Daffodil International University

1. WELCOME

2. Presentation by:
Al-Amin Prince, ID: 141-19-1539
Nusrat Jahan, ID: 141-19-1542
Department of Electronics and Telecommunication Engineering
Daffodil International University.
Dhaka, Bangladesh.
Guided By:
Md. Mosfiqur Rahman
Senior Lecturer,
Department of General Educational Development
Faculty of Science and Information Technology.

3. An Application of
Differential Equation in ETE

4. What is differential Equation?
A differential equation is a mathematical equation that relates some function
with its derivatives. In applications, the functions usually represent physical
quantities, the derivatives represent their rates of change, and the equation
defines a relationship between the two. Because such relations are extremely
common, differential equations play a prominent role in many disciplines
including engineering, physics, economics, and biology.

5. Types
Differential equations can be divided into several types. Apart from
describing the properties of the equation itself, these classes of
differential equations can help inform the choice of approach to a
solution. Commonly used distinctions include whether the equation is:
Ordinary/Partial, Linear/Non-linear, and Homogeneous/Inhomogeneous.

6. Ordinay differential equations
An ordinary differential equation (ODE) is an equation containing a function of
one independent variable and its derivatives. The term "ordinary" is used in
contrast with the term partial differential equation which may be with respect
to more than one independent variable.
𝑑𝑦
𝑑𝑥
= 0, (1 independent variable)

7. Partial differential equations
A partial differential equation (PDE) is a differential equation that contains
unknown multivariable functions and their partial derivatives. PDEs are used
to formulate problems involving functions of several variables, and are
either solved in closed form, or used to create a relevant computer model.
𝑥
𝜕𝑢
𝜕𝑥
+ 𝑦
𝜕𝑢
𝜕𝑦
= 𝑛𝑢, (More then 1 independent variable)

8. WAVE EQUATION
The wave equation is an important second-order linear hyperbolic partial
differential equation for the description of waves as they occur in classical
physics such as sound waves, light waves and water waves. It arises in fields
like acoustics, electromagnetics, and fluid dynamics.
A pulse traveling through a string with fixed endpoints as modeled by the wave equation.

9. The wave equation is a hyperbolic partial differential equation. It typically
concerns a time variable t, one or more spatial variables x1, x2, …, xn, and a
scalar function u = u (x1, x2, …, xn; t), whose values could model, for example,
the mechanical displacement of a wave. The wave equation for u is,
𝜕2 𝑢
𝜕𝑡2 = 𝑎2 𝛻2 𝑢
where ∇2 is the (spatial) Laplacian and a is a fixed constant.

10. ELECTROMAGNETIC WAVE EQUATION
The electromagnetic wave equation is a second-order partial differential
equation that describes the propagation of electromagnetic waves through a
medium or in a vacuum. It is a three-dimensional form of the wave equation.
The homogeneous form of the equation, written in terms of either the electric
field E or the magnetic field B, takes the form:
𝑢2
𝑝ℎ𝛻2
−
𝜕2
𝜕𝑡2
𝐸 = 0
𝑢2 𝑝ℎ𝛻2 −
𝜕2
𝜕𝑡2
𝐵 = 0

11. Where,𝑢 𝑝ℎ =
1
√𝜇𝜀
,
is the speed of light (i.e. phase velocity) in a medium with permeability μ, and
permittivity ε, and ∇2 is the Laplace operator. In a vacuum, vph = c0 = 299,792,458
meters per second, a fundamental physical constant. The electromagnetic wave
equation derives from Maxwell's equations. It should also be noted that in most
older literature, B is called the magnetic flux density

12. Thank You