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You are not logged in. #1 20130111 17:59:45
Introduction to IntegrationHere is a draft of my Introduction to Integration "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20130111 19:06:56
Re: Introduction to Integrationhi MathsIsFun
Replace with eg. "Integration can be used in many ways such as to find volumes and to calculate, for example, centres of gravity, but it is easiest to start with finding the area underneath the graph of a function like this: " You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20130111 19:25:43
Re: Introduction to IntegrationHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20130111 20:51:59
Re: Introduction to IntegrationHi Bob, good suggestion. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #5 20130111 22:39:46
Re: Introduction to Integrationhi Stefy
What! Why have I spent weeks trying to get 21122012 to do calculus properly. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20130111 22:46:21
Re: Introduction to Integrationhi MathsIsFun You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20130112 01:57:09
Re: Introduction to IntegrationHi MIF; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #8 20130112 03:49:06
Re: Introduction to Integration
They are not inverse in the sense a function is inverse. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130112 07:12:18
Re: Introduction to IntegrationI use the word "reverse". "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #10 20130112 07:35:36
Re: Introduction to IntegrationThe tap/tank example is a great analogy for integration! Big stuff made out of smaller stuff it's all Calculus! The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #11 20130112 07:40:44
Re: Introduction to IntegrationHi MIF; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 