Examples
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations: Examples
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
A uniform elastic string of length 60 cm is subjected to a constant tension of 2 kg. If the ends are fixed and the initial displacement is y (x, 0) 60x - x2 for 0 < x <60 while the initial velocity is zero, find the displacement function y (x, t).
Examples
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
One dimensional wave equation: Consider an elastic string tightly stretched between two points O and A. Let O be the origin and OA as x-axis. On giving a small displacement to the string,
Method Of Separation Of Variables
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations: Exercise
Examples
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
A powerful method of obtaining particular solutions of a p.d.e. is known as separation of variables or product method.
Classification Of Partial Differential Equations
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations: Exercise
Examples
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
Let a second order p.d.e. in the function u of the two independent variables x, y be of the form
Subject and UNIT: Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
Partial differential equations arise in connection with several physical and engineering problems in which the functions involved depend on two or more independent variables such as time and co-ordinates in space.
Subject and UNIT: Transforms And Partial Differential Equations: UNIT II: Fourier Series
Transforms And Partial Differential Equations: UNIT II: Fourier Series: Questions And Answers
Subject and UNIT: Transforms And Partial Differential Equations: UNIT II: Fourier Series
Transforms And Partial Differential Equations: UNIT II: Fourier Series: Exercise
Subject and UNIT: Transforms And Partial Differential Equations: UNIT II: Fourier Series
Sometimes the function is not given by a formula, but by a graph or by a table of corresponding values. The process of finding the Fourier series for a tabular form of numerical values is known as Harmonic Analysis.
Subject and UNIT: Transforms And Partial Differential Equations: UNIT II: Fourier Series
Transforms And Partial Differential Equations: UNIT II: Fourier Series: Exercise