Calculus | Math History | N J Wildberger
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- Опубліковано 26 чер 2024
- Calculus has its origins in the work of the ancient Greeks, particularly of Eudoxus and Archimedes, who were interested in volume problems, and to a lesser extent in tangents. In the 17th century the subject was widely expanded and developed in an algebraic way using also the coordinate geometry of Descartes. This is one of the most important developments in the history of mathematics.
Calculus has two branches: the differential and integral calculus. The former arose from the study by Fermat of maxima and minima of functions via horizontal tangents.
The integral calculus computes areas and volumes beyond the techniques of Archimedes. It was developed independently by Newton and Leibnitz, but others contributed too. Newton's focus was on power series, for which differentiation and integration can be done term by term using a formula of Cavalieri, and which gave remarkable new formulas for pi and the circular functions. He had a dynamic view of the subject, motivated in large part by physics.
Leibnitz was more interested in closed forms, and introduced the notation which we use today. Both used infinitesimals, in the form of differentials.
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My research papers can be found at my Research Gate page, at www.researchgate.net/profile/
My blog is at njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!
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Elementary Mathematics (K-6) Explained: / playlist
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Year 9 Maths: • Year9Maths
Ancient Mathematics: • Ancient Mathematics
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Sociology and Pure Mathematics: • Sociology and Pure Mat...
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Math History: • MathHistory: A course ...
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MathFoundations: • Math Foundations
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Famous Math Problems: • Famous Math Problems
Probability and Statistics: An Introduction: • Probability and Statis...
Boole's Logic and Circuit Analysis: • Boole's Logic and Circ...
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Differential Geometry: • Differential Geometry
Algebraic Topology: • Algebraic Topology
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These lectures are FANTASTIC. The professor is an example of an excellent teacher. Good pace, no bells and whistles, and accurate information. Bravo!
Hi, I will be adding some more History of Mathematics videos in a while, and Differential Geometry is likely to be something we discuss. So please check back in a few months.
I just want to express my emotions and gratitude for having this delivered to me for free, in this day and age. (except for my small internet fee) I just realized that having this university level course sent automatically through some wires to anyone on earth is a much grandiose and futuristic utopian thing than, say, landing a few men on the moon.
Very beautifully explained, We need to understand the history to appreciate the subject.These are the contents which you'll never get in books.its really amazing to see how the dots are connected, great Lecture!! tysm sir Wilderberger!!
Thanks for the nice comment Vishwanath.
Vishwanath Teggihalli Very true - Dr Wildberger has done a wonderful service here for the mathematics community of serious teachers and serious students :)
Hi kooky323,
I will be giving some more MathHistory lessons next year, and some will include Number Theory and Abstract Algebra.
These series are of a great values and will remind an important reference to understand the chronology of the field. I hope Dr. Wildberger will post a series of entire mathematical course and concepts with an historical vue because he has the art to explain !
this is awesome..whenever people ask why should I learn calc ill be sending them here. thanks for the content
59 min - Leibniz' notation is very powerful - true, but we mustn't forget that Newton's has its advantages, at least in certain circumstances. Given
y = f(x), there's:
• dy/dx ; d(dy/dx)/dx = d²y/dx² (Leibniz) allows differentials to be treated as mathematical entities in their own right, easing such procedures as implicit differentiation, and pointing the way to differential forms, etc.
It's also essential in making the jump to multi-variate calculus.
df(x,y) = (∂f/∂x)dx + (∂f/∂y)dy
• y' = f '(x); y" = f "(x) (Newton) emphasizes that the result of differentiation is also a function.
This is important in doing physics (Newton's Laws!), where you have, e.g.,
v(t) = x'(t)
a(t) = v'(t) = x"(t)
This is what should be taught in high school. Forget Algebra and Trig -- we need CONTEXT to understand WHAT THE FUCK is being TAUGHT TO US. (Excuse my emotion).
Preparing for my first Calculus course for the upcoming spring. I'm nervous but this lecture helped me understand the big picture. Thanks!
Thank you Dr Wildberger .You have been always very inspirational teacher. Iam a great fan of yours , sir !!!
Thank you SO much! This was infinitely helpful!
Thank you for another excellent lecture Dr. Wildberger! Is there any possibility for some future lectures in Number Theory and Abstract Algebra?
That was perfectly explained. Thanks you!
amazing lecture, the contrast between leibiniz and newton's interpretation is sensational. newtons generalization of barrow's methods is amazing.
This will help a great deal for nationals thank you so much!
I love how rigorous you are, and careful about talking about certain things. Only a mathematician would understand this level of rigor. Getting my BA this year followed by grad school next year in Math!
Excellent video i think you are a great mathematician and a very talentous one!!!
Thank you very much...
Very interesting lecture.
Sir, I really enjoy your lectures. Could you give a lecture on Fundamental Theorem of Calculus?
nice explanation !
This is some real shit.
Dear Professor, Would you please consider giving some talks on differential geometry ??
Great video with lucid and clear explanations as always!!!. Thanx professor.
On the other hand, I would like to know if there is a 'Calculus' video series on your plans. Or if that Math topic is to be covered as a following (part) in one of your other superb Math series.
Isn't very strange that the continued fraction of 4/pi could be in some sence "regular", whereas that of pi is not? Is 4/pi less irrationell than pi?
I thought that log were created to simplify multiplication (instead of multiply 2 huge numbers it were easy to add their log and reverse to get the result...)
Binomial theorem (1+a)^n =/= (1-a)^n or a is +(+a) and -a is -(+a) ? in your integral question i was confused about this question a mines is important or not in BT?
thanks for your Videos.
Who called the 5th postulate the parallel postulate in the first place? It's about lines which are not parallel isn't it? By the way I am really enjoying these lectures, thanks.
Did you noticed Wildberger leaving on the right side and returning on the left? That room has to have the group structure of a circle!
22:37 The two small triangles are NOT similar: one has a right angle and the other, not.
But if the ratio of the two large initial triangles is, say k, then the same ratio holds for the smaller triangles made with the same parallel (to the common line defining a side of the triangle) cutting the two triangles, each smaller triangle being proportional to its larger parent.
Smaller increments should be written as Delta x not as dx where Delta refers to small triangle.
Whose quartet is it in the beginning?
+countersubject889 Haydn's "Fifths" Quartet (Op. 76 No 2).
is this calc 1 or.
*or 2
Rob Robstein is teaching Calculus now??
Im only in 9th grade and find this easy...
The real story of calculus here:
ua-cam.com/video/VfWJ7yxT0aA/v-deo.html
the zeta Reimann hypothesis just for the beautiful minds , but ALLAH knows the solution , thus He is the great mind .
oh dear..............
I like your Videos but you didnt mention any Indian contributions to calculus whereas small bits here and there done by greeks were mentioned in video description.
Considering pioneering things done by Indians like world's first infinite series expansion of trigonometric and inverse trigonometric functions,taylor series,early methods of differentiation,integration,knowledge of derivative vanishing at extreme etc,it is extremely improper to not mention them in video which tries to shed light on historical development of calculus.
I must say that I am extremely frustrated by western approach to history of science and math where this subject is treated as domestic western affair!
I watched your video on Indian contributions but still it was super compact thing which tried to explain indian,chinese,arabian contributions to math in less than 2 lectures while only greek math got more than 4 lectures.
Even sensible and honest people like you are not free from unconscious biases which are ingrained in such academic disciplines.