Solved Example Problems
Subject and UNIT: Transforms and Partial Differential Equations: Unit III: Applications of Partial Differential Equations
When the heat flow is along curves, instead of straight lines, the curves lying in parallel planes, the flow is called two dimensional.
Solved Example Problems
Subject and UNIT: Transforms and Partial Differential Equations: Unit III: Applications of Partial Differential Equations
Consider a homogeneous bar of cross sectional area A. Take the origin O at one end of the bar and the positive x axis along the direction of heat flow.
Solved Example Problems | Partial Differential Equations
Subject and UNIT: Transforms and Partial Differential Equations: Unit III: Applications of Partial Differential Equations
Equation of a vibrating string :- 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.
Solved Example Problems | Partial Differential Equations
Subject and UNIT: Transforms and Partial Differential Equations: Unit III: Applications 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.
Example with Solved Example Problems
Subject and UNIT: Transforms and Partial Differential Equations: Unit III: Applications 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.
Fourier Series | Transforms and Partial Differential Equations
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Questions and Answers - Part A - Fourier Series - Transforms and Partial Differential Equations
Definition, Formula, Solved Example Problems | Fourier Series
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Sometimes the function is not given oy a formula, but by a graph or by a table of corresponding values.
Definition, Solved Example Problems | Fourier Series
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Definition: Root Mean Square Value [RMS Value] (or) Effective value
Formula, Solved Example Problems
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Let f(x) be a periodic function of period 2л in the interval (c, c + 2л). The Fourier series of f (x) is given by
Sine and Cosine series with Solved Example Problems | Fourier Series
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Sine series: To expand f(x) as a sine series in (0,л) or (0,l), extend the function reflecting it in the origin, so f(-x) = −f (x).
Definition, Example, Waveform, with Solved Example Problems | Fourier Series
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Certain functions defined in symmetric ranges of the form (−л, л), (−l, l) can be classified as even and odd functions.
with Solved Example Problems
Subject and UNIT: Transforms and Partial Differential Equations: Unit II: Fourier Series
Periodic functions occur frequently in engineering problems. Such periodic functions are often complicated.