- #1
Justin LaRose
- 17
- 3
Hello,
This is not a homework problem, but a worked example I encountered from Hobson and Riley 3e pg 60, if anyone has the book. If not I took a screen shot. [I actually just decided to post the photos on a blog so no one has to download anything]. http://justinphysicsforums.blogspot.com/2015/10/integration-from-first-principals.html
Okay here's the problem, they go ahead and give a formula for integration from first principals, and they make each rectangle an equal width h, and then they go to say without explanation that the Kth rectangle has an area of
(kh)^2h = k^2h^3
This is the first thing that makes no sense to me.
The second part that doesn't make sense to me is how they change the index in the summation and then I haven't thought too much about anything that follows. They give this formula for the Sum (before taking the limit as n tends towards infinity)
I am having a hard time writing the formula, I am just going to include a picture.
So essentially they are using this formula in the specific example shown in the picture and then I'm just lost as to what they actually did mathematically. I could go back to an easier calculus book and understand this but it would be nice to understand what mathematics they are actually using, because this book gets more and more advanced (I am using it to get ready for Lagrangian and Hamiltonian mechanics as well as quantum mechanics next semester, studying independently).
Any help would be appreciated very much, I am just going to go on, I hope someone can sort of break this down for me because I know calculus and this isn't the easiest way to write this at all, it's making me question this book, I just wanted to review calculus quickly before getting into other things.
Alright thanks,
Justin
This is not a homework problem, but a worked example I encountered from Hobson and Riley 3e pg 60, if anyone has the book. If not I took a screen shot. [I actually just decided to post the photos on a blog so no one has to download anything]. http://justinphysicsforums.blogspot.com/2015/10/integration-from-first-principals.html
Okay here's the problem, they go ahead and give a formula for integration from first principals, and they make each rectangle an equal width h, and then they go to say without explanation that the Kth rectangle has an area of
(kh)^2h = k^2h^3
This is the first thing that makes no sense to me.
The second part that doesn't make sense to me is how they change the index in the summation and then I haven't thought too much about anything that follows. They give this formula for the Sum (before taking the limit as n tends towards infinity)
I am having a hard time writing the formula, I am just going to include a picture.
So essentially they are using this formula in the specific example shown in the picture and then I'm just lost as to what they actually did mathematically. I could go back to an easier calculus book and understand this but it would be nice to understand what mathematics they are actually using, because this book gets more and more advanced (I am using it to get ready for Lagrangian and Hamiltonian mechanics as well as quantum mechanics next semester, studying independently).
Any help would be appreciated very much, I am just going to go on, I hope someone can sort of break this down for me because I know calculus and this isn't the easiest way to write this at all, it's making me question this book, I just wanted to review calculus quickly before getting into other things.
Alright thanks,
Justin