The Guttering Problem (updated
11/05/02)
In this problem imagine a rain gutter having a trapezoidal cross-section. If the "straightened" length of the cross-section is L then what is the shape of this gutter so that it can carry away the most rain water most effectively.
Answer (pdf 278KB)
In this problem imagine a rain gutter having a trapezoidal cross-section. If the "straightened" length of the cross-section is L then what is the shape of this gutter so that it can carry away the most rain water most effectively.
Answer (pdf 278KB)
Numerical
Iterations: (100KB) - (updated 03/10/01)
My advice is for you to download the files directly to your hard drive by right-clicking on the link and then selecting "Save Target As..." - otherwise the Excel files may not work fully in your browser window!
This Excel 97/2000 file allows the user to numerically solve equations by using either of the following methods:
(1). The Fixed Point Method,
(2). The Secant or Linear Interpolation Method,
(3). The Bisection Method,
(4). The Newton-Raphson Method
What is useful here is that the user simply enters the equation into a particular cell on the worksheet (but without an equal sign in front of the equation) together with either one or two initial conditions in further cells. Then the VBA Code "reads" the required equation and evaluates it at the initial conditions. To then produce further iterations a button is pressed on the worksheet. Thus no copying down of formulae is required.
The idea behind the code came from a VERY useful file, DemoFunctionsInVBA (36KB), kindly given to me by John Stanley in which a variety of functions and the many ways in which arguments are passed into them are investigated. See my Excel Programming page for this and other mathematical programming..
My advice is for you to download the files directly to your hard drive by right-clicking on the link and then selecting "Save Target As..." - otherwise the Excel files may not work fully in your browser window!
This Excel 97/2000 file allows the user to numerically solve equations by using either of the following methods:
(1). The Fixed Point Method,
(2). The Secant or Linear Interpolation Method,
(3). The Bisection Method,
(4). The Newton-Raphson Method
What is useful here is that the user simply enters the equation into a particular cell on the worksheet (but without an equal sign in front of the equation) together with either one or two initial conditions in further cells. Then the VBA Code "reads" the required equation and evaluates it at the initial conditions. To then produce further iterations a button is pressed on the worksheet. Thus no copying down of formulae is required.
The idea behind the code came from a VERY useful file, DemoFunctionsInVBA (36KB), kindly given to me by John Stanley in which a variety of functions and the many ways in which arguments are passed into them are investigated. See my Excel Programming page for this and other mathematical programming..