Science & mathematics are not language dependent subjects.It is our luck that we are living in a world where science has come to extreme point.Thanks to Youtube & thanks to IIT professors because both have quality & both of them giving their attention towards us free of cost.
By the way I would like to mention one drawback of cameraman that his timing is not good,when prof is writing the cameraman should focus on paper on which the prof is writing.
@psycool666, Math is a language and not just a way of solving problems. In mathematics sometimes you have to define very specifically what you are describing. sometimes it is convenient or necessary to bound natural numbers as all integers greater than or equal to 1 sometimes you need to describe natural numbers as all integers, sometimes all integers other than 0 is useful. it depends on what you are describing. you could say Alaskan winters are cold. or the killer was cold.
Negative natural numbers doesn't mean the negative part of the natural numbers. It means the negatives of the natural numbers. Also, names are nothing but convention, and at least in India we call the set of negative numbers the set of negative natural numbers,
I'm sorry If I sounded Cocky actually I'm a non-math student, and have been interested in math after my college, so a lot of self learning, It is just that these terms are a bit Confusing , Cuz I read that the number "1" was the lowest Natural number, and I definitely don't doubt on what an IIT professor is lecturing on - Cuz Im from India too, maybe it is just that these Terms aren't STRICTLY DEFINED to apply them Universally
Well your version of the definition is correct, and the smallest natural number is 1, but what I think the lecturer meant was the negative of natural numbers, so basicly its the set of elements -x, where x is an element of natural numbers
But wouldn't set of " Negative INTEGERS " would have fit well rather than set of negative of natural numbers as INTEGERS already contain them as a part of their Complete Set - It is just that it is less confusing where we mention a SET which is already a part of it instead of Creating a Set that isn't actually there
Hi Tarique - your reasoning only holds in a finite interval - I don't know if you are a student , but when/if you take an analysis course, you will see things differently when these relations are considered over infinite intervals. Look up the definitions of "countable" sets - maybe it will help. cheers
I think at 10:20 he's trying to prove that the rationals don't have the completeness property; e.g. he takes a particular set of rationals and shows that it is not bounded above. He also states that this particular set is not bounded below, although he doesn't actually prove it.
at 25:14 it is not actually an axiom, is it? it is a theorem which can be proven through dedekind's divides (or whatever the hell it is called in english). unless what he actually calls an axiom is the insertion of irrational numbers at all
2:37 - He calls the set of rationals "bigger set" than the set of integers. A careless statement, and not true. The set of rationals is "countable" - There is a one-one correspondence with the set of integers. The set of "Reals" is uncountable, and IS bigger.
friend rationals are surely bigger set than integers because consider 3. 3 is an integer and at the same time rational _can be represented 3/1 which makes it rational..........
There is an error with the representation of the number 1/2 on the line. It should be between 0 and 1, but it is shown to be between 1 and 2 in the video.
I am not abl to express my gratitude to thes lecturers in words.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before.............
I am not abl to express my gratitude to thes lecturers.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before.............
IITs, please involve those who constructively-criticize. Take their help. Ask them if they can (1) volunteer in video-editing, (2) elegant slide preparation for a professor, (3) graphic design for more clarity.
For those who criticize accent (hard to improve):
The primary agenda of NPTEL is to propagate knowledge for Indians. with 400+ mother tougues, there are many variations in english accent, but all indians can understand the lectures. For world-audiences they can try to improve further.
@ ebunny5 we care and appreciate the proffs time only if it values us!!!! He is just an amazing guy in knowledge, but in teaching with the greatest of heart i could give him 35%. Students need real teachers not anybody else!!!
@alexlaur2007: listen we care a lil bit of the guy's accent since it deals with our understang and nothng more!!! If I am a real student i would personally give nothing towards his english if i understand him!!!! But the prob he complicates things thats all!!!!
But please see if you can improve the quality of the writing. The images are not very clear. If the visual form is good it is much easier to focus on the content.
I don't know why people are complaining but I can understand %80 of it so I mean you need to focus what he is talking about, then your brain will handle the rest :) Thanks for the free educational videos. It is like having courses at home...
