contract or promise or law
  • verb
  • To cover a wound, as with a bandage
  • To put pages and a cover together to create a book
  • To be limited by a law, agreement, or contract
  • To join people who share something into a group
  • To wrap something with rope
  • To jump energetically
  • To form the physical limit where one area ends
  • To walk, run with long steps in an excited way

color

Copy vocabulary

US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

maybe

Copy vocabulary

US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

our

Copy vocabulary

US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

whole

Copy vocabulary

US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

cut

Copy vocabulary

US / kʌt /

UK / kʌt /

A1
  • noun
  • Act/instance of reducing the size or amount of
  • Small opening made using a sharp object, knife
  • A wound on someone's skin caused by a sharp object
  • verb
  • To reduce the size or amount of something
  • To use knife or scissors to divide, open surfaces

good

Copy vocabulary

US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

inward

Copy vocabulary

US / ˈɪnwəd /

UK / ˈɪnwərd /

B1
  • adverb
  • At the inside of

vector

Copy vocabulary

US / 'vektə(r) /

UK / ˈvɛktɚ /

B2
  • noun
  • Math a quantity that has both size and direction

can

Copy vocabulary

US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

outward

Copy vocabulary

US / ˈaʊtwəd /

UK / ˈaʊtwəd /

B1
  • adjecitve
  • Going away from a place that will be returned to
  • Seeming to be from the outside
  • Concerning how something appears on the outside

octant

Copy vocabulary

US / ˈɒktənt /

UK / ˈɑːktənt /

A1
  • other
  • A measuring instrument for measuring angles to a celestial body; similar to a sextant but with degre

visualize

Copy vocabulary

US / ˈvɪʒuəlaɪz /

UK / ˈvɪʒuəˌlaɪz /

B1
  • verb
  • To create a picture in your mind of something

would

Copy vocabulary

US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

deal

Copy vocabulary

US / di:l /

UK / dil /

A1
  • verb
  • To cope with something - usually troubles
  • To give (something bad e.g. news) to
  • To buy and sell illegal drugs
  • To give out (cards, etc.) to; distribute
  • To do business with someone or to sell products

equal

Copy vocabulary

US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

sum

Copy vocabulary

US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

want

Copy vocabulary

US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

video

Copy vocabulary

US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

line

Copy vocabulary

US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

why

Copy vocabulary

US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

diagram

Copy vocabulary

US / 'daɪəɡræm /

UK / ˈdaɪəˌɡræm /

B1
  • noun
  • A drawing intended to explain how something works
  • verb
  • To show or explain something by drawing a picture

exact

Copy vocabulary

US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

well

Copy vocabulary

US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

divergence

Copy vocabulary

US / daɪ'vɜ:dʒəns /

UK / daɪˈvə:dʒəns /

B2
  • noun
  • Moving away; becoming different or separate

those

Copy vocabulary

US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

interpret

Copy vocabulary

US / ɪn'tɜ:prɪt /

UK / ɪnˈtɚprɪt /

A2
  • verb
  • To express so that others understand it
  • To translate what is said into another language

field

Copy vocabulary

US / fi:ld /

UK / fild /

A1
  • noun
  • Area of study, such as physics or biology
  • Piece of land used to grow crops/raise animals
  • Open area of land, especially without buildings
  • Grassed area where you play some sports
  • verb
  • To respond to something or answer a question
  • To catch or stop a ball during a game

positive

Copy vocabulary

US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

situation

Copy vocabulary

US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

large

Copy vocabulary

US / lɑ:dʒ /

UK / lɑ:rdʒ /

A1
  • adjecitve
  • Big; of great size; broad, tall, wide, or fat

rest

Copy vocabulary

US / rest /

UK / rɛst /

A1
  • noun
  • Time when one relaxes, sleeps, or is inactive
  • State in which there is a lack of motion
  • Part of something remaining after some was used
  • verb
  • To stop working or avoid activity to recover
  • (Of dead person) to lie in a grave
  • To lean, support or place something against
  • To not be tired because you had enough sleep

