# The 10 Best Calculus Textbooks

This wiki has been updated 13 times since it was first published in May of 2017. Math is hard enough as it is, so you don't need bad instruction making it that much more difficult. These calculus textbooks will help guide you through one of the most difficult subjects you're likely to encounter, and they're packed with quizzes, illustrations, and definitions designed for all levels, so even the biggest math-phobes can breathe easy while mastering the material.
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### Editor's Notes

**July 08, 2019: **

This update ensured our list had titles for high schoolers and college students alike, as well as texts directed to the autodidact and those coming back to the discipline after a long break. Our selections were prioritized by clarity, authority, layout, and pedagogical tools that help teach, reinforce, and review the material for a thorough understanding. A few of our choices touch on precalculus, although if you're completely lost on the subject, it's best to brush up with a dedicated precalculus textbook before diving into calculus.

Since we already had a title dedicated to single variable calculus (Calculus Deconstructed), we felt it appropriate to supplant our previous #9 Calculus of a Single Variable with Calculus, 4th Edition, a rigorous book geared toward aspiring mathematicians. As many of our selections are directed toward the beginner and the pupil who may struggle with math, we felt this choice was a good fit for those who are more prepared to take on a challenge.

Calculus, like any branch of math, requires tons of practice for reinforcement, which is why The Humongous Book of Problems made it to our number 2 spot. Like any good textbook, its aim is to help students achieve a solid understanding of the material, as well as the capability to apply their newfound knowledge to real-world situations with independence.

You'll find Stewart's Early Transcendentals as well as Thomas' Calculus, two of the most appreciated titles in the field. An Intuitive and Physical Approach is helpful for the student who needs to align the abstract with the physical world, while our number 1 choice, Graphical, Numerical, Algebraic, is ideal for those who prefer to cut to the chase. It's also excellent if you're preparing to take AP exams, as its content is aligned to test guidelines.

### A Brief History Of Calculus

Today, you can find it implemented in a wide variety of fields from physics to computer science.

Calculus is a branch of mathematics that focuses on **rates of change**. It's used in fields like physics and engineering to determine how a system will behave in the real world. In other words, you may know that an apple will fall from its branch, but calculus can help you determine how fast it will fall and where it will land. It has been an important subject in schools for years and is one that everybody should endeavor to understand.

While many of its earliest principles can be traced back hundreds or even thousands of years to the work of ancient Greek and Egyptian scholars, calculus as we know it today, is often attributed to the work of mathematicians Sir Issac Newton and Gottfried Wilhelm Leibniz during the early 18th century. Both of them took radically different approaches and arrived at surprisingly similar conclusions. Their results were so similar that Newton and his supporters actually accused Leibniz of *plagiarizing* his work, resulting in a controversy that historians still debate today.

Over the years, many great minds have worked to expand and improve the original principles of calculus. Today, you can find it implemented in a wide variety of fields from physics to computer science. Economists, doctors, and business people will even use it when a problem needs to be modeled mathematically. Today, calculus is so integral to so many professional fields that not having at least a basic understanding of it is practically unthinkable. There are many complex ideas that you will need to get a handle on, but don't panic. Just start with the fundamentals and work your way up from there.

### The Core Ideas

Before you begin trying to solve equations, there are a handful of basic concepts that are essential if you or your child are going to succeed in class. This is not a comprehensive list but rather a brief introduction that, hopefully, gets you started on the path to an even better understanding of calculus.

Put simply, limits make it possible for mathematicians to work with very small numbers.

The term **limit** is unavoidable when it comes to high-level mathematics. In plain English, a limit is defined as "the maximum level something can reach" but in math, limits are the values that most closely approach the intended number without ever directly arriving at it. In situations where the actual solution would be infinite, limits allow you to produce an answer that is very close to what is needed but has a finite value. This is achieved using a formula. Put simply, limits make it possible for mathematicians to work with very small numbers. They have been part of the standard approach since practically the beginning and that likely won't be changing any time soon.

Limits are often used to define the values of **functions**. When you input one number into a set of rules and then receive a different number as an answer, you have a function. They are usually noted as algebra problems, where letters are a used in place of numbers until you start to fill them out. In calculus, functions can be used to determine many real-world things like the position of planets over time.

The **derivative** is the rate at which a function changes. When talking about objects in motion, they will often move faster or slower at different times. The act of finding the derivative is *differentiation*. By doing this, you will be able to narrow down the highest and lowest values of a function using a graph. The opposite process is called integration, which, when combing with differentiation, can be used to calculate **integrals**. Sometimes referred to as antiderivatives, integrals allow you to understand the area under a curve where the numbers are constantly changing. Without integrals, it would be impossible to properly measure the area under a curved graph which in turn would make problems in fields like physics extremely difficult to represent.

This all may still look pretty complicated, but don't worry, there are plenty of resources to help reinforce and expand your comprehension of these ideas. With a good teacher and a great textbook, you'll be calculating like a pro in no time. Of course, to get there, you'll need the right tools.

### Tools Of The trade

On the first day of class, students usually get a list with all the supplies they will need. Of course, there's always the standard pens, pencils, notebooks, and textbooks. But in math classes like calculus that are high school level and above, you'll often find that one extra item on the list: a graphing calculator.

Of course, there's always the standard pens, pencils, notebooks, and textbooks.

Scientific calculators are great for most math situations, but their shortcomings become clear when you need to visualize a solution. Like their name suggests, graphing calculators map out the solution to an equation by creating a small graph that appears on the screen. In calculus, the goal is often to build a model that represents a real-world situation. Without a graphing calculator, you would need to sketch out all of the data by hand, which is certainly time-consuming and could lead to you making **serious**, potentially dangerous mistakes.

Since they can do everything that a normal calculator does and much more, graphing calculators are useful in a variety of places outside of the calculus classroom. You'll definitely find that they are often needed in classes like *algebra and trigonometry* where they can perform important functions and help students to check their work. Some can even be attached to lab equipment to record various measurements. But, if you're looking for something a little less academic to do, they can also play games. Just don't get caught playing them in class.

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