Multivariable Calculus Lecture 1 - Oxford Mathematics 1st Year Student Lecture
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- Опубліковано 17 лют 2024
- 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.
I was just telling my friend yesterday, "you know, it's been far too long since I've enjoyed a nice invigorating Calculus lecture!"
what is invigorating Calculus
invigorating lecture, not calculus
@@A_A_12_ *invigorating calculus lecture, which is what was originally posted...
Did your friend look back at you angrily with hate in his eyes?
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.
Yeah. Encourage them to take up gardening. lol
I used to hate maths in the past but watching videos on UA-cam magically I fell in love with it
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.
Those boards are wild!
Um no
they are to scare you
@@AlonsoRules They scare the peasants
The wildest thing about them is that they're all white. You have to change your retinas after every class.
@@aaabbb-py5xd I swear to god! Black boards are the best!!
Took my degrere in Mechanical Engineering... NEVER had such a charming math teacher!
Nothing like getting a degrere. Sort of like getting a degree
just got started on double integrals, this was a great introduction!
One of the most beautiful subjects in mathematics, multivariable calculus. One day i want to teach this and these videos are inspiring me
cant u dream of something better
@@RajKumar-pj6jv u literally wasted ur life commenting a mean comment. Please reevaluate ur attitude
Calculus, not doubt backbone of mathematics.
This video inspires you? Teacher teaching by reading about loud and copying from notes? Get a life dumb
@@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.
no idea whats this is all about I'm just here for the amazing handwriting :) what a enjoy to watch
Several canvas sheets white boards, very helpful to the Professor.
Excellent lecture. I'm teaching a multvariable calculus class this term and this greatly information how I plan to deliver the lectures
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.
@@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.
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…
Brings me back 20 years as an undergrad in Computer Science and Engineering. To this day I still shudder at advanced DiffEq.
I was not a fan of diff eq!
Keep this up!! I LOVE THIS!
Just what i needed
The most absurd blackboard I have ever seen, I suppose serves to remind us that SpaceTime is deformable. The lesson is excellent.
I wish I had her in college for this subject. I got some mad German for a prof, she was nuts.
Mine was Polish
Mine was a donkey in engineering
An excellent teacher!
A teacher TEACHES - this woman just copies her notes onto the whiteboard. You could have got this from a book!
@@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.
Interesting writing on sheets.
In the 21st century, I think chalk and blackboard are still the best writing platform.
Absolutely.
I absolutely hate chalk and prefer whiteboards but it's a matter of preference I guess
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.
3blue1brown is the future
I think it’s probably the nostalgia that still holds you to that opinion.
Amazing lecture
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.
😊..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😊...
Sorry to be a pedant, but shouldn’t they be “slivers”?
لإيجاد المساحة عليك بالتكامل 🙂↕️
Thank you Madam for this very clear presentation !
why am I watching this!
Nice 🎉 can’t wait to next lecture
That’s awesome 🤩
I am very perplexed by the boards she is writing on
Is there a playlist for this series?
🤣
This is year 1! Its crazy mathematics
Gracias a su compatriota SIR ISAAC NEWTON 😊..❤
- How many whiteboards will you need?
- Yes
Excelente
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?
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]
Anyone know what marker she is using?
What exactly is she writing on ?
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
Excellent Teacher ❤
Arigatto senpai ❤
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.)
J'aime bien les tableaux coulissants !
❤❤❤
Que bien ... !
I don't get what's the scaler field PSI and how to compute in that integral (Ψ dxdy)?
What timestamp in the video are you referring to?
Great lecture! One question, for example 2, why is f(x,y) = 1? Can anyone provide a clear explanation?
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.
I wanna a lot of vedio in Chapterwise in Mathematics. Because I need.
Interesting , thanks
Umph, just mastered single integrals when double integrals pops up!!
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😅
Nice
It appears to be quite common for teachers in the English speaking world to write whole sentences on the board.
Not just English speaking world do that.
Xllent
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
Thank you.
Ah yes the perfect video for when I'm about to sleep 😴
Ja gut. Es sind die " Basiscs " ( Riemann Integration in R^2 über Normalgebiete ect ect) aber trotzdem gut vorgetragen.
Why not preprepare all this on slides to save keeping writing on the boards all the time?
