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 I

Machine designers have to deal with several number of equations in their design projects. There are a number of ways to solve for roots of algebraic and transcendental equations. Sometimes, the roots could be obtained by direct methods. However, there are many more that could not. The classical equation such as f(x) = e-x - x cannot be solved analytically. For this case, the only alternative is an approximate solution technique.

There are several methods available to solve the root finding problem such as "bracketing methods" and "Open methods".

The bracketing methods require 2 initial guesses for the root. These guesses must "bracket" the root. The numerical methods using bracketing methods consist of the following techniques:
  • The Bisection Method: The idea of this technique is incremental search that related to the sign change. Sometimes, this technique is called binary chopping, or Bolzano's method.
  • The False-Position Method: It's the improved technique from the bisection methods. It replaces the curve f(x) by a straight line and gives a false-position of the root. The false-position method is also called the linear interpolation method.
However, my favorite technique in root finding method is not the bracketing methods but the open methods.

The bracketing methods are said to be convergent. In contrast, the open methods are based on formulas that require a single starting value of x. They sometimes diverge. However, when the open methods converge they usually do so much more quickly than the bracketing methods.

The followings are the root finding techniques using open methods.
  • Simple One-Point Iteration
  • The Newton-Raphson Method: 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. It's my favorite one.
  • The Secant Method: Instead of using the first derivative of the function to find the slope as in The Newton-Raphson Method, the first derivative in secant method can be approximated by a finite divided difference.
In the next post, let's see how we can use Microsoft Excel VBA again to solve the root finding problems using the Newton-Raphson Method. I'll show you the simple VBA code that you can copy & paste into your excel file and use it as the module to calculate for the root of your equation.


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