What is Calculus? In this video, we give you a quick overview of calculus and introduce the limit, derivative and integral.
We begin with the question “Who invented Calculus?” Next, we talk about the two main tools you’ll study: derivatives and integrals. To understand both of these you’ll first learn about limits. After you learn how to compute the derivative and integral for basic functions and apply them to real-world problems, you’ll move up to higher dimensions and study things like “partial derivatives” and “multiple integrals.”
What to watch next:
The Tangent Line & the Derivative
Product Rule for Derivatives
How to Study For a Test
How to Study Physics
How to Study Programming
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Written and Produced by Michael Harrison
Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google for over 5 years before leaving to found Socratica.
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In short, algebra runs into issues when trying to solve problems dealing with infinity and zero. Essentially, when trying to solve infinitesimals with algebra, you run into paradoxes, such as dividing by zero, a function approaching a point that is too small to analyze, or a function resulting in a solution that goes to infinity, or if a function is impossible to solve algebraically, but you need to still know what it does at a certain point. Mathematicians were puzzled by this for thousands of years, and then came calculus, which resolved these paradoxes. Calculus has the power to do what algebra can't; yet, you often cannot solve calculus without algebra! In fact, in Isaac Newton's 'Principia', he used algebra and geometry as proofs for his calculus. They are important to each other, and go hand in hand. If you need to know what a function is doing at an instantaneous point in time (Differential Calculus), you need an approximation over a combination of numbers, or need to know the area under a curve (Integral Calculus), what a function looks like when it goes towards infinity or gets close to a specific number (Infinite Series), or when you still need to know what a function looks like that's impossible or too complex to graph, plot, or solve (Taylor Series/Approximations), then calculus is what you need. It is incredibly powerful, and without it, modern engineering, space flight, air travel, modern medicine, biology, physics, economics, and computer science would not be possible.
Differentiation is used to find the smaller straight lines in a curve by zooming in and integration in simple terms means to add the small lines we've found by using differention , correct me if am wrong.
0:30 i dont understand about functions, what is that, why they have to draw curve like 0:30 , and why does have to start like that? what is that curve for? What is it for? What is the history of that curve? Why do we need to learn curve? Anyone who understand this please reference me a link video to understand. Thank you so big much. May god bless us all.
I consider myself pretty strong in algebra (I'm wrecking it this semester, 95 in the class), and I'm taking pre-calc next semester and have no idea what to expect. I also have to take Calc 1 and Calc 2 (I'm a computer science major). Before this video, calculus was literally just a word to me. I now completely understand what I have to look forward to next fall after pre-calc. Thanks!
Funny thing is I could easily write a program to calculate this, but doing it the math way is difficult. In my Physics class I wrote powershell scripts in class on my laptop to do physics calculations so I could plug in numbers and get answers. The instructor seemed impressed.
It would be nice to get names of presenters, or their 'nom de...videos' (?) so we could refer more directly with the presenter. The woman presenting awesomely hilarious and effective Python vids would become 'Salima' rather than 'the hot chick in blue', and the calculus presenter would be 'George' rather than the 'dude who explains skinny rectangles in calculus'. In either case, more hilarious hot-chick Python vids and more 'skinny rectangle dude' calculus videos please!
how do we find the function itself? this is bugging me. i mean in real life we have to determine the function and the curve right? how do we do it? derivative and integral tells us about what to do AFTER getting the function/equation. but my question is how do we develop the equation or function from say a car travelling at different speeds over a course of time.
I still find it difficult to understand, starting from scratch, there are still a few terms which is assumed that the learner understands. It would be great if even words like derivative and integrals are broken down even further. Thank you very much for the video too!
I've always been really frustrated because we start learning calculus from limits, while no one ever explained to us what we were actually doing. I'm glad I watched this video before finishing highschool! Thanks a lot.
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