Differential Calculus

Bookmark added to your notes.
View Notes

Basic Differential Calculus

Part of calculus that cuts something into small pieces in order to identify how it changes is what we call differential calculus. Derivative is that part of differential calculus provides several notations for the derivative and works some problems and to actually calculate the derivative of a function. Formula of differentiation is used to solve mostly on roots, polynomials, and more usually variables rose to powers.Application of rules of differential calculus  allows us to differentiate functions that, up to a certain point, we are unable to differentiate.

Significance of Differential Equations

A substantiated magnitude of differential equation as a procedure for identifying a function is that if we know the function and perhaps a couple of its derivatives at a specific point, then this data, along with the differential equation, can be utilized to effectively find out the function over the whole of its domain.

Types of Differential Equations

A Differential Equation exists in various types with each having varied operations. 

  1. Ordinary Differential Equations.

  2. Partial Differential Equations.

  3. Linear Differential Equations.

  4. Nonlinear differential equations.

  5. Homogeneous Differential Equations.

  6. Nonhomogeneous Differential Equations

As an outcome of manifold creation of life around us, multitude of operations, numerous activities, therefore, differential equations, to model the countless physical situations are attainable. The classification of differential equations in different ways is simply based on the order and degree of the differential equation. So, let’s find out what is an order in differential equations.

Order of Differential Equation

Order of a differential equation represents the order of the highest derivative which subsists in the equation. Actuarial Experts also name it as the differential coefficient that exists in the equation. There are basically 2 types of order:-

  1. First order differential equation

  2. Second order differential equation

Application of First Order Differential Equation

Modeling is quite an apt mechanism of writing a differential equation in order to explain a physical process.

Nearly all of the differential equations whether in the medical or engineering or chemical process modeling that are there are for a reason that somebody modeled a situation to devise with the differential equation that you are using.

Area Problem And Volumes of Solids of Revolution Problems

Interpretations of definite integrals allow us to approximate the amount of area which lies between a function and the x-axis.

Furthermore, The volume of a solid of revolution and volume of the object, looking at the method of cylinders/shells we obtain by rotating a region encompassed by two curves (one of which may be the x or y-axis) around a horizontal or vertical axis of rotation. We also consider looking for solids that could be identified by treating them as a solid of revolution.

FAQ (Frequently Asked Questions)

1. What is meant by the Integral Calculus?

Part of calculus that connects (integrates) the small pieces together in order to identify how much there is is known as integral calculus. Among its many applications, it is also used to find work done by physical systems and measuring pressure behind a dam at a given depth.

2. What are the uses and applications of Calculus?

Calculus makes it quite practical for solving problems as diverse as tracking the position of a rocket, flying saucer or anticipating the pressure building up behind a dam as the water level climbs. Computers have become a highly valued tool for solving calculus related problems that were once regarded unreasonably difficult.

3. What does the substitution rule for indefinite integrals say?

The Substitution Rule is one of the more common and useful integration techniques – that will allow to integrate a wider variety of functions. The integrals will all need some manipulation of the function before integrating.

4. What does the chain rule, product rule and the quotient rule for indefinite integrals say?

With the clear understanding of the chain rule of calculus, we will be able to differentiate a wider variety of functions. In addition, application of Product Rule and the Quotient Rule allows us to differentiate functions that, up to a certain point, we are unable to differentiate.