Math 2B. Calculus. Lecture 03. Definite Integral.
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- čas přidán 2. 10. 2013
- UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 03. Single-Variable Calculus -- Definite Integral --
View the complete course: ocw.uci.edu/courses/math_2b_ca...
Instructor: Natalia L. Komarova Ph.D.
License: Creative Commons CC-BY-SA
Terms of Use: ocw.uci.edu/info
More courses at ocw.uci.edu
Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations.
Recorded on October 2, 2013
Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), ocw.uci.edu/courses/math_2b_ca.... [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (creativecommons.org/licenses/b....
She's a non-stoping advanced course in math. Just marvellous.
3:32 damn that quick straight line tho
She is PhD .....
I liked it
Math lecturers never understand that confused students can't ask questions in class because they don't even know if they have questions or not because they're totally confused.
I should actually say that one day in class; "I don't have any idea of what you're talking about. The textbook is incomprehensible, should I drop the class?"
I honestly wonder what would happen if someone actually said the truth. Do lectures really believe nobody has any questions?
But otherwise, this is actually a good lecture. I like how she shows how to calculate a definite Integral via the actual definition using partitions and the limiting process before going into subtracting anti-derivatives. That's really the correct order to teach the material.
I think she's a lot better than other members of the department at UCI. Though I find the common final exam policy to be totally unfair to students since it forces them to fight internally, reducing cooperative learning, resulting in a net-loss of learning among the general student body -- this has got to be one of the stupidest policies in practice at any college or university for a class as universally important as Calculus. We should be getting every single student to master the subject, not beat them down and force them to fight each other just to learn a basic skill that's essential to all of society's future. It's a moronic policy that should be eliminated.
Sometimes I don't ask questions because I get ahead of the lecturer anyway so if I just wait til they explain their thing my question will be answered.
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Yup. I am one of those when it comes to this math. It helps to know the terms and rules; and exceptions to rules. Must have an extremely good memory for thousands of details.
Rightly said. However, the formulation of mainstream calculus is so flawed that it requires you to be an abstract learner which most students are not.
My New Calculus is the first rigorous formulation in human history:
drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
It is 100% geometry with no ill-formed concepts such as limits, infinity or infinitesimals.
From India, ur method of making understand is unique.
For all the people saying she’s a “copy and paste” teacher, literally all your teachers are like that. Every teacher has to plan and make sure they have material ready, and if some of them visibly refer back to notes, then they do. I’ve taught in some capacity in college education for years now and all the professors I’ve taught along always have notes with them. You have to remember that they do research in this field that is far more complicated than what they are teaching. They use these notes to make sure they don’t deviate from the set standards made by the department by putting in their own work and also to make sure they follow along a cohesive straight line. If many of you students, I am still a student too, would see she’s using it to keep her place and make sure she drives home the important points, you wouldn’t be complaining about her “copying and pasting.” Trust me, there are plenty more worse ways to teach calculus and I think she’s doing a good job.
Jblog100 not necessarily required any sort of materials....
I second that. It's inevitable however that somewhere along ones academic career, there will be some professor who will wing lectures on the spot, with no pre-made lectures notes at hand and no particular textbook required for that class. Trust me, in those cases, the same people complaining about "copy and paste" are the ones BEGGING for material straight out of a book. What people are referring to as "copy and paste" should actually be referred to as having a PLAN. As you mentioned, the life of the average professor tends to be very busy, but that's something that none of those students complaining would understand.
She is nice and crazy
True
All my teachers in the last year of high school are not a copy and paste. The presentation is different from class to another .
This makes me feel like going back to my A'levels in Uganda. I enjoyed PURE MATHEMATICS those days and I managed to get an A.
You should.
I think I'm falling in love with math. It's such a beautiful subject!
For those who said that she is a bad or copy paste teacher don't forget it's an advanced course in math,as well as the audiences are not kids.
That doesn't excuse bad teaching. Why the hell are you paying so much for lessons when you can get better lessons on other youtube channels for free?
We read these stuff in class 12 here in India.
@@anjukumarimahto8479 This isn't really advance or college level. America has Calculus I and II in High School too. Some just end up doing Calculus in their Freshman year of college of they do stats in High School.
Explicit Tech yea but she’s hot so I’m okay with it
Advanced? This is baby level math even for engineers, and for mathematicians, math doesn't even get serious until they take a first course in real analysis.
I dont even know how I ended up here. I dont get it but I'm still watching.
Thanks professor for Integrals Definition and Partial.
She has given quality of teaching from point to point
This stuff is way way over my head.
I had trouble with Algebra in High School...barely passed the course, and then failed Intermediate Algebra miserably and took Business Math as a Senior as it is the type of math I use day to day.....I watched a few minutes of this video and it gave me flashbacks to how my head would start spinning with confusion in Intermediate Algebra.
Valla bundan matematiği dinlerseniz tabii ki de öğrenemezsiniz tamamen ezber ve kâğıda kitaba kalınmış bir anlatim hic öznellik yok bu şekilde anlatsam tum öğrencilerim sınıfı bosaltir gider.