HEY VIEWERS...Prof Ray is great but i fond another professor who is EXTREMELY GOOD when it comes to teaching CALCULUS if you are interested. copy and paste the following. trust me you won't regret it!......
some people are so ungrateful. the lecturer is taking his valuable time to teach us for free but instead of being thankful, some viewers have nothing but negative things to say.
if you are getting a high paying job opportunity to work abroad or in a global company that deals with multinationals, would you turn it down or would you accept it and adapt to the accents?
please stop being so closed minded. if you cannot understand him, pause and play back but don't be negative or insulting.
It's not that hard to understand him or any of the IIT professors, just focus on what he is saying more. I have had 2 teachers with a heavy accent, so I guess I have gotten used to it
Yes, download them, open them in a movie editing program, and slow it down by a factor of like .9 or so :) You can download them using DVD video soft.
Nice teaching and the Kolkata accent was nice as well! Just one small correction at around 52.00 where he says any S which is a subset of R has a supremum. It should be any S which is bounded above has a supremum. For e.g N which is a subset of R does not have a supremum.
In simple words, he is saying, between any two different real numbers, no matter how close together, there are infinitely many other real numbers. So there is no number larger than any number on the real number line or no number smaller than any number on the real number line
I warned you my fellow Christians, THE END IS COMING! Depart now from all form of unrighteousness such as fornication, homosexuality, pornography, watching violent entertainment, drug abuse, smoking, gambling, cursing, bullying, revelries, pursuit of money and idolatry etc. LEST YOU BE FOUND NOT WORTHY TO ENTER THE KINGDOM OF GOD.
A volcano situated in the US will erupt not far from now, when this happen you will know that this warning is from God.
You must be in a very advanced high school :) I learned some of this in my grade 12 (America), and have extended these ideas in my freshman year of college. My masters degree doesn't include this because it will already have been covered :) More advanced/addictional topics will be covered than real and complex analysis.
You must learn how to talk:)) you said something like this:"the things we learn....is the thing you learn"Correct form:"the things we learn...are the things you learn"
Embarrasingly inept. Why bother videoing these lectures if 1/2 our time is watching Prof Ray writing indecipherable symbols on his acetate. He should have referred to pre-printed & readable lecture notes !!
Much better to read a textbook - this is a tortuous & deeply inefficient way to learn Calculus.
It has nothing to do with depth. I am referring to his pedagogical style. Amongst the worst I have seen. Complete geek unable to communicate or inspire. And wretched handwriting.
It actually has much to do with depth. Did you actually think he was teaching Calculus? Far from it. This would be a class called Analysis of Real Numbers. Inspiration does not come from a teacher but from within. So your statement remains true to you.
That isn't bad, but to truly go over everything he is saying, you need to understand concepts past Calc 3 to prove theorems from Calc 1. Many Calc 1 classes go over some of what he discusses; however, not everything as there is not enough time nor understanding of students yet.
It is not possible to understand advanced calculus or complex analysis without understanding the structure of real numbers & analysis.
However, most of the calculus they teach constitute, application of formulas, few fundamentals, substitutions, logical steps, finding similarities & parallelalities.
Unfortunately, this & other presentations by Dr. Ray is not visible.
I urge him to present a clearer & visible version of his lectures.
Also, please give more examples on the number line.
Seems like a great teacher and very passionate about his profession, too bad I don't know anything about math at this kind of level... I really want to advance my very basic mathematics skills. It's going to take alot of work though.
IMPOSSIBLE to read his handwriting! And worse of all: too often it's impossible to understand his VOCALIZATION of the English language. This is SAD. Because an intro. to Calculus is sorely needed on YouTube. . . . sad sad sad. :(
Pertaining to 13:57. All he is saying is that if we can show there exists some n such that (2r/n + 1/n < 2-(r^2)) then it would follow that 2r/n + 1/(n^2) < 2-(r^2) since 1/(n^2) < 1/n. He ends the proof with an appeal to the Archimedean property to show the existence of such a n.
The lecturer makes a glaring logical error on the slide displayed at 13:54!
Assuming, X = 2r/n + 1/n^2, Y = 2r/n + 1/n and Z = 2 - r^2, then the professor correctly deduces: (1) X less-than Z and (2) X less-than Y ... however, he goes on to make the incorrect deduction that: (1) and (2) => Y less-than Z. That is bad mathematical deduction.
