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### Completing the Square for Conic Sections

When the equation of a conic section isn't written in its standard form, completing the square is the only way to convert the equation to its standard form. The steps of the process are as follows: [more…]

### Finding the Key Parts of All Hyperbolas

A *hyperbola* is the set of all points in the plane such that the difference of the distances from two fixed points (the *foci*) is a positive constant. Hyperbolas always come in two parts, and each one is [more…]

### Rules for Adding and Subtracting Matrices

To add or subtract matrices, you have to operate on their corresponding elements. In other words, you add or subtract the first row/first column in one matrix to or from the exact same element in another [more…]

### Logarithm Basics

*Logarithms* are simply another way to write exponents. Exponential and logarithmic functions are inverses of each other. For solving and graphing logarithmic functions [more…]

### Pre-Calculus Workbook For Dummies Cheat Sheet

Pre-calculus uses the information you know from Algebra I and II and ratchets up the difficulty level to prepare you for calculus. This cheat sheet is designed to help you review key formulas and functions [more…]

### The Most Important Derivatives and Antiderivatives to Know

The table below shows you how to differentiate and integrate 18 of the most common functions. As you can see, integration reverses differentiation, returning the function to its original state, up to a [more…]

### The Sum Rule, the Constant Multiple Rule, and the Power Rule for Integration

When you perform integration, there are three important rules that you need to know: the Sum Rule, the Constant Multiple Rule, and the Power Rule.

The Sum Rule for Integration tells you that it’s okay to [more…]

### How to Solve Compound Functions Where the Inner Function Is *ax* + *b*

Some integrals of compound functions *f*(*g*(*x*)) are easy to do quickly in Calculus. These include compound functions for which you know how to integrate the outer function [more…]

### Solve Compound Functions Where the Inner Function Is *ax*

When figuring Calculus problems, some integrals of compound functions *f* (*g*(*x*)) are easy to do quickly. These include compound functions for which you know how to integrate the outer function [more…]

### Integration by Parts with the DI-agonal Method

The DI-agonal method is basically integration by parts with a chart that helps you organize information. This method is especially useful when you need to integrate by parts more than once to solve a problem [more…]

### How to Solve Integrals with Variable Substitution

In Calculus, you can use variable substitution to evaluate a complex integral. Variable substitution allows you to integrate when the Sum Rule, Constant Multiple Rule, and Power Rule don’t work. [more…]

### How to Use Integration by Parts

When doing Calculus, the formula for integration by parts gives you the option to break down the product of two functions to its factors and integrate it in an altered form. To use integration by parts [more…]

### Calculus II For Dummies Cheat Sheet

By its nature, Calculus can be intimidating. But you can take some of the fear of studying Calculus away by understanding its basic principles, such as derivatives and antiderivatives, integration, and [more…]

### Understanding Infinite Series in Calculus

In calculus, an *infinite series* is "simply" the adding up of all the terms in an infinite sequence. Despite the fact that you add up an infinite number of terms, some of these series total up to an ordinary [more…]

### Evaluating Limits in Calculus

The mathematics of limits underlies all of calculus. Limits sort of enable you to zoom in on the graph of a curve — further and further — until it becomes straight. Once it's straight, you can analyze [more…]

### Calculus: How to Solve Differentiation Problems

In calculus, the way you solve a derivative problem depends on what form the problem takes. Common problem types include the chain rule; optimization; position, velocity, and acceleration; and related [more…]

### Calculus: Techniques of Integration

You'll find that there are many ways to solve an integration problem in calculus. The following list contains some handy points to remember when using different integration techniques: [more…]

### Solving Integration Problems in Calculus

Calculus riddle: What do the Mean Value Theorem, the Washer and Shell Methods, and the Arc Length and Surface of Revolution formulas have in common? They all involve integration. Integration is very fancy [more…]

### Calculus Workbook For Dummies Cheat Sheet

To effectively work through calculus problems, you have to understand a number of topics: the process of evaluating limits, methods of solving various differentiation and integration problems, and the [more…]

### Classifying Differential Equations by Order

The most common classification of differential equations is based on order. The order of a differential equation simply is the order of its highest derivative. You can have first-, second-, and higher-order [more…]

### Distinguishing among Linear, Separable, and Exact Differential Equations

You can distinguish among linear, separable, and exact differential equations if you know what to look for. Keep in mind that you may need to reshuffle an equation to identify it. [more…]

### 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…]

### Differential Equations For Dummies Cheat Sheet

To confidently solve differential equations, you need to understand how the equations are classified by order, how to distinguish between linear, separable, and exact equations, and how to identify homogenous [more…]

### How to Do an Area Approximation Using Sigma Notation

Sigma notation comes in handy when you’re approximating the area under a curve. For example, express an 8-right-rectangle approximation of the area under [more…]