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.
how can you show 9 slides at the same time?😊
#mathematicsbypankajkumar
I have seen my share of university classrooms and auditoria...
But never have I seen such a huuuuuge whiteboard.
Do we get access to the lecture notes?
courses.maths.ox.ac.uk/course/view.php?id=4941
That unwieldly cascade of flaccid whiteboards is diabolical.
Those boards should be black and the board marker should be white. Basic human factors.
Is there such a thing as a white magic marker? I've never seen that.
Really?! Perhaps you should inform the printers of books, magazines and newspapers.
Plus writing other colors, like red or blue, on a black board wouldn't show up very well.
Nah, green boards contrast better.
@@adrianwright8685 you are comparing apples to oranges.
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!
When she erased the marker with her finger @35:50 🤯
So easy. My name is Hyun woojin.
Sitting on my forklift ignoring all my work duties watching this because why not
Imagine as a professor to write full all these whiteboards...
... and find out at the end that you used a PERMANENT marker
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.
where can i get access to the online notes?
courses.maths.ox.ac.uk/course/view.php?id=4941
@@OxfordMathematics thanks!!!!
those boards are such a weird choice for one of the most prestigious universities in the world
In what way?
They are great. What are you talking about.
@@michaelcolbourn6719 Most mathematicians that I know of prefer chalkboards. Also, the way these boards wobble when you write on them makes them look cheap.
I dont think boards really fo matter now dont they?
@@RedBar3D I prefer to inscribe clay tablets
Advanced mathematics was contrived simply to determine where a cannon ball will land given sufficient gunpowder.
other lectures?
Patience is a virtue, a virtue that leads to beautiful mathematics :) soon we'll be gifted with the next video :D
Love her style
I once took a course from Einstein...it was all relative to me.
Too fast for me even with the writing down. (1) dydx?
👍👏
Virtual pizarra deberían hacer
21:37 "slivers", not "slithers", haha
Yes. Maybe it's a Freudian because the integral sign looks like a snake.
👍👍👍
Niceclassmathmatics
Where’s Dan?
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!
At first sight I read this as multiverse calculus 😂😂😂😂😂😂
Edward Witten be like
Interesting that she says slither when she means sliver. I suppose this is an example of hypercorrection.
i noticed that too. Thought maybe it was a Britishism but I looked it up and it seems not.
Where was she at my college
Don't miss her other lecture, "Feeding your very, very hungry lion by hand"
I lost 2 universities because of limits integrals derivates who i stoped to understand...at 46 is to late to start to understand..
Genial
Now I am going to third year. And I have no any sufficient classes. 😢
got fooled by the curves.
iss aache to meri jee ke teacher hai jo bina dekhe sab kuch karate hai
Maybe
@@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
Jee teachers explain toughest concepts to you like you are five
Isse ache to Mera 12th Ka teacher tha. Ye Kuch bhi Nahi Sikha rahi bas copy paste hai
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.
Good stuff but I’m like, “Pull the board down instead of up”
But then the students wouldn't be able to take notes because the board would disappear.
Its nice to have it still visible later on
Her i’s have no dots on them!!
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.
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?
How can I want to study medicine in this university ???
Ни слова без шпоры, а если бумажки потеряет, то?
Dear Lecturer,
As these integrals are of a rather elementary nature, obviously the problem sheets exact this aesthetic property : but it might make more sense to use them as a way of building up to something interesting -
(1) an Earl-styled inapplicability of fubini’s theorem
(2) a calculation relevant to the explication of time dependence found in a study of maxwell’s electromagnetism - as opposed to having just one example in the corner of some problem sheet #7 or something
(3) the generalization to not just a more involved multilinear coordinate system - but to OPERATORS! One finds in a study of quantum mechanics.
Im not saying its obvious how this jump is going to be taken care of… but there’s room i believe for more inspiration in this particular course.
Nor am i suggesting an actual way of building up to this ‘peculiar’ form of generalization…
Its more general than spherical polars in my opinion however
This way, if or when you make glaring mistakes-of-avoidance in your symmetry arguments - theres a greater domain of correctness to ‘catch’ this. Instead of it being kind of hidden in the corners of the collective mind
Powerpoint would have ruined this lecture!
should have used a machine to project on a screen what she is reciting instead of writing every word...