Really did not expect an IIT prof. to make mistakes like these.
You're absolutely right. It is a wrong deduction. I gave up on these lectures a few months ago, cause I simply couldn't get my head around that. I thought I was missing something but I suppose, I wasn't.
I agree. However, having said that, I found other nptel lectures on mathematics quite helpul. Eg. the one on probability and stochastic maths was pretty informative - esp. for me because I use a lot of that in my field.
Oh, I agree. I just am a very slow learner and simply thought I was missing something in his 'deduction'. And I don't have a field of yet but I will continue watching these. Refreshing, really, after 18 years of schooling where I was forces to simply accept anything in a text book, devoid of any logical or mathematical proof. I suppose it's a taste of things to come in university. Anyways, I'm blabbering, thank you for your help.
I think you mis-understood it. He says that if he can find an 'n" such that Y<Z is satisfied, then automatically X<Z will be satisfied. Hope it clarifies.
Please view the playlist titled 'Mathematics in this channel for the complete lecture series in a sequence. Note that the lecture number is given in the description of the video.
I prefer Kahn Academy.
anotherjoe50 1 month ago in playlist Core Science - Mathematics
I Love The Video Lecture 1 Real Number It Can Increase My Knowledge
anakmudajaman 1 month ago
Good, I like that you share this video, I wish success always Lecture 1 - Real Number
AntoMelta 1 month ago
Nice Video That You Share , So Very Nice Thanks You Lecture 1 Real Number
willamricard 1 month ago
I Really Like The Video From Your Lecture 1 Real Number
imegatrone 1 month ago
Your Video Lecture 1 - Real Number Is Very Useful Sharing
bundawartini 1 month ago
If anybody is to grumble, it is about the quality of the video youtube provides.
medwatt 1 month ago
thanku sir.
saikumarmanchalaa 2 months ago
sir i m highly obliged to u sir
pritamprpatil 3 months ago
Science & mathematics are not language dependent subjects.It is our luck that we are living in a world where science has come to extreme point.Thanks to Youtube & thanks to IIT professors because both have quality & both of them giving their attention towards us free of cost.
By the way I would like to mention one drawback of cameraman that his timing is not good,when prof is writing the cameraman should focus on paper on which the prof is writing.
jonmeclon 4 months ago
Comment removed
jonmeclon 4 months ago
Comment removed
jonmeclon 4 months ago
Video is not clear
amdineshkaundal 5 months ago
Negative Natural numbers ?? ---- but aren't natural numbers the ordinary counting numbers 1, 2, 3,...
(or) is it that there is no universal agreement about which set of numbers is designated by the term "natural numbers"!!
psycool666 7 months ago
@psycool666, Math is a language and not just a way of solving problems. In mathematics sometimes you have to define very specifically what you are describing. sometimes it is convenient or necessary to bound natural numbers as all integers greater than or equal to 1 sometimes you need to describe natural numbers as all integers, sometimes all integers other than 0 is useful. it depends on what you are describing. you could say Alaskan winters are cold. or the killer was cold.
happypup70 7 months ago
@psycool666
Negative natural numbers doesn't mean the negative part of the natural numbers. It means the negatives of the natural numbers. Also, names are nothing but convention, and at least in India we call the set of negative numbers the set of negative natural numbers,
ls600h1 1 month ago
@ls600h1
I'm sorry If I sounded Cocky actually I'm a non-math student, and have been interested in math after my college, so a lot of self learning, It is just that these terms are a bit Confusing , Cuz I read that the number "1" was the lowest Natural number, and I definitely don't doubt on what an IIT professor is lecturing on - Cuz Im from India too, maybe it is just that these Terms aren't STRICTLY DEFINED to apply them Universally
psycool666 1 month ago
@psycool666
Well your version of the definition is correct, and the smallest natural number is 1, but what I think the lecturer meant was the negative of natural numbers, so basicly its the set of elements -x, where x is an element of natural numbers
ls600h1 1 month ago
@ls600h1
But wouldn't set of " Negative INTEGERS " would have fit well rather than set of negative of natural numbers as INTEGERS already contain them as a part of their Complete Set - It is just that it is less confusing where we mention a SET which is already a part of it instead of Creating a Set that isn't actually there
psycool666 1 month ago
thank you very much proffessor S.K. Ray. Your lecture is very much appreciated.