throughout

Copy vocabulary

US / θru:ˈaʊt /

UK / θruˈaʊt /

A2
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over/across an entire place/thing; in every part

along

Copy vocabulary

US / əˈlɒŋ /

UK / əˈlɔ:ŋ /

A1
  • adverb
  • As a companion; taken with someone
  • preposition
  • At a point on a line

out

Copy vocabulary

US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

Copy vocabulary

US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

minus

Copy vocabulary

US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

region

Copy vocabulary

US / 'ri:dʒən /

UK / ˈridʒən /

A2
  • noun
  • Part of a country, of the world, area, etc.

completely

Copy vocabulary

US / kəmˈpli:tli /

UK / kəmˈpliːtli /

A1
  • adverb
  • In every way or as much as possible

think

Copy vocabulary

US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

back

Copy vocabulary

US / bæk /

UK / bæk /

A1
  • adjecitve
  • Farthest from the front e.g. in a classroom
  • adverb
  • Have returned to a place you were before
  • noun
  • The part of a chair that the upper body leans upon
  • Location at the rear of something
  • The reverse of side something
  • Area on the rear of your body
  • verb
  • To bet money on something
  • To go backwards in a car
  • To support and encourage someone or some cause

far

Copy vocabulary

US / fɑ:(r) /

UK / fɑr /

A1
  • adjecitve
  • A long way away
  • Being a long way away
  • adverb
  • To a large degree or extent

leave

Copy vocabulary

US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

essentially

Copy vocabulary

US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

value

Copy vocabulary

US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

about

Copy vocabulary

US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

care

Copy vocabulary

US / keə(r) /

UK / kɛr /

A1
  • noun
  • Treatment you receive for your health or safety
  • Something that a person worries about
  • verb
  • To feel interest, concern, or worry
  • To look after someone or something

even

Copy vocabulary

US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

like

Copy vocabulary

US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

Copy vocabulary

US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

respect

Copy vocabulary

US / rɪ'spekt /

UK / rɪˈspɛkt /

A2
  • noun
  • Behavior that follows the established rules
  • Admiration for someone
  • Regard or admiration for someone or something
  • verb
  • To follow the established rules
  • To think very highly of another person

then

Copy vocabulary

US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

first

Copy vocabulary

US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

hard

Copy vocabulary

US / hɑ:d /

UK / hɑː(r)d /

A1
  • adjecitve
  • Difficult to do; difficult to understand
  • (Of facts) not able to be misunderstood; clear
  • (Of alcohol) strong
  • Involving or requiring lots of work, effort, care
  • Being full of pain, trouble, and problems
  • Strong
  • (Of edge) clear; sharp
  • Difficult to bend, break or cut; solid
  • adverb
  • With lots of force, power, or impact

true

Copy vocabulary

US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

should

Copy vocabulary

US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

here

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

integration

Copy vocabulary

US / ˌɪntɪ'ɡreɪʃn /

UK / ˌɪntɪˈɡreʃən /

B1
  • noun
  • Act of bringing things together into a whole

try

Copy vocabulary

US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

obviously

Copy vocabulary

US / ˈɒbviəsli /

UK / ˈɑːbviəsli /

A2
  • adverb
  • In a way that is obvious/easy to see or understand

fairly

Copy vocabulary

US / 'feəlɪ /

UK / ˈfɛrli /

A2
  • adverb
  • Quite; pretty; between very and a little
  • In a manner that is right and acceptable

side

Copy vocabulary

US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

use

Copy vocabulary

US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

guess

Copy vocabulary

US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

net

Copy vocabulary

US / net /

UK / nɛt /

A2
  • adjecitve
  • Remaining amount after something is taken away
  • noun
  • Internet
  • Crossed rope, fibers with partly open pattern
  • Crossed ropes that make up the back of a goal
  • verb
  • To catch or cover something in a mesh, often fish
  • To gain or earn a certain amount of money
  • To hit a ball into a goal during a sports event

