The Essence Of Calculus (Review)
A Review Of The YouTube Series - The Essence of Calculus
https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
I am studying A Level Maths this year and A Level further Maths next year so I am relatively good at Maths. Calculus is a topic which I feel comfortable doing and I can get the questions right.
Most of the time however, I am just plugging numbers into formulas and memorizing rules without actually appreciating whats going on.
When I was initially taught calculus I was given brief explanations but the series has helped me a lot because it has given me multiple ways to actually understand what was going on and why the rules and formulas work.
For anyone learning Calculus, I highly recommend watching episodes 1, 2, 3, 7, and 8. These give great ways to understand and visualize differentiation and integration mainly using shapes and graphs.
For the more advanced people who have learnt about: the chain rule, product rule, implicit differentiation and exponentials (these are covered in C3 and C4 on my exam board), I recommend watching all the videos.
Before, the reasoning behind why all these rules worked was quite fuzzy but now I actually understand what's going on. I particularity enjoyed the product rule video because the use of shapes made it very easy to understand what was happening.
Episode 10 covered a further Maths topic which I hadn't studied yet so was more challenging to understand. The video still gave me a decent understanding where I feel when I do cover the topic; I will easily be able to grasp it. I don't think the video is necessary to watch but will still aid your overall understanding.
The series is pretty much 3 hours long which may seem long and did put me off initially. If you can just find 20 minutes a day to watch 1 video however; I definitely think it will be worth your time.
The Paradox Of The Derivative (A Very Brief Insight Into The Series)
Just to give you an idea of what the series is like; I will talk about the paradox of the derivative covered in episode 2.
Think about a distance time graph.
You know the gradient gives the speed.
Now lets think about what gradient means. It means the change in the y values divided by the change in x values (some of you might think of this as rise/run).
Now think about what speed means. It means how far something travels over a given amount of time.
So if I asked you what is the speed at a point in time you could find the derivative of the distance-time curve and tell me what the speed is at a time (same as what the gradient of the curve is).
Yes?
But how can something have a speed at a single moment?
But we just defined speed as a distance traveled in a given time (Distance traveled divided by time = speed). At an instantaneous point in time the car doesn't travel any distance so how can we say how fast it is traveling?
Also if we want to find the gradient. How can we find a gradient when we only look at a single point? To calculate the gradient we need the change in y values and the change in x values. At a single point there are no changes though.
From this we can see it seems wrong to say a point has a gradient and yet it is what people believe when they do calculus questions.
For the answers to these kind of questions check out the series. The link is given again below.
https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
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