kauboibiboppu 8 months ago 3
@19tarique
Hi Tarique - your reasoning only holds in a finite interval - I don't know if you are a student , but when/if you take an analysis course, you will see things differently when these relations are considered over infinite intervals. Look up the definitions of "countable" sets - maybe it will help. cheers
chpsanders 9 months ago
Thanks for the lecture.
humairayouth 9 months ago
I think at 10:20 he's trying to prove that the rationals don't have the completeness property; e.g. he takes a particular set of rationals and shows that it is not bounded above. He also states that this particular set is not bounded below, although he doesn't actually prove it.
mgunar 10 months ago
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mgunar 10 months ago
Comment removed
mgunar 10 months ago in playlist Core Science - Mathematics
great lecture...anyone who doesn't like the lectrure or disagree with the content pls fuck off losers....
u1sewa 1 year ago
at 25:14 it is not actually an axiom, is it? it is a theorem which can be proven through dedekind's divides (or whatever the hell it is called in english). unless what he actually calls an axiom is the insertion of irrational numbers at all
R2rGangstaFC 1 year ago
2:37 - He calls the set of rationals "bigger set" than the set of integers. A careless statement, and not true. The set of rationals is "countable" - There is a one-one correspondence with the set of integers. The set of "Reals" is uncountable, and IS bigger.
chpsanders 1 year ago
@chpsanders
friend rationals are surely bigger set than integers because consider 3. 3 is an integer and at the same time rational _can be represented 3/1 which makes it rational..........
19tarique 9 months ago
8:33
There is an error with the representation of the number 1/2 on the line. It should be between 0 and 1, but it is shown to be between 1 and 2 in the video.
MyOverflow 1 year ago
Thank you so much for this lecture sir. I am most grateful.
jericho4004 1 year ago
This has been flagged as spam show
I am not abl to express my gratitude to thes lecturers in words.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before.............
pranavun 1 year ago
I am not abl to express my gratitude to thes lecturers.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before.............
pranavun 1 year ago
Very important basic proof at 10:20.
Does the set B = {q: q^2 <2 } contain a largest member? Nice job. Simple and clear.
jdbrown371 1 year ago
Great video!
ehecutor 1 year ago
Construction des nombres réels en moins d'une heure !
harakikan 1 year ago
I had this confusion for l.u.b always but after after this lecture everything is very clear thanx a lot
TheSainaba 1 year ago
Good job i don't understand the topic but thats because i'm a high school junior
m8ko 1 year ago
Ref [54:12] Archemidian Property Application (1): (small typo)
I think you meant (1/n < eplsilon) not the other way. (refer [35:16])
BTW: Love the lectures. Keep up the gr8 work
ankurtangirala 1 year ago
...err...doesnt 1/2 go between 0 and 1??? minute 8
pablito12sc 1 year ago
@pablito12sc lol
gerbilsqueex 1 year ago
hey byScrooby, why did u type such a comment at this page? What do u mean by "God's murder"?
mawaddah2010 1 year ago
IITs, please involve those who constructively-criticize. Take their help. Ask them if they can (1) volunteer in video-editing, (2) elegant slide preparation for a professor, (3) graphic design for more clarity.
For those who criticize accent (hard to improve):
The primary agenda of NPTEL is to propagate knowledge for Indians. with 400+ mother tougues, there are many variations in english accent, but all indians can understand the lectures. For world-audiences they can try to improve further.
espre05 1 year ago 2
@ ebunny5 we care and appreciate the proffs time only if it values us!!!! He is just an amazing guy in knowledge, but in teaching with the greatest of heart i could give him 35%. Students need real teachers not anybody else!!!
@alexlaur2007: listen we care a lil bit of the guy's accent since it deals with our understang and nothng more!!! If I am a real student i would personally give nothing towards his english if i understand him!!!! But the prob he complicates things thats all!!!!
crimelife6 1 year ago
This has been flagged as spam show
Research "chemtrails" here on YouTube. Check my vids I film it all the time. Wake up and wake others!
TrutherD1 1 year ago
i love numbers..
PiousPrincess 1 year ago
"God: Hidden Science" - Google it!
byScrooby 2 years ago
Wow, I never understood the contradiction in the proof of root 2 being irrational!
