Questions about Calculus, the Mathematics of Change

[Opine]

I am attempting to master the mathematics of Calculus. How long did it take you to work through a Calculus textbook?

So far, I learned about how algebra and geometry are useful tools for describing relationships between static quantities. But we need a new mathematical operation to describe change.

The distance travelled by a car, carrying a family on vacation, for example, has a speedometer that measures instantaneous speed, to which the sum of points adds up to average speed. Can we think of average speed as the sum total of the points between two terminal points, where each point is a different instanteous speed?

I am hoping to develop a true artificial consciousness one day and I'm not sure what I need to study for that. I assume Calculus is one.

 

[DaveC426913]

Even if I were to reveal the truth it would not serve you. As it is due to the very thing that makes us all unique, namely genetics. Even if Michael Jordan were to tell you his secrets it would not serve you in becoming a great athlete.

 

[Pinball1970]

I am attempting to master the mathematics of Calculus. How long did it take you to work through a Calculus textbook?

So far, I learned about how algebra and geometry are useful tools for describing relationships between static quantities. But we need a new mathematical operation to describe change.

The distance travelled by a car, carrying a family on vacation, for example, has a speedometer that measures instantaneous speed, to which the sum of points adds up to average speed. Can we think of average speed as the sum total of the points between two terminal points, where each point is a different instanteous speed?

I am hoping to develop a true artificial consciousness one day and I'm not sure what I need to study for that. I assume Calculus is one.

You not worked it out?

 

[James R]

I am attempting to master the mathematics of Calculus.

Does your super-genius self not already understand Calculus?

How long did it take you to work through a Calculus textbook?

That's not how most people learn Calculus.

So far, I learned about how algebra and geometry are useful tools for describing relationships between static quantities. But we need a new mathematical operation to describe change.

Okay, but bear in mind that time rates of change are only one application of differential calculus.

The distance travelled by a car, carrying a family on vacation, for example, has a speedometer that measures instantaneous speed, to which the sum of points adds up to average speed.

It does not. To calculate an average of a set of numbers, you need to add up the numbers and divide by the number of numbers there are. For example, to find the average of the numbers 4,5 and 7, you calculate: 4+5+7=16 and then divide by 3 (because there are three numbers), to get a result of 5.3333...

Can we think of average speed as the sum total of the points between two terminal points, where each point is a different instanteous speed?

You can think of it that way, but if you do you won't understand what average speed is.

Average speed is just the total distance travelled divided by the time taken. So, if you drive 100 km in your car and it takes 2 hours, then your average speed if 50 km per hour.