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

change

Copy vocabulary

US / tʃeɪndʒ /

UK / tʃendʒ /

A1
  • noun
  • Exchange of one set of clothes for another
  • Money in the form of coins instead of paper
  • Money returned after giving too much
  • Act of making or becoming something else
  • verb
  • To exchange one set of clothes for another
  • To exchange one kind of money for another
  • To replace something with another thing
  • To make or become something else
  • To go from one train, bus, etc. and go to another

simple

Copy vocabulary

US / 'sɪmpl /

UK / ˈsɪmpəl /

A1
  • adjecitve
  • Not hard to understand or do; not complex
  • Having only a few parts; not complex
  • Being ordinary or normal
  • Being plain; without a lot added for style

space

Copy vocabulary

US / speɪs /

UK / spes /

A1
  • noun
  • Empty area kept for a specific reason, like a car
  • Empty area with nothing in it
  • Area in the sky where the stars are
  • Area between written words on a page
  • verb
  • To make a certain distance or time between

show

Copy vocabulary

US / ʃəʊ /

UK / ʃo /

A1
  • noun
  • False display of love, emotion or action
  • An event for displaying or promoting goods
  • Play, opera or theater production
  • Presentation that is broadcast on TV or radio
  • verb
  • To be easily seen or displayed
  • To display your emotions or feelings
  • To let someone see something; display
  • To explain or teach how something is done
  • To lead someone somewhere; point them to something
  • To prove something to be true, correct
  • To reveal or allow something to be seen

between

Copy vocabulary

US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

volume

Copy vocabulary

US / ˈvɒlju:m /

UK / ˈvɑljum, -jəm /

A2
  • noun
  • Number or amount of something e.g. sales
  • Amount of space that something takes up
  • One book that is part of a set of books
  • Level of sound produced by radio or television

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

flux

Copy vocabulary

US / flʌks /

UK / flʌks /

B2
  • noun
  • A state of flow and change

take

Copy vocabulary

US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

bit

Copy vocabulary

US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

cancel

Copy vocabulary

US / 'kænsl /

UK / ˈkænsəl /

A2
  • verb
  • To end a legal, business, or other agreement
  • To stop a planned event from happening

direction

Copy vocabulary

US / də'rekʃn /

UK / dɪˈrɛkʃən, daɪ- /

A2
  • noun
  • When someone tells people what to do
  • Describes the way you are going, e.g. North

way

Copy vocabulary

US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

entire

Copy vocabulary

US / ɪn'taɪə(r) /

UK / ɛnˈtaɪr /

A2
  • adjecitve
  • Complete or full; with no part left out; whole

other

Copy vocabulary

US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

answer

Copy vocabulary

US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
  • To solve a test question or a problem

solution

Copy vocabulary

US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

across

Copy vocabulary

US / əˈkrɔs /

UK / əˈkrɔs,əˈkrɑs /

A1
  • adverb
  • Distance from one side to another
  • (Go) from one side to the other of something

symmetrical

Copy vocabulary

US / sɪˈmetrɪkl /

UK / sɪˈmɛtrɪkəl /

B2
  • adjecitve
  • Having parts that are exactly the same

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

little

Copy vocabulary

US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

offset

Copy vocabulary

US / ˈɒfset /

UK / ˈɔ:fset /

B1
  • adjecitve
  • (Of printing) using inked plates
  • noun
  • Compensation or counterbalance
  • verb
  • To compensate for or counterbalance the effect of

vary

Copy vocabulary

US / ˈveəri /

UK / ˈveri /

A2
  • verb
  • To change something and make it different
  • To be changeable, both up and down

wall

Copy vocabulary

US / wɔ:l /

UK / wɔl /

A1
  • noun
  • High, flat side of a room or building

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

surface

Copy vocabulary

US / 'sɜ:fɪs /

UK / ˈsɚfəs /

A2
  • adjecitve
  • Of the top layer; not deep or meaningful
  • noun
  • Top layer of the ground or of water
  • Nature or emotions that show, but may not be true
  • Outside or upper layer of something
  • verb
  • To give (road) a top layer
  • To appear after being hidden, unseen, or unknown
  • To come to the top of something; emerge
  • To come to the top level of water, mud, etc.