This guy is good :p
sponsoredwalk1 2 years ago
This course is the equivalent of Calculus II & III right?
This course looks as if it will drop heavily off the deep end very quickly...
sponsoredwalk1 2 years ago
Not really, this is concider has a part of Real analysis, also called Adv. Calculus which come after Cal.3
DideeKawaii 2 years ago
It's real analysis, not advanced calculus, nor calculus 3.
It's basically the REAL treatment of calc 1 and 2, complete with proofs.
apoptosis11656 2 years ago
Actually, I think that this corresponds to the very first class of Real Analysis introduction or advanced calculus!
or, at least it is on my university (UNAL, Bogota (Col))
SEBS32 2 years ago
Good and clear explanations.
But please see if you can improve the quality of the writing. The images are not very clear. If the visual form is good it is much easier to focus on the content.
jdrajdrajdra 2 years ago 2
I don't know why people are complaining but I can understand %80 of it so I mean you need to focus what he is talking about, then your brain will handle the rest :) Thanks for the free educational videos. It is like having courses at home...
atarikg 2 years ago
HEY VIEWERS...Prof Ray is great but i fond another professor who is EXTREMELY GOOD when it comes to teaching CALCULUS if you are interested. copy and paste the following. trust me you won't regret it!......
Calculus1 Lecture1
or if you are doing college algebra....
College Algebra - Lecture 1 - Numbers
you won't regret it!
ebunny5 2 years ago
Comment removed
ebunny5 2 years ago
some people are so ungrateful. the lecturer is taking his valuable time to teach us for free but instead of being thankful, some viewers have nothing but negative things to say.
if you are getting a high paying job opportunity to work abroad or in a global company that deals with multinationals, would you turn it down or would you accept it and adapt to the accents?
please stop being so closed minded. if you cannot understand him, pause and play back but don't be negative or insulting.
ebunny5 2 years ago 51
It's not that hard to understand him or any of the IIT professors, just focus on what he is saying more. I have had 2 teachers with a heavy accent, so I guess I have gotten used to it
Arycke 2 years ago 6
whats hee sayingggg
!!!!!!!!!!!
arlinda1101 2 years ago
Does anybody know how to take these videos & make them go in super slow motion..??
please & thanx
pimpinyodaddy 2 years ago
Yes, download them, open them in a movie editing program, and slow it down by a factor of like .9 or so :) You can download them using DVD video soft.
Arycke 2 years ago
thank u =)
pimpinyodaddy 2 years ago 2
Try To Download It with Youtube Downloader Then Slow It Down Hehehe ^_^
deathnote854 2 years ago
Nice teaching and the Kolkata accent was nice as well! Just one small correction at around 52.00 where he says any S which is a subset of R has a supremum. It should be any S which is bounded above has a supremum. For e.g N which is a subset of R does not have a supremum.
ravidesparate 2 years ago
Need help guys: Why does he introduce te relation 1/n2<1/n. I agree on the values but I don't see the logic of it.
mochiam 2 years ago
guys is there a trancript of this lesson. He is a good teacher but his accent is killing me :-)
mochiam 2 years ago
I can understand him I just wish he wrote bigger and clearer. But this is a great supplement to the class.
pizzintea 2 years ago
strangely I can understand his writings but not his vocalisation. But I don't despair I'll get used :-) HAs someone post some notes of the course?
mochiam 2 years ago
go to the nptel website , you will find a web course there too.
luckyankraj 2 years ago
Forget waterboarding, we have a new form of enhanced interrogation!
Tacomadome24 2 years ago
dude this is awesome it is a very well explained art of rational numbers. I am enjoying the facts, the logic, and the math.
ddaggitt107665 2 years ago
Ref: 16 to 17 minutes
In simple words, he is saying, between any two different real numbers, no matter how close together, there are infinitely many other real numbers. So there is no number larger than any number on the real number line or no number smaller than any number on the real number line
alfatourist 2 years ago
For real number do you mean rational plus irrational?
mochiam 2 years ago
This has been flagged as spam show
.