If she's a teacher in UCI is beacuse she's really good at what she does, might not be the best transmitting the information but still, I respect her knowledge :)
Sorry but ,Did u get what she explains
Sorry , but I am not getting your perception about her teaching skills.
You said that ,she does not have the best analysis skils about anything or something but u should notice that she just trying to explain the topic in another way
So I think u should appreciate her skills
@@skantsir6326 he does lol 😂😂
@N Y Math is not for you. Some students will spend entire lifetime blaming professors for not teaching them well, but it really is just you. It’s ok, you can still survive and thrive in this world while avoiding calculus.
@N Y AHAHAH FUCK ME IM DYING READING YOUR COMMENT, honestly if you don't like professors, don't attend their classes. It is what I did during COVID, especially for my calc class where my teacher was horrendous, external resources also came helpful with an essay on neutrino oscillation, because our classes were terrible (online classes).
Without these basics, there won't be signal transmission, not even ethernet. We will not have internet, mobile phones, not even telephone and basic radio station. She teaches well. Interaction does not help in teaching advance mathematics (as oppose to elementary mathematics). When you know Laplace transform, Z transform, Advance signals, you will understand she is good.
this is good i have liked her way of teaching
Yes, you are right. Anyone who says learning calculus is unnecessary and they will never use it has been short-change.
I've never had a good calculus lesson until today
So NASA is poor in mathematics?
Does anyone know how at 22:25 she divides everything in the brackets by n except for the first 3 inside the brackets. I get that the n's cancel out initially, but wouldn't dividing through by n put one back in the denominator?
I’ve noticed that mathematicians have a certain handwriting, physicists a certain kind, chemists a different kind, and they are all different.
interesting. Care to elaborate here?
different nomenclatures train the wrist in different movements
Nonsense. Handwriting forms in early years, when we still don't know what we will do for a living.
@@sanjakosovic nope. Our handwriting tendencies shift wildly as we live our life and we adapt new habits as we go about our lives.
@@stephenharris2957 Not in my experience. People learn how to form letters in early childhood. As they grow up, their hand becomes more stable and experienced, so they write faster and their handwriting flows better, but the shape of letters rarely changes. Your handwriting definitely establishes by the late teenage years and, unless you change it deliberately or get an illness that affects writing, doesn't change much.
you are absolutely good Dr Natalia
Oh my gosh I'm do glad to see this! I definitely needed some refreshing on the subject.
Tnx, very helpful for someone who is being introduced in intergration
You are genius mam in the world of mathematics
¡¡Excelente y bonita profesora !!
As an electrical engineer, she is doing a damn good job. Wish I had her in my Calc classes. The ones I had wasn’t near as clear as her. True understanding actually happens when the class is complete. You do need to revisit it in the aftermath to comprehend it all. It all clicks at that time.
@@shalinitiwari119 this is a very basic class, and to graduate from math department you'll need to learn more advanced stuff. This class is optional, students who take it are those who haven't studied calc in hs or want to revisit the topic.
@@shalinitiwari119 this stuff is too easy
I am also physics professor of India .your teaching style is very good
perfect, I like the way you teach , thnks so much !
This style of lecture is now considered old. The times have changed. Unfortunately, not enough students today would appreciate this. However, as a math instructor, I still appreciate this style of learning.
This video is from 2013, it's understandable this is old
@@eliteintelectual.9948 sheesh
Good, I love this type teaching
国や言葉が違っても式を見れば分かるのが数学の楽しい所☺️The interesting part of mathematics is that I can understand by looking at the formula even if the country or language is different.
Muy excelente explicacion
Where is Math 2B. Calculus. Lecture 02?
Молодец Наталия, понятно объясняет 👍
Natalia is in a great need of decent clothing. The outfit is just right for hitting the beach not for teaching math at university.
@@gailmcfarland8140 oh no, how dare she showed her bare shoulder skin! She must be banished from teaching for all eternity and wrapped in burqa.
Loved the fact that she chose to put on this shirt
In other lectures, she is actually wearing a bikini under her work clothes. Not kidding!
How students understands these complicated integration differentiation Calculus. Nothing enters inside my head or brain
Đây là tích theo định nghĩa ban đầu của nó phải không ?
Perfect. Awesome.!
Very amazing way of teaching ma'am
Please make videos on fractional calculus.
All fractional derivatives are nonlocal properties
Thanks for guide us❤️❤️❤️
Love you ma'am......
Xa
Thanks a lot. You have remembered to me back days
was she trying to define the answer or was she trying to answer it in a vague way. I think they didn't get to U sub to solve it yet in the class huh.
Is it necessary to take the sample points to be the right most points of the subintervals .
You should go with graphical analysis then you know why sample points .
En 22:28 la "n" no se cancela, sino que se simplifica por su inverso multiplicativo.
