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.

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.
  1. Guess the initial value of the root --> select x0
  2. Calculate delta x using the formula as shown above
  3. Calculate xN using xN = x0 + delta x
  4. Check whether the error of xN is within the allowable tolerance or not --> abs(xN - x0) < tolerance
Then the VBA code will be like this.

' ================================================
' Created by Suparerg Suksai
' Mechanical Design Handbook
' The Newton-Raphson Method - Numerical Methods
' ================================================

Function f(x As Double) As Double
f=Exp(-x)-x ' This is the function we want to find the root
End Function

Function fDeriv(x As Double) As Double
End Function

Function RootNewtonRaphson(x0 As Double)
End Function

To calculate the root of e-x - x = 0 we then type the following formula in the Microsoft Excel spreadsheet,

In any cell, type "=RootNewtonRaphson(1)", where 1 is the guessing value of the root.
The program will then show the result of 0.567143290409784.

We can recheck the calculation result by entering the following formula into excel,


Then the result is 0. That means one of the roots of of e-x - x = 0 is 0.567143290409784


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