Math Teacher Solving his own Calculus Exam
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- Опубліковано 1 чер 2024
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The Exams:
English: www.researchgate.net/publicat...
German 1: www.researchgate.net/publicat...
German 2: www.researchgate.net/publicat...
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Today we take a look at my test on applications of differential and integral calculus, which includes maximization and extremal value problems, reconstruction of functions and also some physics and area interpretations. Can I solve it myself, what are the challenges? Let's find out! =D
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0:00 Intro
1:07 Exam Outline & Information
6:16 Exercise 1 Maximizing a Cylinder
12:19 Exercise 2 Reconstructing a Polynomial
21:26 Exercise 3 Application of Integrals
27:00 Part B Solids of Revolution
31:54 Part C & D Densities and Approximations
1x1=2, it’s basic terryology
Let’s not forget that the integral of ln(x) is 1/x!
@@elshons1576 I always forget about the factorial
the cylinder problem seemed a nice complexion of the conventional cylinder in sphere problems
Question 1 chad way (no derivatives or solving for x): V(x)=π(4x^2-x^4)=π(4-(x^2-2)^2). Since something squared is greater than or equal to 0, V(x) has a maximum of 4π for 2-x^2=0. Hence h=4-x^2=2+2-x^2=2.
nice.
thank you papa i love your content
For the last problem, in the d section, i think you can divide it into 3 shapes: on the top you get a truncated cone, which has volume of pi*h*(R^2 + r^2 + Rr) / 3, on the bottom a cylinder and a semisphere, both with side/radius 1, with this i got 4pi for the volume, which is 7% more than the actual volume.
If you want some Hard exercises for second year undergrads in math cheek ' Cassini - oraux X-Ens Analyse 1/2/3' it is French, but you can translate it !
are you french bro? if yes : t'as fait prepa chef?
@@A-curious-scientific1 Jpense qu'il est marocain
aren't oral exams easier since the technically require less time and meant to test the thinking process of the student
so les concours are much harder
@@absurat ah okk en tout cas oe les cassinis masterclass!
@@kuroisan2698 idk I'll be able to tell you the next year when it will be my turn to pass X ENS hopefully I'll be "admissible"
Glad to see a new Video so soon!
Interesting to see how more advanced calculus is in Germany (at least in your state) than at least in my province in Canada (which isn't the greatest in terms of their math education). The coverage and difficulty would be suitable for a 2nd course in calculus in university (or in a fast-paced engineering calculus) course in the universities I studied at.
questions were really good except for the last one, these really gave me some new ideas
In the first problem we can take the point of intersection of cylinder and curve as (x,y) where we assume that x=t and y will be -t²+4 and then we can simply solve it .
I got the same answer.
The questions are really nice, I especially liked the second one. But if we give something like this to our students, they'll probably start a revolution lol, well, unless we already solved very similar examples in class.
why don't you challenge your students by letting them solve it in class? I would love to do it like that.
Nice exam. Seems that students have to have true understanding of subject.
glad you liked it!!! :)
Cool exam! I’m glad I’ve never been in charge of writing a calculus exam. I feel like it would be way too evil. (Electrical Engineering graduate student here… Yes I can think of some truly evil exams with complex numbers and drop in some Maxwell’s equations and wave impedances for Multivariable Calculus or Hilbert Transforms and Fourier Transforms for a nice integration by parts problem).
Ye, it's kinda hard to find a good balance :'D
We want an exam review about abstract algebra
Hi! Love your videos so much!
I was wondering where can i buy the same board you use in your videos. Hope you'll see my comment :)
I really hope your channel picks back up in views soon. You definitely deserve it! Glad brilliant is supporting you on your journey back to the top (:
I've subscribed and hit the notification bell. Can't wait for more doses of happiness!
Your moustache are amazing!
Hallo ich bin ebenfalls angehender Mathe/Physiklehrer.
Mit welchem Programm hast du die Körper, wie z.b. den zylinder unter der parable gezeichnet?
oder allgemein funktionen
Mit welchem Programm erstellst du die Klausuren?
Vielen Dank.
TexStudio zur Formattierung. Latex, Desmos und Photoshop für die Graphiken =)
There is a run of videos called "what is a manifold" that goes into great depth, beginning at basic concepts, often starting with point set topology and building from there. I would highly recomend to anyone interested in higher dimension curvature and tensor calculus.
The reason I mention it is that the teacher who presents on the vids sometimes corrects himself and apologizes for committing "micro aggressions". A good example would be saying, "this problem is very simple..." or "the answer is 42, obviously." Where obviously is the offending word.
Anyway, if he was dead he'd be rolling over in his grave by your egregious microaggressions, actually you may do it enough that it doesn't qualify as micro anymore... It's just aggression😂
21:52 "Fapsters and Sons"
No fucking way 💀
:D
Hi Jens, Robert here. I'm a 19 year old gymnasium (only europeans know) student in third and final year. I have math on A-level. I'm fairly confident that 95% of my class wont make it past assignment 2 (reconstructing the polynomial) where 70% wont make it past 1st assignment, mainly because the subject of actually applying calculus to problems is almost non-existent in danish curriculums (the stuff present is very standardized assignments, thus not presenting a real life example). Can you please shortly ellaborate on what class you have (is it gymnasium, uni or whatever)?
Basically Gymnasium, but the slow version where we have 3 years of Abitur instead of 2!
Where do you teach ?
Great video, thanks for sharing. Where did you purchase the vertical sliding boards from?
Some supplier in Germany
@@PapaFlammy69 Do you mind sharing the name please?
@@Par2030 I know you can purchase those kinds of boards from clearidge.
Thanks @@WilliamCacilhas . Unfortunately they do not deliver to the UK.
@@Par2030 The only other places I know of are CCBC a Canadian company and US Markerboard. Perhaps one of those may deliver to the UK.
In the exercice 1 i don't understand why the 0 of the derivative is the way to optimize the cylinder
This can of course be proved rigorously from the definition of the derivative but the intuition behind it is to imagine you are walking across a hill, then the highest point is the summit wich is also the point where you stop moving uphill and start moving downhill, therefore the rate of change or the derivative changes sign from + to - therefore it mus be 0 right at the summit. You can do a simmilar thought experiment for traveling down and then up do it turns out that the derivative being 0 implies a local minimum or maximum
@@michacieszynski9455ok yeah i understand
Your approximation of 40% at the end there was close enough to correct (the actual value is 40.625). As someone who struggles to do maths in their head, I found that quite impressive.
thanks :)
Challenging test! What was the grade average?
About a C :)
cylinder problem is interesting!
Thx =)
Less goo
Tunç kurt?
👋
Are you German?
It’s interesting. This channel use to have a lot more views. I wonder what happened
It's terrible. I might as well quit, wouldn't make much of a difference it seems.
and it's not the quality of the videos that is off, it just seems to be the disinterest of the youtube community
And UA-cam in general.
The Algorithm is not pushing his videos for some reason... sometimes, it just takes time and then It starts pushing them... Let's make some more comments to show engagement!
videos on gpt and other llms are quite promoted these `days`. there's math there to explore and explain, but most explainers are through the eyes and experience of programmers.
love the video i just didn't like the part where you use decimals...
33:34 WTF is this?! I thought this is supposed to be math and not physics with approximations and that stuff. You should rather let your students prove that the dual space of a banach space is a banach space itself XD
:D
Leistungskurs oder Grundkurs
Grundkursniveau basically