also

Copy vocabulary

US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

kind

Copy vocabulary

US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

delete

Copy vocabulary

US / dɪ'li:t /

UK / diˈlit /

B1
  • verb
  • To remove or erase something

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

last

Copy vocabulary

US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

part

Copy vocabulary

US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

theorem

Copy vocabulary

US / ˈθɪərəm /

UK / ˈθiərəm, ˈθɪrəm /

B2
  • noun
  • A statement that can be proved

calculate

Copy vocabulary

US / 'kælkjʊleɪt /

UK / ˈkælkjəˌlet /

B2
  • verb
  • To find an answer using mathematics
  • To make an educated guess about something

with

Copy vocabulary

US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

negative

Copy vocabulary

US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)
  • Subtitles section
  • In the last video we used the divergence theorem to show that the flux across this surface right now, which is equal to the divergence of f along or summed up throughout the entire region, it's equal to 0.
  • And what I want to do in this video is think a little bit.
  • When you get an answer like 0, you want to think about why is it?
  • This is saying that there's no net flux across the surface right over here.
  • Or if you sum up all of the divergences in this volume, you are getting 0.
  • So why is that?
  • Well, the simple way to think about it is, when we took the divergence of f, this vector field f is hard to visualize, but the divergence of f is fairly easy to visualize.
  • The divergence is equal to 2 times x.
  • So over here you're going to get, as you go further and further in this direction, as x becomes larger, your divergence becomes more and more positive.
  • So you have kind of a divergence of 2 right over here.
  • You have a divergence of 1 along that line.
  • And you have a divergence of 0 right there.
  • And that's also true, obviously, as you go higher.
  • Because you're just changing the z.
  • You're not changing the x.
  • So all over here you have positive divergence.
  • Over there you have positive divergence, and not just along that plane.
  • But if you go in the x direction as well, this whole region of space, you have positive divergence, I guess you could say, in the positive x side of our octant.
  • But then as you go on that side, on the other side, you have negative divergence.
  • And this diagram is symmetric with respect to the zy plane.
  • And so those divergences cancel them out.
  • You would have had a positive flux across the surface or a positive value right over here.
  • Instead of calculating it for this region, we had calculated for region that was just between x is 0 and 1.
  • So let's just think about that region.
  • So that region that would have been cut off right over here.
  • That would have been cut off right over there.
  • And so the back-- I guess you could say the back wall of that, the back wall of this, would have been the zy plane.
  • Now if we care about this volume-- so we're essentially eliminating the rest of it.
  • So let me try to eliminate it as best as I can, change the colors.
  • So if I eliminate that part of it over there and all maybe even what we see, all of that-- I should have deleted that first.
  • So if we eliminate the back part of it and we're just dealing with it when x is positive, then our entire solution that we did in the last video would have been the exact same, except now x is going to vary between-- instead of negative 1 and 1,
  • it'll vary between 0 and 1.
  • And so our bounds of integration, x is going to go between 0 and 1.
  • And then in that situation, our final answer-- this part, this would be between 0 and 1.
  • That would all be 0.
  • And we would be left with 3/2 minus 1/2.
  • 3/2 minus 1/2 is 1 minus 1/6, which is just going to be 5/6.
  • And so when you just think about this part of it-- this side of it, this one that I've just drawn-- you had a positive flux of 5/6.
  • On the other side you had a negative flux of 5/6.
  • And then they canceled out.
  • One way to interpret that is, if we thought about the entire surface, like what we saw in the last video, then you had an aggregate inward flux in the last video.
  • That's why it was negative.
  • And then it's completely offset by an outward flux right over here, the positive.
  • You had a negative divergence in that other region, and you have a positive divergence that completely offsets it in this region right over here.