Multivariable Calculus Lecture 1 - Oxford Mathematics 1st Year Student Lecture

This is the first of four lectures we are showing from our 'Multivariable Calculus' 1st year course. In the lecture, which follows on from 'Introductory Calculus' which our students took in their first term, Sarah introduces the subject before going on to focus on Multiple Integrals in 2D.
You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): • Oxford Mathematics Stu...
All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.

[@VDP207]

I was just telling my friend yesterday, "you know, it's been far too long since I've enjoyed a nice invigorating Calculus lecture!"

[@turjjopaul1190]

what is invigorating Calculus

[@A_A_12_]

invigorating lecture, not calculus

[@revolution545]

@@A_A_12_ *invigorating calculus lecture, which is what was originally posted...

[@Shyguy71588]

Did your friend look back at you angrily with hate in his eyes?

[@briteness]

It is a real public service for Oxford to make classes available for free on youtube. Exposure to something like this could potentially change somebody's life.

[@palanthis]

Yeah. Encourage them to take up gardening. lol

[@leroux-ianni]

I used to hate maths in the past but watching videos on KZbin magically I fell in love with it

[@leonardobrunorende5363]

Took my degrere in Mechanical Engineering... NEVER had such a charming math teacher!

[@Shyguy71588]

Nothing like getting a degrere. Sort of like getting a degree

[@swizzbeats1212]

Those boards are wild!

[@aaabbb-py5xd]

Um no

[@AlonsoRules]

they are to scare you

[@aaabbb-py5xd]

@@AlonsoRules They scare the peasants

[@guilhermegoncalves110]

The wildest thing about them is that they're all white. You have to change your retinas after every class.

[@adi8oii]

@@aaabbb-py5xd I swear to god! Black boards are the best!!

[@AllanSitte]

It has been 27 years since I took a calculus course. Bringing back many dust bin memories for sure. And... she is good. A pleasure to watch this presentation.

[@JonathanLang-nu2lx]

just got started on double integrals, this was a great introduction!

[@differentialtopology]

One of the most beautiful subjects in mathematics, multivariable calculus. One day i want to teach this and these videos are inspiring me

[@RajKumar-pj6jv]

cant u dream of something better

[@differentialtopology]

@@RajKumar-pj6jv u literally wasted ur life commenting a mean comment. Please reevaluate ur attitude

[@zaibacademia]

Calculus, not doubt backbone of mathematics.

[@kousik8042]

This video inspires you? Teacher teaching by reading about loud and copying from notes? Get a life dumb

[@lugia8888]

@@differentialtopology hes not wrong. you could be traveling or spend time with your kids. instead you want to teach something that is easily available online? dont be stupid. youre wasting your time and hes trying to save you time. dont be sensitive.

[@markjordan7800]

no idea whats this is all about I'm just here for the amazing handwriting :) what a enjoy to watch

[@mathematica7531]

Several canvas sheets white boards, very helpful to the Professor.

[@marygaleac]

I have wanted to be a mathematician for 50 years…..2x=10….x is!??….is as far as I got…..I just couldn’t get my head around equations…..or any other maths….later on in life I could pretty much workout a monkey double at evens and 11/4….in the world of bookmaking…..I have read books on most of the greats….mainly before during and after Newton…..or Hooke….contentious topic I know……but this stuff is mesmerising to watch…..I have absolutely no idea what she is talking about but just love it…

[@AhmadKhan-dn6yh]

Keep this up!! I LOVE THIS!

[@mitchjacobs7603]

Excellent lecture. I'm teaching a multvariable calculus class this term and this greatly information how I plan to deliver the lectures

[@blackimp4987]

not for offending anyone but this way of teaching makes students sleep or struggle to keep up copying the boards. Change rythm, ask questions to your students, emphasize some parts. This has been a constant stream of words thou clear and linear. It's no different than reading the textbook - that's exactly what I did for many classes I had in my engineering studies as it was much more effective and time and energy saving for me studying my textbooks at home than wasting hours for going to my universities, listening to hypnotic lessons not memorizing or understanding half of what I could alone at home.... except for a very few where the professors were very good at merging notions from different texts and had the capability of making things clearer or more interesting - like my professor of linear dynamic systems - or you simply couldn't pass the exams if you didn't pick notes at lessons because they didn't follow a specific textbook.

[@OxfordMathematics]

@@blackimp4987 As mentioned elsewhere, this is the first part of the process. Lectures are followed by tutorials where students in pairs go through the work with their tutor. There is a tutorial on this channel (albeit a few years old). Thanks for the feedback.

[@ohsnapohsnap7346]

Just what i needed

[@magouero]

Thank you Madam for this very clear presentation !

