We spent 45 hours on research, videography, and editing, to review the top choices for this wiki. Math is hard enough as it is, so you don’t need bad instruction making it that much more difficult. The calculus textbooks here 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. When users buy our independently chosen editorial picks, we may earn commissions to support our work.

10. Applied Calculus

Get out of the theoretical and into the material world with “Applied Calculus: For Business, Economics, and the Social and Life Sciences,” a work that was created to build a foundation in basic concepts through concise instruction as well as through thorough exercise sets.

  • Updated and expanded
  • In both hardcover and paperback
  • Digital version not for some devices

Brand McGraw-Hill Scie
Model pending
Weight 4.6 pounds
Rating 3.7 / 5.0

9. Calculus of a Single Variable

Having a firm base is essential to mastering any science, and Calculus of a Single Variable lays out and thoroughly explores a new concept in each chapter. It is built like a fine argument, layering on new information that integrates with what you already know.

  • Biographies of mathematicians
  • Vocabulary is well-defined
  • Ebook edition has formatting errors

Brand Brooks
Model pending
Weight 4.5 pounds
Rating 3.8 / 5.0

8. Thomas’ Calculus

A standard of math courses for over 50 years, Thomas’ Calculus is still one of the top options on the market. It devotes itself primarily to practical applications of the material, rather than getting bogged down in theory, making it perfect for hands-on learners.

  • Answer key shows work
  • Ideal for introductory classes
  • The choice of stem majors

Brand Thomas’ Calculus
Model pending
Weight 5.5 pounds
Rating 4.5 / 5.0

7. Calculus with Applications

Calculus with Applications is written with non-math types in mind, as it takes examples and applies them to other fields, such as medicine and social science. It will also bring you up to speed on the algebra you’ll need, so don’t worry if you’re a little rusty going in.

  • Uses real data in problems
  • Good for business majors
  • Doesn’t explain solutions in depth

Brand Pearson
Model pending
Weight 3.9 pounds
Rating 3.6 / 5.0

6. An Intuitive and Physical Approach

Math is the language of nature, and An Intuitive and Physical Approach lays this out clearly, showing how you can see the scientific basis of everything that surrounds you, helping you to relate to the material and appreciate the structure of the universe.

  • Encourages creative thinking
  • Uses down-to-earth writing
  • Shows relationships with physics

Brand An Intuitive and Physic
Model pending
Weight pending
Rating 4.5 / 5.0

5. Calculus Deconstructed

For those autodidacts out there, Calculus Deconstructed presents this subject with plentiful examples and historical notes, which makes self-learning in this area a little less stressful. You won’t need any prior knowledge of proofs, either.

  • Starts with info on precalculus
  • Problems of varying difficulty
  • Shorter than other comparable titles

Brand The Mathematical
Model pending
Weight 2.2 pounds
Rating 4.5 / 5.0

4. The Humongous Book of Problems

The Humongous Book of Problems isn’t a textbook per se, but it does make an excellent companion for those learners who want more practice than their school-issued volumes can give them. It’s got over 1,000 problems, so you’re sure not to finish it too quickly.

  • Annotations help build comprehension
  • From an award-winning teacher
  • Best for introductory-level review

Brand Alpha Books
Model pending
Weight 2.5 pounds
Rating 4.2 / 5.0

3. Calculus and Its Applications

Calculus and Its Applications does a fine job of making the material as intuitive as possible, demonstrating how math can be accessible and useful in the real world. If you have trouble relating to calculus, or you want to keep students engaged, this is the book you need.

  • Keeps info from being intimidating
  • Applies math to business world
  • Explanations are clear and concise

Brand Calculus and Its Applic
Model pending
Weight 3.3 pounds
Rating 4.9 / 5.0

2. Graphical, Numerical, Algebraic

If you prefer textbooks that get straight to the point, Graphical, Numerical, Algebraic doesn’t bury its concepts in flowery language or extended examples. This keeps the illustrations simple, which makes it less likely to confuse beginners.

  • Good fit for engineering students
  • Ideal for advanced placement exam
  • Several quizzes per chapter

Brand Graphical, Numerical, A
Model pending
Weight 3.6 pounds
Rating 4.9 / 5.0

1. Early Transcendentals

Early Transcendentals is an excellent guide for working a math problem, giving you a step-by-step look into the process, rather than just providing an answer and moving on. This makes it ideal for self-directed learners, as there are no gaps in the instruction.

  • Loose leaf version available
  • Relates material to real life
  • Builds appreciation for the subject

Brand Brooks
Model pending
Weight 6.2 pounds
Rating 4.6 / 5.0

A Brief History Of Calculus

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.

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.

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.