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You are not logged in. #1 20130105 15:04:07
The Structural Analysis  mathematics of the futurePart one. Introduction. "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #2 20130105 20:08:22
Re: The Structural Analysis  mathematics of the futurehi 21122012 You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20130105 22:46:20
Re: The Structural Analysis  mathematics of the futureThe integral at the bottom is incorrect. It needs the integration constant C. 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 20130106 00:58:29
Re: The Structural Analysis  mathematics of the futureWatch longer, Stefy. He puts in definite limits. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #5 20130106 01:44:11
Re: The Structural Analysis  mathematics of the futureHi 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 #6 20130106 06:03:50
Re: The Structural Analysis  mathematics of the futureHi bob. "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #7 20130106 06:08:30
Re: The Structural Analysis  mathematics of the futurehi You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #8 20130106 06:17:23
Re: The Structural Analysis  mathematics of the futureI want to notice that the left drawing has bottom and top limits is two values: because:
While let only look. It has to be postponed in subconsciousness then to associate with the told Last edited by 21122012 (20130106 06:23:19) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #9 20130106 06:22:29
Re: The Structural Analysis  mathematics of the future
What is f ? You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20130106 06:25:03
Re: The Structural Analysis  mathematics of the future
I there added. That absolutely correctly there had to be two blue points and any red. Last edited by 21122012 (20130106 06:53:17) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #11 20130106 06:46:36
Re: The Structural Analysis  mathematics of the futurePlease use the edit button to add to posts. Multiple posts to yourself are difficult to follow. 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. #12 20130106 10:35:07
Re: The Structural Analysis  mathematics of the futureIf a formula: to represent in the form of segment of the line: which will be expressed by a formula: that the bottom limit  value of argument: of the function , the top limit  value of argument: of the function . The first point of a segment of line  value of a derivative: , the last point of a segment of line  value of a derivative: . The line on which located the segment of line has a formula: . If all line  f (t): And if the line consists more than of one part: or P.S. Last edited by 21122012 (20130106 11:58:51) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #13 20130106 11:47:59
Re: The Structural Analysis  mathematics of the futureThen, what is the integral of f(x)=x? 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 #14 20130106 11:57:21
Re: The Structural Analysis  mathematics of the future
This phrase has in itself no concept of integral. Write a formula. Last edited by 21122012 (20130106 12:03:24) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #15 20130106 12:03:10
Re: The Structural Analysis  mathematics of the futureI think you know well what I mean.. 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 #16 20130106 12:06:09
Re: The Structural Analysis  mathematics of the future
Last edited by 21122012 (20130106 12:15:06) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #17 20130106 12:15:06
Re: The Structural Analysis  mathematics of the futureThe first one. 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 #18 20130106 12:16:45
Re: The Structural Analysis  mathematics of the future
What exactly do you want to learn about this integral? It is a half of the area of a square. Last edited by 21122012 (20130106 12:19:08) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #19 20130106 12:20:31
Re: The Structural Analysis  mathematics of the futureWell I think it will be x^2/2+1000. 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 #20 20130106 12:33:21
Re: The Structural Analysis  mathematics of the future
For example so? Last edited by 21122012 (20130106 12:41:35) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #21 20130106 20:11:49
Re: The Structural Analysis  mathematics of the futurehi 21122012,
I think this means: If this is correct, then I understand post #8. Now I review post #12.
I call this "integration by change of variable": I understand this. Then
Did you mean ? I think you are saying: "Use a partial sign when the integral is indefinite" Is this correct ? I regret that I do not understand the diagram in post #14 . Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #22 20130107 06:42:47
Re: The Structural Analysis  mathematics of the futureHi Bob
Sense of written in post#8  is represented on the chart in post #14 !!! image as a function increment: in the form of the sum: of identical points is used: The distance between the next points will be equal: In the Cartesian system of coordinates the distance between the next points equal is used then points from which the segment of line consists are: Points of a piece are inadequate and matter equal to value of derivatives at argument change. Bob, look this animation. When on the right the green segment of line increases in a size at one a point up at the same time on the right its equivalent the area of a circle increases by one circumference and so up to the end: more and more points in a segment of line  more and more circumferences in a circle. Circumferences of the various size  a points of various value. In the beginning the circumference is equal to zero  the point is equal to zero. At the end the circle is equal to a maximum  a point same.
Part second. Geometrical and graphic interpretation of concept a derivative on the example of function If it is badly visible it is possible to look here. Last edited by 21122012 (20130107 17:15:35) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #23 20130107 19:31:44
Re: The Structural Analysis  mathematics of the futurehi 21122012 You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #24 20130108 01:19:55
Re: The Structural Analysis  mathematics of the futureHi 21122012 I have made a spreadsheet using Excel. The first row shows values of 'r' from 0 to 1 in steps of 0.1 The second row shows values of f(r) = pi r^2 The third row uses the trapezium rule to calculate (approximately) the area of each section. The fourth row adds these up to give the area under the graph of f(r) Using the final value as a correct volume of a cone I calculated the height of the cone. The fifth row shows the height for each r value. The final row shows the volume, calculated using the correct formula. As expected this value agrees with your area under graph calculation for the final column (P). This should happen because I used the coluimn P values to compute 'h'. But it does not show that your area under graph figures are correct. So the integration at the start of this post does not give correct volumes. Why do you think this is ? Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #25 20130108 02:22:39
Re: The Structural Analysis  mathematics of the futureHi Bob;
You do not have to worry about that. It will be posted again 26 more times over 3 threads. 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. 