Differential Calculus

Differential Calculus is a tool of mathematical analysis that helps find the rate of change concerning the dependent variable. Applications include finding maximum and minimum values of operations to solve and optimise practical problems. Among the two calculus theories, differential calculus is one of the more traditional branches. Another calculus that is an integral part of this, is known as integral calculus. Calculus can be used by biologists, physicists, engineers, etc., to measure many variables like bacteria, construction of curved shape structures by architects, measurement of electric wires required for a particular connection, etc. 

Differential Calculus and its Applications

Differential calculus can be used in different life decisions like economic growth, developing finances, etc. It can be applied in engineering, medical sciences, statistics, research and development, physics, graphics, chemistry, mathematics, biological sciences, etc. 

Engineering

In engineering, differential calculus can be used in architecture, electronics, aerospace, etc., to measure the materials required to construct a particular shape of the building, to measure the length of a cable that is needed to connect two mediums and while planning and launching missions or other happenings. 

Medical Sciences

Determining the bacterial or fungal growth rate is based on different variables, including temperature, food items, liquid matters, etc., which can be calculated by using differential calculus.

Physics

Calculus that helps calculate the mass, momentum, trajectory, position, magnetism, gravity, etc. in physics.

Statistics

 Statistical data can be created using calculus which can help in the development of surveys and formulating business plans for various companies. 

Research

A research analyst uses calculus to determine operational, efficient, productional, developmental, and target sources and expand the results of the research. 

Graphics

3D models could be created with the help of differential calculus that determines the measurements and adaptability of the models. 

Chemistry

In chemistry, differential calculus is used to determine the rate of chemical reactions and to provide the necessary information required to determine the reaction of molecules and subject matter.

Biological Sciences

In biological sciences, derivatives are used to find the contractions of muscles, the dissolution of drugs in the bloodstream, and the increase or decrease of bacteria on any surface or matter. 

Differential Calculus in Mathematics

Differential Calculus in mathematics involves determining the change in the movement of particles, atoms, molecules, stars, etc., that can move in real-time. 

Differential Calculus can be used in various fields. There are a variety of formulas and concepts that carry specific value. There are three basic calculus concepts one needs to know. These include:  

• Limits

• Derivatives 

• Integrals

The process of finding the value of a derivative is called differentiation. Integral calculus is simplified as the study of an area underneath a curve. Derivatives form part of the primary function of differential calculus. Differentiation has concepts that are applied in almost all fields of quantitative streams. Integration’s reverse process is called differentiation. In physics, the equation F = ma is related to Newton’s second law of motion. Differential calculus study materials can be used to understand this concept better. 

Derivatives are used to determine the maxima and minima of a function. Derivatives that are involved in equations are called differential equations. The derivatives are applicable in analysis, differential geometry, mensuration theory and algebra. There are certain basic properties and formulas in differential calculus, and they are as follows: 

• Operational Property

• Reciprocal Property

• Constant Multiple Property

• Chain Rule Property