I warned you my fellow Christians, THE END IS COMING! Depart now from all form of unrighteousness such as fornication, homosexuality, pornography, watching violent entertainment, drug abuse, smoking, gambling, cursing, bullying, revelries, pursuit of money and idolatry etc. LEST YOU BE FOUND NOT WORTHY TO ENTER THE KINGDOM OF GOD.
A volcano situated in the US will erupt not far from now, when this happen you will know that this warning is from God.
.
conceil8 2 years ago
Comment removed
alexlaur2007 2 years ago
but the things we learn in our 11 grade is the thing u learn in ur college in masters
iitiansrocks 2 years ago
You must be in a very advanced high school :) I learned some of this in my grade 12 (America), and have extended these ideas in my freshman year of college. My masters degree doesn't include this because it will already have been covered :) More advanced/addictional topics will be covered than real and complex analysis.
Arycke 2 years ago
@iitiansrocks
It's the same in Scotland (or it was when I was a schoolboy). This is secondary school stuff, not "college" mathematics.
And his accent is perfectly clear and understandable!
SLRL1A1 2 years ago
You must learn how to talk:)) you said something like this:"the things we learn....is the thing you learn"Correct form:"the things we learn...are the things you learn"
alexlaur2007 2 years ago
@iitiansrocks what the hell are you talking about? Maybe we're like 2 years behind at most but 11th grade material in masters degree? Absolutely not.
thejugglenaut91 1 year ago
@iitiansrocks ur deluded man...
dis comes from an indian
17thsavior 1 year ago
A must see Xj7sExS-UKw
2009uzzi 2 years ago
It was funny, but i'm not sure it's meant to be.
sirspammer 2 years ago
Embarrasingly inept. Why bother videoing these lectures if 1/2 our time is watching Prof Ray writing indecipherable symbols on his acetate. He should have referred to pre-printed & readable lecture notes !!
Much better to read a textbook - this is a tortuous & deeply inefficient way to learn Calculus.
g1j2k3 2 years ago
No, actually he is just going more in depth into the development of the number system. A little different actually...
Beefstew2011 2 years ago
It has nothing to do with depth. I am referring to his pedagogical style. Amongst the worst I have seen. Complete geek unable to communicate or inspire. And wretched handwriting.
g1j2k3 2 years ago
It actually has much to do with depth. Did you actually think he was teaching Calculus? Far from it. This would be a class called Analysis of Real Numbers. Inspiration does not come from a teacher but from within. So your statement remains true to you.
pizzintea 2 years ago
At my school, this class is called Advanced Calculus.
x1101011x 2 years ago
That isn't bad, but to truly go over everything he is saying, you need to understand concepts past Calc 3 to prove theorems from Calc 1. Many Calc 1 classes go over some of what he discusses; however, not everything as there is not enough time nor understanding of students yet.
pizzintea 2 years ago
1/2 is between 1 and 2 ??? (8:12) this is the first time i heard of ^_^
nuzzleTOO 2 years ago
hahahahahaha
taroooqaa 2 years ago
and 1/3 is between 1 and 3.
MrZhuKeeper 2 years ago
It is not possible to understand advanced calculus or complex analysis without understanding the structure of real numbers & analysis.
However, most of the calculus they teach constitute, application of formulas, few fundamentals, substitutions, logical steps, finding similarities & parallelalities.
Unfortunately, this & other presentations by Dr. Ray is not visible.
I urge him to present a clearer & visible version of his lectures.
Also, please give more examples on the number line.
alfatourist 2 years ago
really good video with good explanations but I couldn't read the handwriting :(
schneemann1991 3 years ago
i made it 1 minuet before i got so bored
dirtyroom1 3 years ago
how is this relavent to calculus this is not calculus calculus is about functions people already know about natural rational numbers etc
MathMikie 3 years ago
please read :"what is mathematics" book then you will come to know the importance.....
Royalshippie 2 years ago
Seems like a great teacher and very passionate about his profession, too bad I don't know anything about math at this kind of level... I really want to advance my very basic mathematics skills. It's going to take alot of work though.
landgrader6 3 years ago 4
IMPOSSIBLE to read his handwriting! And worse of all: too often it's impossible to understand his VOCALIZATION of the English language. This is SAD. Because an intro. to Calculus is sorely needed on YouTube. . . . sad sad sad. :(
Austyg 3 years ago
WOW..this is a gold mine of info. i only wish i was not done with my mathematical studies per my science degree. keep it up Dr!
smokey566 3 years ago 3
Great lectures except that I can't read the darn thing. Too bad.