[@emnaboughizane4940]

Amazing lecture

[@logicae4096]

Brings me back 20 years as an undergrad in Computer Science and Engineering. To this day I still shudder at advanced DiffEq.

[@Narxes081206]

I was not a fan of diff eq!

[@Ludwig1954]

An excellent teacher!

[@childofthe60s100]

A teacher TEACHES - this woman just copies her notes onto the whiteboard. You could have got this from a book!

[@arsenvokrug4198]

@@childofthe60s100I’m quite happy for her to have her notes to hand. 1) She wrote them in the first place. 2) It saves any annoying omissions that she would have to correct later, disrupting her flow. 3) She speaks quite naturally when amplifying the content of her notes.

[@hainguyenle2006]

Nice 🎉 can’t wait to next lecture

[@johnAshpool]

In the 21st century, I think chalk and blackboard are still the best writing platform.

[@dragomirtsonev319]

Absolutely.

[@kudzem]

I absolutely hate chalk and prefer whiteboards but it's a matter of preference I guess

[@jesuisravi]

this whiteboard thing would be OK if she were using a pen with a broader tip. As it is here, with the marker she is using, it is hard to read.

[@aa2339]

3blue1brown is the future

[@ZaWarudo69]

I think it’s probably the nostalgia that still holds you to that opinion.

[@muntadheradil9393]

That’s awesome 🤩

[@MLFranklin]

I need to show this to my daughter and show her that it's not just nerds like me that do calculus. It's normal nice looking people that do it, too.

[@ArtemisiaSayakaRandazzo]

The most absurd blackboard I have ever seen, I suppose serves to remind us that SpaceTime is deformable. The lesson is excellent.

[@user-rv7fl3nd1x]

😊..me recuerda el ingreso a la facultad de ingeniería de la "universidad nacional de mar del plata ". (UNMDP) ARGENTINA. Greetings from mar del plata argentina😊...

[@patrickthibault8119]

Interesting writing on sheets.

[@joseluisrodriguez2605]

Excelente

[@user-rv7fl3nd1x]

Gracias a su compatriota SIR ISAAC NEWTON 😊..❤

[@Md.ShabujMia-wu3ou]

Excellent Teacher ❤

[@Skank_and_Gutterboy]

I wish I had her in college for this subject. I got some mad German for a prof, she was nuts.

[@MrBPC76]

Mine was Polish

[@kenn756]

Mine was a donkey in engineering

[@hybridepigenes]

why am I watching this!

[@futureteacher1]

لإيجاد المساحة عليك بالتكامل 🙂‍↕️

[@valentinvetements]

The fundamental thing is to know how to use these formulas with multiple variables and if it is possible to improve the operation in less time and less step if in the case of the lack of data the achievement of the result is variable depending on the conditions

[@MrBPC76]

I am very perplexed by the boards she is writing on

[@iGasteiz]

Is there a mistake at minute 30:15 in the video? It seems there is an error in the transcription of the limits of integration. It incorrectly uses a1 and a2 as the limits for x, which should actually be a1 and b1 for the correct lower and upper limits, respectively. Similarly, for y, the limits should be a2 and b2 instead of the b1 and a2 that are shown. Could you please clarify?

[@jeffryborror4883]

You are correct that her specification of the rectangular domain is inconsistent with the limits on the integrals. Rather than changing the integrals, it would be clearer to write the domain as [a1,a2] x [b1,b2]

[@hemil__]

Arigatto senpai ❤

[@Vito-yp5wh]

Thank you.

[@MyScotty7]

This is year 1! Its crazy mathematics

[@El_Girasol_Fachero]

Excellent class. Greetings from Peru

[@DJMARCOAV1]

Interesting , thanks

[@isalutfi]

❤❤❤

[@user-wr4yl7tx3w]

Is there a playlist for this series?

[@michaelgasiciel9317]

🤣

[@bellinivernon]

Que bien ... !

[@mumumumah]

Just wondering - are questions not allowed at Oxford, or were students told not to ask questions since this is being recorded? (Were students even present? Never heard a class this quiet.)

[@childofthe60s100]

Typifies the definition of "A Lecture": "A process by which the notes of the lecturer get into the notes of the student, without passing through the minds of either." No wonder students these days are talking about poor value for money. She could have handed out copies of her notes and gone for a brew!

[@MrMusicM67]

Anyone know what marker she is using?

[@alexos8741]

- How many whiteboards will you need? - Yes

[@bernie5178]

J'aime bien les tableaux coulissants !

[@koee4400]

I don't get what's the scaler field PSI and how to compute in that integral (Ψ dxdy)?

[@amritlohia8240]

What timestamp in the video are you referring to?

[@xl000]

What exactly is she writing on ?

