Mth102 Differential Equation

8/2/2019 Mth102 Differential Equation

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TERM PAPER

REVIEW

OF

MTH102ON

TOPIC:-APPLICATION OF DIFFERENTIAL EQUATION

Submitted by:

PRAVEEN KUMAR SINGH

ROLL NO. : A30SECTION: RC1903A30

REG. NO.: 10905912

INTRODUCTION:-

A differential equation is a mathematical equation for an unknownfunction of one or several variables that relates the values of the function itself and its

derivatives of various orders. Differential equations play a prominent role in engineering,

physics,economics, and other disciplineDifferential equations arise in many areas of science and technology:

whenever a deterministic relationship involving some continuously varying quantities

(modeled by functions) and their rates of change in space and/or time (expressed as

derivatives) is known or postulated. This is illustrated in classical mechanics, where themotion of a body is described by its position and velocity as the time varies. Newton's

Laws allow one to relate the position, velocity, acceleration and various forces acting on

the body and state this relation as a differential equation for the unknown position of thebody as a function of time.

An example of modelling a real world,finding the velocity as a function of time involves

solving a differential equation.
http://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Variable_(mathematics)http://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Deterministic_system_(mathematics)http://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Newton's_Lawshttp://en.wikipedia.org/wiki/Newton's_Lawshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Function_(mathematics)http://en.wikipedia.org/wiki/Variable_(mathematics)http://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Deterministic_system_(mathematics)http://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Newton's_Lawshttp://en.wikipedia.org/wiki/Newton's_Laws


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Differential equation:-

Differential equations are mathematically studied from several different perspectives,

mostly concerned with their solutionsthe set of functions that satisfy the equation. Onlythe simplest differential equations admit solutions given by explicit formulas; however,

some properties of solutions of a given differential equation may be determined withoutfinding their exact form. If a self-contained formula for the solution is not available, thesolution may be numerically approximated using computers. The theory ofdynamical

systemsputs emphasis on qualitative analysis of systems described by differential

equations, while many numerical methods have been developed to determine solutions with

a given degree of accuracy.

Contents

1 Directions of study

2 Nomenclatureo 2.1 Examples

3 Related concepts

4 Connection to difference equations

5 Universality of mathematical description 6 Notable differential equations

o 6.1 Biology

o 6.2 Economics

7 References

Examples

In the first group of examples, let u be an unknown function ofx, and c and are knownconstants.

Inhomogeneous first order linear constant coefficient ordinary differential equation:

Homogeneous second order linear ordinary differential equation:

Homogeneous second order constant coefficient linear ordinary differential

equation describing the harmonic oscillator:
http://en.wikipedia.org/wiki/Dynamical_systemshttp://en.wikipedia.org/wiki/Dynamical_systemshttp://en.wikipedia.org/wiki/Numerical_methodshttp://en.wikipedia.org/wiki/Differential_equation#Directions_of_studyhttp://en.wikipedia.org/wiki/Differential_equation#Nomenclaturehttp://en.wikipedia.org/wiki/Differential_equation#Exampleshttp://en.wikipedia.org/wiki/Differential_equation#Related_conceptshttp://en.wikipedia.org/wiki/Differential_equation#Connection_to_difference_equationshttp://en.wikipedia.org/wiki/Differential_equation#Universality_of_mathematical_descriptionhttp://en.wikipedia.org/wiki/Differential_equation#Notable_differential_equationshttp://en.wikipedia.org/wiki/Differential_equation#Notable_differential_equationshttp://en.wikipedia.org/wiki/Differential_equation#Biologyhttp://en.wikipedia.org/wiki/Differential_equation#Economicshttp://en.wikipedia.org/wiki/Differential_equation#Referenceshttp://en.wikipedia.org/wiki/Harmonic_oscillatorhttp://en.wikipedia.org/wiki/Dynamical_systemshttp://en.wikipedia.org/wiki/Dynamical_systemshttp://en.wikipedia.org/wiki/Numerical_methodshttp://en.wikipedia.org/wiki/Differential_equation#Directions_of_studyhttp://en.wikipedia.org/wiki/Differential_equation#Nomenclaturehttp://en.wikipedia.org/wiki/Differential_equation#Exampleshttp://en.wikipedia.org/wiki/Differential_equation#Related_conceptshttp://en.wikipedia.org/wiki/Differential_equation#Connection_to_difference_equationshttp://en.wikipedia.org/wiki/Differential_equation#Universality_of_mathematical_descriptionhttp://en.wikipedia.org/wiki/Differential_equation#Notable_differential_equationshttp://en.wikipedia.org/wiki/Differential_equation#Biologyhttp://en.wikipedia.org/wiki/Differential_equation#Economicshttp://en.wikipedia.org/wiki/Differential_equation#Referenceshttp://en.wikipedia.org/wiki/Harmonic_oscillator


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First order nonlinear ordinary differential equation:

Second order nonlinear ordinary differential equation describing the motion of a

pendulum of length L:

In the next group of examples, the unknown function u depends on two variables x and tor

x andy.

Homogeneous first order linear partial differential equation:

Homogeneous second order linear constant coefficient partial differential equation

of elliptic type, the Laplace equation:

Third order nonlinear partial differential equation, the Kortewegde Vries equation:

REFERENCE:-

40th Edication

Higher Engineering Mathematics book byDr. B.S. GREWAL

Google wikipedia.com

www.math world.com
http://en.wikipedia.org/wiki/Pendulumhttp://en.wikipedia.org/wiki/Laplace_equationhttp://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equationhttp://www.math/http://en.wikipedia.org/wiki/Pendulumhttp://en.wikipedia.org/wiki/Laplace_equationhttp://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equationhttp://www.math/

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Mth102 Differential Equation