Applications of Differential Calculus

 Applications of Differential Calculus

“Nothing takes place in the world whose meaning is not that of some

 maximum or minimum”

                                                                                                        - Leonhard Euler

Early Developments

    The primary objective of differential calculus is to partition something into smaller parts (infinitesimal parts), in order to determine how it changes. For this reason today’s differential calculus was earlier named as infinitesimal calculus. Applications of differential calculus to problems in physics and astronomy were contemporary with the origin of science. All through the 18th century these applications were multiplied until Laplace and Lagrange, towards the end of the 18th century, had brought the whole range of the study of forces into the realm of analysis. The development of applications of differentiation are also due to Lejeune Dirichlet, Riemann, von Neumann, Heine, Kronecker, Lipschitz, Christoffel, Kirchhoff, Beltrami, and many of the leading physicists of the century.

• Differential calculus has applications in geometry and dynamics.

• Derivatives of function, representing cost, strength, materials in a process, profit, etc., are used to determine the monotonicity of functions and there by to determine the extreme valuesof the quantities represented by those functions.

• Derivatives of a function do find a prominent place in many of the modelling problems in engineering and sciences.

• Differential calculus has applications in social sciences and medical sciences too.

APPLICATIONS OF INTEGRATION

                                                     APPLICATIONS OF INTEGRATION

  

DEFINITE INTEGRATION

LEARN ENGLISH GRAMMAR - TENSES - SIMPLE PRESENT, PAST and FUTURE TENSES

 LEARN ENGLISH GRAMMAR - TENSES - SIMPLE PRESENT, PAST and FUTURE TENSES

Reference Link : https://youtube.com/watch?v=M6_JlXYTEXQ&feature=shares

IMPORTANT OF LEARNING TENSES

The foundation of the English language is its tenses. Choose the tense that best expresses the topic; otherwise, the statement or question will convey the opposite of what you intended to say or write. Proper tense usage implies the use of the suitable verb form and auxiliary.

Integration Formula

 Integration Formula

Integral Calculus

Introduction

Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus in the mid-17th century. Leibnitz, a German philosopher, mathematician, and political adviser, importantly both as a metaphysician and as a logician, was a distinguished independent inventor of the Differential and Integral Calculus. Sir Isaac Newton had created an expression for the area under a curve by considering a momentary increase at a point.

In effect, the fundamental theorem of calculus was built into his calculations. His work and discoveries were not limited to mathematics; he also developed theories in optics and gravitation.

One cannot imagine a world without differentiation and integration. In this century, we witnessed remarkable scientific advancement owing to the ingenious application of these two basic components of Mathematics. Calculus serve as unavoidable tool for finding solutions to the variety of problems that arise in physics, astronomy, engineering, chemistry, geology, biology, and social sciences.

Calculus deals principally with two geometric problems.

(i) The problem of finding SLOPE of the tangent line to the curve, is studied by the limiting process known as differentiation and

(ii) Problem of finding the AREA of a region under a curve is studied by another limiting process called Integration.

 

Remote Sensing

https://www.youtube.com/watch?v=vzfGMMEEz5w

                                                              INTEGRATION BY PARTS

Pick the odd one out