Calculus with GeoGebra

Introduction to Calculus – All You Need To Know

Mathematics, also known as the “language of numbers” is divided into a lot of branches. Indeed, Calculus is one of the most...

Written by Masooma Asif · 2 min read >
What is Calculus?

Mathematics, also known as the “language of numbers” is divided into a lot of branches. Indeed, Calculus is one of the most important branches to exist. Used in a variety of areas, from professional use to being a part of the most basic activities of our lives, calculus has an undeniable importance in human lives. 

Walking through its history, the purpose of its invention, and its practical uses, this post will help you better understand what exactly it is.  

History:

Modern calculus was developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Working independently, Newton first developed calculus and used it to understand motion and dynamic change. On the other hand, Leibniz developed the notions used in it. 

Before the development of calculus, the calculation in mathematics was limited to the objects that were still. With its development, people were now allowed to study motion. 

Calculus thus began to be used in various fields. Astronomers began using it to study the orbits of planets and stars; chemists and physicists began using it for studying the motion of electrons and protons, the behavior of different states of matter, the motion of falling objects, and so on.  

Types of Calculus:

There are two types: Differential and Integral

  • Differential Calculus:
    Precisely speaking, the derivative at a particular point represents the behavior of the function when near to that point. 
    In simpler words, this branch studies the behavior and rate of change in different quantities. It allows the study of the rates of change of slopes and curves, along with calculating the maximum and minimum values.
    It involves the use of derivatives, differentials, and functions primarily. Another important aspect is the use of graphs.
  • Integral Calculus:
    Also known as anti-derivatives, integration is the reverse of differentiation. The objective here is to find the quantity at which the rate of change is known to us. 
    It enables one to calculate the total size and values for example the area under the curve or volume. Here, a number or variable is integrated into a more complex equation. 

Practical Uses:

Calculus has quite a lot of practical applications in various fields. Its earliest uses involved applications in navigation and astronomy.

Today, it is used in chemistry, physics, computer science, robotics, economics, engineering, and more.   

  • Navigation:
    In the 17th and 18th century, the ship navigators had to have the features of measuring both time and angles. These features were developed borrowing concepts from calculus.
    Moreover, these concepts also enabled sailors to determine their positions and the distance ships had to travel to reach a specific location.
  • Chemistry:
    Generally, calculus is used when working with kinetics and thermodynamics. It can also be used to calculate rates of radioactive decay. Additionally, the analysis of oxidation and concentration of chemical solutions through Beer’s law were also facilitated through its concepts.
  • Physics:
    A few of the physics concepts that use calculus include heat, electricity, light, dynamics, and kinematics. Calculus also sets up differential equations for calculating velocity and rate of change.
    Many important physics laws are also derived through its help including Newton’s law of motion, Lorentz force law, Maxwell’s electromagnetic equation, Einstein’s theory of relativity. 
  • Economics:
    In economics, calculus helps study and derive information from the demand and supply curves as well as other graphs and curves. Moreover, it allows economists to compute marginal cost, marginal revenue, maximum/minimum profit, etc.
  • Medical:
    Calculus is used to predict birth and death rates. It also helps in the research process and experiments for example determining and comparing rates of growth under different conditions.

Apart from these applications, calculus enjoys great influence as well as importance in several other fields. 

Conclusion:

Calculus is one powerful tool, having a huge role ever since its development. With increasing importance and relevance, strong skills in calculus do not only improve one’s academic performance, but also provide a competitive advantage in the professional field. To learn more about it, get yourself enrolled in our course right away!

Written by Masooma Asif
Syeda Masooma Asif is an undergraduate student at LUMS. With an Economics major, Masooma is deeply passionate about research in developmental economics aiming to provide consultancy services for the challenges faced by the less-developed economies. She also shares a passion for content writing, and through writing articles for Airschool she aims to contribute towards providing accessible education for all regardless of geographical or social disparities. Profile

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