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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_Laws8/2/2019 Mth102 Differential Equation
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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_oscillator8/2/2019 Mth102 Differential Equation
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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/Recommended