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Showing posts from May, 2009

### Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

### How to calculate spring force online I found a very useful web site about computation. Try it and you'll love it.Wolfram|Alpha's long-term goal is to make all systematic knowledge immediately computable and accessible to everyone. We aim to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute whatever can be computed about anything. Our goal is to build on the achievements of science and other systematization of knowledge to provide a single source that can be relied on by everyone for definitive answers to factual queries.Wolfram|Alpha aims to bring expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Our goal is to accept completely free-form input, and to serve as a knowledge engine that generates powerful results and presents them with maximum clarity.Wolfram|Alpha is an ambitious, long-term intellectual endeavor that we intend will deliver increasing capabilities ov…

### Numerical Methods - The Newton-Raphson Method to Solve Mechanical Design Problems Part II In the previous post, we talked about several root finding techniques. In this post, we're going to see how we can use Microsoft Excel VBA to find the roots using Newton-Raphson Method.

As we know that Newton-Raphson Method is the most widely used of all root-locating formulas. The Newton-Raphson method uses the slope (first derivative) of the function to find the root. That means, in the VBA code, we have to find the first derivative of the function in order to find the root. We already have the VBA code to find the first derivative and we're going to use it again in Newton-Raphson Method.

The Newton-Raphson Method uses 2 terms of taylor series to approximate delta x as shown below.

f(x) = f(x0) + (xN - x0)f'(x0) = 0
(xN - x0)f'(x0) = -f(x0)
xN - x0 = -f(x0)/f'(x0)

delta x = -f(x0)/f'(x0)

The followings are the procedure to find the root using Newton-Raphson Method.
Guess the initial value of the root --> select x0Calculate delta x using the formula as shown…

### Numerical Methods - First derivative using Excel VBA code In the previous post, Numerical Methods - First derivative using Excel formula, we know how to calculate the first derivative of functions using formula in Microsoft Excel. In this post, let's see how we can simplify it by using Excel VBA code.

The VBA is just like this.

' ================================================
' Created by Suparerg Suksai
' Mechanical Design Handbook
' http://mechanical-design-handbook.blogspot.com
'
' First Derivative - Numerical Methods
' ================================================

Function f(x As Double) As Double
f = 5 * (x - 3) ^ 3 - 4 * x ^ 2 - Sin(2 * x)
End Function

Function fDeriv(x As Double) As Double
Const h = 0.00001 ' Step size
fDeriv = (-f(x + 2 * h) + 8 * f(x + h) - 8 * f(x - h) + f(x - 2 * h)) / 12 / h
End Function

The highlighted (yellow) text is the function that we want to calculate for the first derivative. We can simply replace it with new function. The remaining code still remains the same.

We have to put…