In 22:28 the "n" is not canceled, but simplified by its multiplicative inverse.
Eso significa cancelar: un número en R se opera con su inverso (aditivo o multiplicativo) y resulta la identidad (de ahí las leyes cancelativas en anillos). Simplificar entra en el contexto de fracciones para indicar que el numerador y el denominador son coprimos.
Интегральчик , обожаю их
يمه المُدرسة تخبل وربي لو درسني اصير انشتاين بلرياضيات 😍😍😍
#طالب_عراقي_وعندك_الحساب
النجف الاشرف.... قتلة الحسين
@@ammarif618 ما افتهمت حبيبي شنو تقصد 🤔🤔
Love your lectures
Hello bro.. can u help me ….…
how can I know the nth derivative of lnx
Does anyone know where the lecture 2 is?
Wow this is amazing i really enjoyed her lesson
I like the way she refers to the variables as this guy. I do the same as well.
I have never understood subjects without practical examples and applications
Where is lecture 2
Why does the sample need to be chosen randomly?
Maam your teaching style is outstanding
Where i can use these in my job, (other than teaching)
3:30 I was always amazed at the hidden depth of certain undergrad classes, I find myself going back to my old notes now.
That right there is fundamental for numerical integration, but when I took Calc 2 I had no idea
The way of your teaching is awesome.Mam I will try to do my level best.
Lol
Amazing!!
Hi
She should divide the board into sizable spaces so that he can write on each one after the other random writing can confuse the students .she is good above it all
Formidable prof... Explications et démonstration très assimilable👋👌
she has a gift for teaching calculus. pride the word 'calculus'!!!!!
Iam Egyptian..and this great teacher 👌👌
Where is going this class, i mean in which country.
I am from India.
Can I get the maths syllabus of your country?
Fellow math prof here. I always wonder my most profs in math copy theorems and write word for word on black board or chalk board. I tend not to write out sentences and long paragraphs on board, partly because my handwriting is terrible. What is the reason they re-write what's in book on the board?
Mam where are you please make video on black body effect
At 15:41 why xi got it like that I'm confused.
Thank you so much...
Its great To learn here
When you were explaining a student he must have a Doubt like ; what about n in the term 3/n you didn't divide by n why...?
Awesome lecture
I don't know what they are doing here and how does it relate to daily living
Thank you becouse you explean the mathematics very good
Integral is so important to remember.
she is the best
How to introduce differential calculus mam
Great work
I m remember when I was grade 12 student at the back home my country
Still I didn't forgot about mathematics
Love it
This is way above my level, I don't know what I'm doing here.
Me too😂😂😂
@@tomasjorge244 Me too
When I was young I learnt that 1+6 = 16 (which is correct putting the numbers close together)
Hello teacher! Tích phân vô cùng đơn giản
Love you teacher
Need the graphic over Energy Calorific water in icening...
Thank Teacher
Sum of the rectangules is area under the curve. Is trivial today.
Very good!
Nice to see here with calculus
if you have a good relationship with your parents, math will be easy.
there's no conection
I dont have the first part but i have the second one hmm
How
I had terrible relationship with my father who was the devil himself. I was very bad in maths and scientific subjects in general in school. But I had very good relationship with my wonderful mother ( may she is in heaven now). I was good in languages and history in school.
@Norr Carr Lane Thank you so much. God bless you.
Damn I miss attending lectures
Thank you! Math ease
Thank u!!
What's that hanging black thing at 2:57
Ayush Tiwari, I was thinking the same thing. 🤔
I SAW THIS VIDEO, HERE I SAW THE MISTAKE ON 9:36.AS PER DIAGRAM AREA OF INTEGRAL a To b of f(x) is A1+A2 =total area covered by the graph.
Below the x-axis indicate negative region but area is always positive:(A1-A2!=A)
Sureshbhai patel (Ahmedabad,India)
it's called geometric area and can be negative or in other words we can say" A1+A2=A" where A2 is negative
@@Scora996 What do you mean about geometric area? I can't understand
I am sure you are not give proper answer.
Integral o to 2!!(pai) find area .? Iam requesting you to send answer with calculation.or send me photo of this type of solution then i assure that you are right.:Thanks
Perfect 😇
13:15 Can there be a negative area??
Why have I fallen in love with this teacher ?! 🤔
Extraordinarily teacher from india
She has explained integral here in great detail.. She is really good.
大学入学する前のワクワクする感じ思い出した
Mam your markers quality is so good ....Not stop Evan once .....If you wrote this much in India the marker would have stopped 10-15 times during 1 hours lecture .....
高颜值，高智商的老师
Beautiful professor
She looks great in that updo.
You are so great wif
Don't mind there comments, you did which is right. We are not competing with other who doesn't want to obey your rules in classroom. If they want to learn learn for the lesson you are giving to them. Give them assignment. So that they will think which is right for the solution you given to them. If they can't solve it, ask there parents if they know the solution if not they could ask there friends or brother or sister.
Good explanation