Calculus is the mathematical branch that deals with the study of change. It is instrumental in deducing consequences in quantitative modeling systems involving change. The applications of calculus are far greater than simple algebra. This mathematical branch requires a certain degree of abstract thinking and imagination.1 Let us dive into this article to explore the various applications of calculus in our day-to-day life.

## What are the Basic Concepts You Need to Know in Calculus?

Calculus mainly involves studying changes over small intervals of time. The three important concepts you need to understand in calculus are:2

• Limits

The limits in calculus describe the concept of numerical values that keep getting closer to approaching a given value. The value toward which it moves is known as the limit. Limits help in understanding the behavior of number sequences and functions.

• Derivatives

Derivatives refer to the instantaneous rates of change of a function concerning a variable at a point. It is similar to the algebraic concept of slope. It helps predict the rate at which one quantity changes into another.

• Integrals

Integration is a way of adding pieces to make a whole. Integrals calculate the areas of 2D objects and volumes of 3D objects.

## How The Significance of Calculus Grew

Both differential and integral calculus help solve many paradoxes that were almost impossible to deduce earlier. This mathematical branch is especially effective in cases involving large quantities of data. It has helped enhance learning methods and develop modern tools and equipment. Calculus has enabled mathematicians and philosophers to understand and improvise on the basic concepts of space, time, and motion.1,3

## Applications of Calculus in the Real World

In physics and math, you can apply calculus concepts directly. However, in most other areas involving a real-world approach, you may need to employ calculus concepts indirectly. Let us find out how people implement calculus in real life.

### 1. Engineering and Construction

Engineers and architects employ calculus in construction surveys. They use it to improve the structural design of shock-proof buildings, drainage systems, bridges, tunnels, and roads. Experts use integral and differential calculus concepts to understand and study the weight, height, area, and other variables essential for designing structures.4,5

### 2. Economics

Economists use calculus to determine the margin values of products and study the correct time of buying and selling commodities. Since economics involves constantly changing market prices and business goals, one can employ calculus concepts to facilitate estimations and patterns. This technique helps firms and agencies chalk out beneficial plans of action.3,6

### 3. Healthcare and Research

Calculus has wide applications in clinical research and medical applications. In the medical field, calculus concepts are applicable in predicting the chances of success of a trial, the rate of disease spread, and the effects of medicines on human cells.4 In biology, calculus helps study evolution principles and predict the growth rate of bacterial cultures and tumors.5

### 4. Aeronautics

Calculus estimations help explore the movements and velocities of planetary bodies. Spacecrafts can be designed based on the study of speed, dimensions, and time using calculus. Experts predict orbital velocity and gravitational forces that assist in planning space missions.6

### 5. Meteorology

Meteorologists use calculus notions to predict climate and weather-related conditions. Factors such as wind speed, atmospheric pressure, and temperature are the variables used to design weather forecasts.5

### 6. Statistics

Although statistics is another mathematical branch, the knowledge of calculus helps prove statistical results. Calculus lets statisticians develop a range of possibilities to predict situations accurately and design business goals around them. Most business schools require students to study calculus within their regular courses.6

Studying calculus gets quite tricky at times. However, if you can correlate the concepts with their applications in real-world situations, the learning becomes more effective. There are indirect applications of calculus in many fields. For example, credit card companies use it for payments; automobile companies use it to enhance a vehicle’s safety features; and math teachers use it to understand deep mathematical concepts.4 Calculus has shown invaluable benefits in technological growth and progress.