Question 1

What is calculus and why is it important?

Accepted Answer

Calculus is the mathematical study of change. It lets you model how matter, particles, stars, and other parts of the universe move and change. You can use formulas to model real-world phenomena accurately. Using limits, derivatives, and integrals, calculus allows you to study continuous change at any level of resolution. Calculus is important for several reasons. It governs the laws of finance, biology, chemistry, aerospace, and many other fields and makes much of modern technology possible.

Question 2

What are the different types of calculus?

Accepted Answer

The most basic type of calculus is differential calculus. Differential calculus is concerned with dividing things into smaller parts and understanding how things change over time. Building upon this foundation is integral calculus. With integrals, you can combine an infinite number of small parts to understand the total effects of any number of changes. Furthermore, there are both single variable and multivariable calculus. These types of calculus are as they sound — dealing with a single variable to solve problems or dealing with multiple variables.

Question 3

What should I learn before calculus?

Accepted Answer

Before learning calculus, it is important to have a strong mathematical foundation in algebra, geometry, and trigonometry. All of these types of mathematics are important in calculus, as you will be using algebra in every single operation, studying the building blocks of geometric shapes like circles, and using trigonometric functions like sine, cosine, and tangent. In addition, calculus is cumulative, meaning each new topic builds upon the topics before it. By having a firm grasp of algebra, geometry, and trigonometry, you’ll have an easier time applying them to new concepts.

Question 4

For what careers is calculus important?

Accepted Answer

Calculus is important to several different careers outside of mathematics. For example, finance and economics are calculus-dependent, as much of modern finance relies on it for its core principles. Calculus is also fundamental for any hard sciences such as physics, chemistry, astronomy, and biology. And software engineers greatly benefit from understanding calculus. Other types of engineering also require a firm grasp of calculus, whether mechanical, electrical, or other. There are many other fields where calculus is important, including medicine, teaching, and more.

Question 5

What are some of the applications of calculus?

Accepted Answer

Calculus is at the core of nearly every branch of science: computer science, physics, engineering, business, medicine, statistics, economics, and more. It allows you to find optimal solutions in complex or changing systems. In physics, calculus forms the basis for everything from electromagnetism to classical mechanics. In finance, the concepts of stochastic calculus and Brownian motion help you to understand fluctuating asset prices. In medicine, calculus is used to compute the ideal angle for a branching blood vessel, allowing doctors to maximize flow. Calculus is also at the core of many software programs performing backend calculations for a wide range of applications. Astronauts and aerospace engineers, for example, use calculus to model the flight trajectories and aerodynamics of air and space vessels.