Calculus is a very advanced branch of mathematics usually taught to engineers and scientists in their first year of university and is really only important to a beginner robot builder at the very advanced stage if you are deeply involved in machine learning and deep learning with artificial intelligence.
Most people in AI suggest that there are 3 main types of mathematics that you must learn with calclus being one of them along with linear algebra, statistics and probability.
So lets go on to describe what calculus is and why it is important to robotics and other fields of study.
The word itself calculus comes from the Latin word for pebbles and dates back to the 1600s.
Basically the Romans used to put pebbles on an abacus as a way to do basic arithmetic and mathematics.
So the word is related to our everyday adding macines which were called calculators.
For some strange reason you may also notice that dentists in the last 20 years have started to refer to the buildup on your teeth not just plaque but calculus. Ask your dentist why because I have no idea.:)
Now Calculus is a branch of mathematics that is all about motion and the change of motion.
We will soon get into what that means and perhaps we will talk about the importance in using calculus in describing motions of space capsules and such but lets try to get it into simpler terms.
Why use calculus.
Well…the main reason with robotics and machine learning is data.
Ai generates millions and millions of pieces of data and the essence of AI is to be able to make sense of the data and predict what to do based on studying and analyzing what this data has shown up to that point and beyond.
Anyone who has every collected a large number of pieces of data either in a science experiment in grade 6 or in a fortune 500 company will amost immediately start putting this data onto a graph.
Now we will soon find out that graphs are an important part of calculus because mathematicians want to study these graphs of millions of pieces of data and measure them and the rate of change of that data and somehow make sense out of it.
So one simple use of calculus is to make sense of vast amounts of data often shown in a graphical form.
So to simplify things lets mention some real world examples of why people use calculus;
- – ROBOTICS in AI we just mentioned that there is a need to study and analyze vast amounts of data
- – ECONOMICS – in Economics there is also a need to study data and how the numbers in an economy are changing
- – ARCHITECTURE – when building a wire span bridge there is a need to determine the length of the wire between the various join parts and perhaps how they will react with high wind and bridge movement
- – SPACE- engineers need to plot the trajectory of space ships and other flying crafts and this particular field seems to use calculus more than any other
- – STOCK MARKET – huge amounts of financial data needs to be studied and profit forecasted
- – SPORTS BETTING – again huge statistics are compiled and there is a need to predict or use probability along with calculus to make sense of this data
Now there are two main branches of calculus those being differential calculus and integral calculus and you will also see these terms thrown around: functions, limits, derivatives, theorems, areas under curves, tangents and more.
Now lets get into trying to explain these two main branches of calculus and keep in mind that you should have at least a basic background in algebra where you use terms like x and y and x squared and having a long line of these variables including when they are in a division form.
You will soon start drawing a handful of special symbols that are specific to calculus that look like a long S shape and arrows pointing to the right and alot of functions with variables in brackets over top of other functions with variables in brackets.
If you picture the hollywood movie with the actor Russel Crow called Beautiful Mind where he had chalkboards full of data and equations then that is what you are in for.
Or any time there is a picture of Einstein near a chalkboard that is what you will get.
Now it is certainly difficult at the advanced stages but its not that hard to do some basic integration and differentiation….if you really feel you must. And I suspect that 95% of us don’t need to worry about it unless you are an engineer already.
For now we are just hoping to get you comfortable with the words and you can decide if you want to go to other sites or courses to actually learn it.
Again, you don’t need calculus for building robots unless you are already an engineer and you are creating new forms of deep learning. Most AI that you will need to use will already be written or in the cloud and you will just be calling upon other peoples code.
But you don’t want to sound like a dummy if you are in a room with engineers and they are throwing around all kinds of calculus terms and making reference to tensorflow, open CV and neural links based on newtonian physics!