[@vedantkumar1101]

‌I wanna a lot of vedio in Chapterwise in Mathematics. Because I need.

[@pdr0663]

Sorry to be a pedant, but shouldn’t they be “slivers”?

[@bahmanfarnudi563]

'Slither' is informal British for 'sliver'.

[@h10horseinfo]

Great video....didn’t understand a word but I'm sure it will help my shopping. Could a kind person tell me in simple terms what practical use this has....It’s another world to me but I'm glad there are no pathological cases!

[@sharmatvpresents616]

Xllent

[@wysad3]

If only Sarah could be in every school teaching maths, I felt I understood even when I didnt, if she could teach me from fundamentals all the way through - Please digitize Sarah

[@mindsetTunner679]

#mathematicsbypankajkumar

[@Heather-nk6bv]

Nice

[@cheongdaniel8696]

Great lecture! One question, for example 2, why is f(x,y) = 1? Can anyone provide a clear explanation?

[@amritlohia8240]

Because if you work through the definition of a double integral with f(x,y) = 1, you'll see that it just sums up the areas of all the infinitesimally-small rectangles covering the region without multiplying them by anything (since multiplying by 1 leaves a number unchanged), and so it calculates the total area of the region.

[@michaelkoch6863]

Ja gut. Es sind die " Basiscs " ( Riemann Integration in R^2 über Normalgebiete ect ect) aber trotzdem gut vorgetragen.

[@Nur_Md._Mohiuddin_Chy._Toha]

👍👍👍

[@Chiavaccio]

👍👏

[@georgeh1352]

Umph, just mastered single integrals when double integrals pops up!!

[@JupiterThunder]

I did the first type of problem at school aged 16. Additional maths O level. That was 40 years ago. Now it's so advanced it's done at university😅

[@0riigiinal-fx8me]

Love her style

[@andreasmaaan]

That unwieldly cascade of flaccid whiteboards is diabolical.

[@pmosh1]

When she erased the marker with her finger @35:50 🤯

[@Okamine]

Ah yes the perfect video for when I'm about to sleep 😴

[@RagHelen]

It appears to be quite common for teachers in the English speaking world to write whole sentences on the board.

[@ngc-fo5te]

Not just English speaking world do that.

[@ErikS-]

I have seen my share of university classrooms and auditoria... But never have I seen such a huuuuuge whiteboard.

[@user-ev5uh8zo6j]

So easy. My name is Hyun woojin.

[@RedBar3D]

those boards are such a weird choice for one of the most prestigious universities in the world

[@michaelcolbourn6719]

In what way?

[@kassiogomes8498]

They are great. What are you talking about.

[@RedBar3D]

​@@michaelcolbourn6719 Most mathematicians that I know of prefer chalkboards. Also, the way these boards wobble when you write on them makes them look cheap.

[@MuhammadUmar-zb6hf]

I dont think boards really fo matter now dont they?

[@Alexander-iq5yq]

@@RedBar3D I prefer to inscribe clay tablets

[@marcelogaldames2306]

Genial

[@Michael43713]

Why not preprepare all this on slides to save keeping writing on the boards all the time?

[@ngc-fo5te]

As a retired lecturer I always found writing led to a better lecture - you tend to go over things at a more sedate pace. Lecturing from slides often leads to rushing things - and also a board has more room for asides.

[@TokyoTransit]

how can you show 9 slides at the same time?😊

[@jeffmilroy9345]

Advanced mathematics was contrived simply to determine where a cannon ball will land given sufficient gunpowder.

[@IsmailPbx]

Do we get access to the lecture notes?

[@OxfordMathematics]

courses.maths.ox.ac.uk/course/view.php?id=4941

[@DellHell1]

Those boards should be black and the board marker should be white. Basic human factors.

[@richardbryanesq]

Is there such a thing as a white magic marker? I've never seen that.

[@adrianwright8685]

Really?! Perhaps you should inform the printers of books, magazines and newspapers.

[@markjenkins8242]

Plus writing other colors, like red or blue, on a black board wouldn't show up very well.

[@atomic4650]

Nah, green boards contrast better.

[@DellHell1]

@@adrianwright8685 you are comparing apples to oranges.

[@eyebidder]

I once took a course from Einstein...it was all relative to me.

[@chico15analitico15]

Virtual pizarra deberían hacer

[@ErikS-]

Imagine as a professor to write full all these whiteboards... ... and find out at the end that you used a PERMANENT marker

[@markbrown585]

Did that once! You then eliminate all permanent markers from the room so you can’t make that mistake again…. It’s easy to do while you are focused during the lecture.

[@quarstrongforce]

Too fast for me even with the writing down. (1) dydx?

[@saifullahashique]

other lectures?

