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### Defining Homogeneous and Nonhomogeneous Differential Equations

In order to identify a nonhomogeneous differential equation, you first need to know what a homogeneous differential equation looks like. You also often need to solve one before you can solve the other. [more…]

### Using the Method of Undetermined Coefficients

If you need to find particular solutions to nonhomogeneous differential equations, then you can start with the method of undetermined coefficients. Suppose you face the following nonhomogeneous differential [more…]

### How to Work with Probabilities on the TI-84 Plus

You can use the TI-84 Plus graphing calculator to calculate probabilities such as permutations and combinations and to generate random integers and decimals. Do you need to calculate the number of ways [more…]

### How to Start and Quit Probability Simulation on the TI-84 Plus

With the Probability Simulation application that comes preloaded on the TI-84 Plus family of calculators, you can simulate many common activities, like rolling dice. As the application performs simulations [more…]

### How to Use Probability Simulation on the TI-84 Plus

Before you toss coins, roll dice, pick marbles, spin spinners, or draw cards, you need to know how to access the commands at the bottom of the TI-84 Plus Probability Simulation screen, how to seed the [more…]

### How to Simulate Rolling Dice on the TI-84 Plus

The Probability Simulation application on the TI-84 Plus calculator can simulate rolling from one to three dice at a time. It can even roll weighted dice. When rolling only one die at a time, the application [more…]

### How to Save Probability Simulation Data on the TI-84

The data that appears in any Probability Simulation table on the TI-84 Plus can be saved to lists so that you can, after exiting the application, statistically analyze this data. [more…]

### Probability Simulation Settings Editor on the TI-84 Plus

The Probability Simulation on the TI-84 Plus application contains four simulators (Tossing Coins, Rolling Dice, Picking Marbles form an urn, and Spinning a Spinner) that work much the same way. Some information [more…]

### How to Simulate Tossing Coins on the TI-84 Plus

The Probability Simulation application on the TI-84 Plus graphing calculator can simulate tossing from one to three coins at a time. It can even toss weighted coins. When tossing only one coin at a time [more…]

### How to Simulate Picking Marbles on the TI-84 Plus

The Probability Simulation application on the TI-84 Plus can simulate picking one marble at a time from an urn that contains from two to five different types [more…]

### How to Simulate Spinning Spinners on the TI-84 Plus

The Probability Simulation application on the TI-84 Plus can simulate spinning a spinner that is divided into two to eight sections of equal or unequal areas. It will not simulate the spinner landing on [more…]

### How to Simulate Drawing Cards on the TI-84 Plus

The Probability Simulation application on the TI-84 Plus can simulate drawing a card from one to three decks of cards. It even allows you to specify whether or not the card is placed back in the deck before [more…]

### How to Use Arithmetic Vector Operations in R

One set of arithmetic functions in R consists of functions in which the outcome is dependent on more than one value in the vector. Summing a vector with the [more…]

### The Benefits of Using R

Of the many attractive benefits of R programming language, a few are easy to recognize. It’s actively maintained, it has good connectivity to various types of data and other systems, and it’s versatile [more…]

### How to Perform Multiple Calculations with Vectors Using R

R is a vector-based language. You can think of a *vector*as a row or column of numbers or text. The list of numbers {1,2,3,4,5}, for example, could be a vector. Unlike most other programming languages, R [more…]

### How to Repeat Vectors in R

In R, you can combine a vector with itself if you want to repeat it, but if you want to repeat the values in a vector many times, using the c() function becomes a bit impractical. R makes life easier by [more…]

### How to Construct Vectors in R

A *vector* is the simplest type of data structure in R. The R manual defines a vector as “a single entity consisting of a collection of things.” A collection of numbers, for example, is a numeric vector [more…]

### How to Store and Calculate Values in R

Using R as a calculator is very interesting but perhaps not all that useful. A much more useful capability is storing values and then doing calculations on these stored values. [more…]

### How to Vectorize Your Functions in R

Vectorized functions are a very useful feature of R, but programmers who are used to other languages often have trouble with this concept at first. A *vectorized* [more…]

### How to Put Arguments in Your R Functions

Most functions in R have arguments that give them more information about exactly what you want them to do. If you use print("Hello world!"), you give the argument [more…]

### How to Install, Load, and Unload Packages in R

You install a package in R with the function — wait for it — install.packages(). Who could’ve guessed? So, to install the fortunes package, for example, you simply give the name of the package as a string [more…]

### How to Do Basic Arithmetic in R

Since R is statistics platform, it has a rather complete set of arithmetic operators, so you can use R as a fancy calculator if the need arises. [more…]

### How to Round Off Numbers in R

Although R can calculate accurately to up to 16 digits, you don’t always want to use that many digits. In this case, you can use a couple functions in R to round numbers. To round a number to two digits [more…]

### How to Use Mathematical Functions in R

In R, of course, you want to use more than just basic operators. R comes with a whole set of mathematical functions. R naturally contains a whole set of functions that you’d find on a technical calculator [more…]

### How to Change Values in a Vector in R

Changing values in a vector in R is actually pretty simple. To illustrate, let’s assume that you created two vectors containing the number of baskets that Granny and Geraldine made in six basketball games [more…]