Isrek1 3 years ago
Prof Ray:
If possible, please redo the same lecture on real numbers at a more fundamental level.
I was a able to understand clearly the first 13 minutes.
I was lost when you entered into bounds..
after which I could not keep up.
santacharlie 3 years ago
Pertaining to 13:57. All he is saying is that if we can show there exists some n such that (2r/n + 1/n < 2-(r^2)) then it would follow that 2r/n + 1/(n^2) < 2-(r^2) since 1/(n^2) < 1/n. He ends the proof with an appeal to the Archimedean property to show the existence of such a n.
Saimerro 3 years ago
This is basically an audio lecture seeing that I can't make out the writing on the board.
rob2edn 3 years ago
i find him hard to understand
mremile72 3 years ago
That's because you watch too much TV.
horneyvirus 3 years ago
The lecturer makes a glaring logical error on the slide displayed at 13:54!
Assuming, X = 2r/n + 1/n^2, Y = 2r/n + 1/n and Z = 2 - r^2, then the professor correctly deduces: (1) X less-than Z and (2) X less-than Y ... however, he goes on to make the incorrect deduction that: (1) and (2) => Y less-than Z. That is bad mathematical deduction.
Really did not expect an IIT prof. to make mistakes like these.
iitzeus 3 years ago
It wasn't meant to be a deduction
He said it "suffices" to find Y instead of X, because, as you say, (1) and (2)
nicejobifyoucangetit 3 years ago
Yes, he said it "suffices" but that doesn't validate any order relation between Y & Z in the above example.
There's no logical way in which one can go from (1) & (2) to Y gt/lt/eq Z. This is precisely the mistake the professor makes in the video.
iitzeus 3 years ago
You're absolutely right. It is a wrong deduction. I gave up on these lectures a few months ago, cause I simply couldn't get my head around that. I thought I was missing something but I suppose, I wasn't.
TintedReasoning 3 years ago
I agree. However, having said that, I found other nptel lectures on mathematics quite helpul. Eg. the one on probability and stochastic maths was pretty informative - esp. for me because I use a lot of that in my field.
iitzeus 3 years ago
Oh, I agree. I just am a very slow learner and simply thought I was missing something in his 'deduction'. And I don't have a field of yet but I will continue watching these. Refreshing, really, after 18 years of schooling where I was forces to simply accept anything in a text book, devoid of any logical or mathematical proof. I suppose it's a taste of things to come in university. Anyways, I'm blabbering, thank you for your help.
TintedReasoning 3 years ago
I think you mis-understood it. He says that if he can find an 'n" such that Y<Z is satisfied, then automatically X<Z will be satisfied. Hope it clarifies.
deepanshu1212 3 years ago
He made no mistake.
He said:
1) X < Y
2) if Y < Z then X < Z
Basically, if he can find an n such that Y < Z, then that n will also work to make X less than Z.
x1101011x 2 years ago
Great lectures and i look and learnt mamy things. Thanks alot
panoxalbar 3 years ago 11
Excellent series of lectures, watched them all.
just two comments:
1) lecture 21 on line integrals seems to be out of sequence
2) There seems to be at least one lecture missing - perhaps on double integration.
Fubini's theorem is mentioned but never discussed.
xgy2 3 years ago
thanx a lot .
u will help me a lot.
coolkanu007 3 years ago
Thanks a lot.
This is true education.
panchtatvam 3 years ago
Excellent summary of the basic properties of Real numbers and how they are derived as well as why they are important. Thanks again!
jonahansen 4 years ago
Good video - thanks! You might want to take a look at 41:00; there is a technical glitch there where the writing doesn't appear.
jonahansen 4 years ago
will u categorized the topics coz mathematics is broad subject. i want to learn calculus, probability.
09185513717 4 years ago
can you give the lectures in a sequence ?..because it is hard to know which is lecture 1 and so on.....
saggisomesh1 4 years ago
Please view the playlist titled 'Mathematics in this channel for the complete lecture series in a sequence. Note that the lecture number is given in the description of the video.
Thanks
NPTEL Web admin
nptelhrd 4 years ago