[@differentialtopology]

Patience is a virtue, a virtue that leads to beautiful mathematics :) soon we'll be gifted with the next video :D

[@user-hm2gb6pm6b]

If rain is easily understood why not integrals Rain is .......the only topic more targeted

[@user-dr8bm6bt3m]

Niceclassmathmatics

[@strangercydonian]

where can i get access to the online notes?

[@OxfordMathematics]

courses.maths.ox.ac.uk/course/view.php?id=4941

[@strangercydonian]

@@OxfordMathematics thanks!!!!

[@huissenm8752]

got fooled by the curves.

[@javierfigueroa8862]

Sitting on my forklift ignoring all my work duties watching this because why not

[@S-xc]

Doesn't one of these students explain to me what is happening? What is this? Is it a philosophy in mathematics? I am just a simple student from Iraq. I was looking for arithmetic sequences and derivative rules.

[@bfybfy438]

Powerpoint would have ruined this lecture!

[@drgilbertourroz]

The boards are cool for lectures from the XX century. I used to teach that way, copying every detail in the board, and erasing it and writing again. I did that from 1980 through the late 1990s. The only advantage of these multiple board with respect to the single board is that you don’t have to erase them (until later, when the lecture is done). Since the late 1990s, at the school I used to teach, we started using computers and projectors. We had a projector where I could write my lecture on paper and show it in the screen. This had a couple of advantages: (1) less effort. It is much easier to write on a paper on a table than to write on a board. And (2) I could face the class, watch reactions from my students as the lecture progressed, being able to attend to student’s questions right away, instead of showing them my back for more than half of the time. The computer, projector, and class management software (Blackboard, first, then Canvas) made the teaching experience much delightful.

[@tinchote]

I guess that depends on a lot of factors. The only math teacher I had that used the projector had a lot of backslash from the students, and I understand where they come from, it was a lot harder to follow the lecture, because the slides induced a faster pace, it was not always easy to follow where to look in the slide, and information disappeared quicker than it would on a several-board class, so it was harder to understand what was being said having no reference to the previous material.

[@ngc-fo5te]

Get some more experience and listen to the students and you'll switch back. I did.

[@sydneyhart]

Where’s Dan?

[@norwalkian]

Don't miss her other lecture, "Feeding your very, very hungry lion by hand"

[@jdaniel3185]

I lost 2 universities because of limits integrals derivates who i stoped to understand...at 46 is to late to start to understand..

[@KAFKUBA]

Where was she at my college

[@jej3451]

21:37 "slivers", not "slithers", haha

[@MLFranklin]

Yes. Maybe it's a Freudian because the integral sign looks like a snake.

[@bahmanfarnudi563]

'Slither' is informal British for 'sliver'.

[@AchryaPrashant]

At first sight I read this as multiverse calculus 😂😂😂😂😂😂

[@BlueMushroomSmurfCat]

Edward Witten be like

[@vedantkumar1101]

Now I am going to third year. And I have no any sufficient classes. 😢

[@EnderWorrior]

iss aache to meri jee ke teacher hai jo bina dekhe sab kuch karate hai

[@calculus8399]

Maybe

[@kousik8042]

​​@@calculus8399laude Tera Oxford Harvard... Wo 100 percent sahi bola... Jee teacher hamare desh me ..muh me rahta he topic ...ye chomu notes dekh ke padha rahi

[@bruhsusaltamash8141]

Jee teachers explain toughest concepts to you like you are five

[@kevink7529]

Isse ache to Mera 12th Ka teacher tha. Ye Kuch bhi Nahi Sikha rahi bas copy paste hai

[@YoungMeasures]

Her i’s have no dots on them!!

[@richardbryanesq]

Think of all the time saved around the world if we didn't add a dot to an I, or an apostrophe. Enormous time savings; enormous.

[@user-ff5pd8ro2k]

I can't believe a teacher needs to read her papers to write down such a simple maths in the board. Is that an University or a child school?

[@TurdBoi-tf5lf]

a* university. The pronunciation of "U" in university is like a "y" so we don't use an before it. This is basic English.

[@DadgeCity]

Interesting that she says slither when she means sliver. I suppose this is an example of hypercorrection.

[@jeffryborror4883]

i noticed that too. Thought maybe it was a Britishism but I looked it up and it seems not.

[@bahmanfarnudi563]

@@jeffryborror4883 Slither is indeed informal British for sliver.

[@yaseensaid5962]

How can I want to study medicine in this university ???

[@amyers01]

Good stuff but I’m like, “Pull the board down instead of up”

[@kassiogomes8498]

But then the students wouldn't be able to take notes because the board would disappear.

[@markbrown585]

Its nice to have it still visible later on