# 2 posts tagged with "Math"

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## Johns Yu's Apps 2

The following blogposts were written by John Yu for apps he had created on MecSimCalc. John Yu was a student researcher working with MecSimCalc for 8 months. We will miss you John!

## Algebraic Operation on Complex Numbersโ

This blog post is dedicated to the Algebraic Operation on Complex Numbers app created by John Yu.

The Algebraic Operation on Complex Numbers app is intended for students taking a linear algebra course. This app helps students better grasp how operations are performed with complex numbers. The app lets you perform 4 types of operations: addition, subtraction, multiplication, and division. Addition and subtraction using complex numbers is best performed using vectors and the app walks users through the steps using visual aids. Multiplication and division using complex numbers is best performed using euler form and the app provides excellent visual aids to assist students in learning the step-by-step process. Learning how to perform operations on complex numbers is very important for any engineering student. Complex numbers have many practical applications particularly in electrical and computer engineering where these skills will be invaluable. Students who use this app will find themselves better prepared for their future engineering courses.

## Understanding Vector Fieldsโ

This blog post is dedicated to the Understanding Vector Fields app created by John Yu.

The Understanding Vector Fields app lets you visually generate a vector field. The app takes in an equation representing your vector field and plots each vector on a graph. It is useful in a variety of applications. Vector calculus is a very important skill and many engineering students take a calculus class dedicated to this subject. You can plot simple equations like the flow of a river with the equation . You can plot more complicated vector fields like a magnetic field using the equation .

## John Yu's Apps

The following blogposts were written by John Yu for various apps he had created on MecSimCalc.

## Pairwise Testing Generatorโ

This blog post is dedicated to the Pairwise Testing Generator app created by John Yu.

### About the Pairwise Testing Generatorโ

The pairwise testing generator is an app that can generate a set of test cases with up to 5 independent variables. The app uses a technique called Taguchi Orthogonal Arrays such that every pairing of variables appears in at least one test case. This method is significantly more powerful and more efficient compared to brute-force testing. You can get full testing coverage of your program using significantly less test cases. This can save you a lot of time and a lot of money depending on the size of your program.

### Why I made this appโ

Software testing is a critical step in the software development lifecycle. There are countless opportunities for mistakes and defects to come up at any point in the development of software. Fixing code is equally as important as creating code. Finding these bugs early in the development lifecycle will help to mitigate issues that come up later. The hard part of testing code is generating test cases. Full code coverage often comes with a huge set of test cases which is expensive and time consuming. A small set of test cases is cost effective but lacks code coverage. I made this app to help software engineers generate test cases that can provide adequate code coverage in a reasonable amount of test cases. This saves you a lot of time and money and improves the quality of your code.

## Simple Linear Regression and Discrete Probability Distributionโ

This blog post is dedicated to the Simple Linear Regression and Visualizing Discrete Probability Distributions apps created by John Yu.

### About the Simple Linear Regression and the Discrete Probability Distribution Appโ

The simple linear regression app can generate a regression line from your set of data points. The app is intended to be a helpful tool for Statistics students to understand how the linear regression line is calculated. There are no statistical libraries used in the calculation of the regression line. All calculations are done using equations from my statistics textbook. The app will calculate the regression line as well as show you how the calculation is performed. In statistics, there are many formulas that can calculate a regression line. This app uses the simplest equation to help students gain a better understanding of how the regression line is calculated.

The Discrete Probability Distribution app can visualize common probability distributions in Statistics. This app is intended to be a helpful tool for students taking Statistics to understand how these probability distributions work. The user can play around with the parameters of the distributions defined in the app inputs to understand how these parameters impact the graph.

## Truth Table Generatorโ

This blog post is dedicated to the Truth Table Generator app created by John Yu.

### About the Truth Table Generator Appโ

The truth table generator is an app that can generate a truth table by defining a logical expression. You can define a logic expression simply by typing it into the app inputs. The app will evaluate your expression with each possible combination of inputs and return the expected output. This app is intended to be used by students taking a digital logic class who need to quickly generate a truth table. Sometimes a logic expression may be very complicated to evaluate by hand. This app can generate a truth table with any expression no matter how complicated it is. Students will find this app by helpful for verifying your truth table. The app has been tested multiple times to ensure that the expected outputs are correct.