Application of differential equation in ETE
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This document provides a summary of a presentation on applications of differential equations in electronics and telecommunications engineering. It begins with introducing the presenters and their department at Daffodil International University in Bangladesh. It then defines what a differential equation is and describes common types like ordinary and partial differential equations. Specifically, it discusses the wave equation and electromagnetic wave equation, which are important second-order linear partial differential equations used in fields like acoustics, electromagnetics, and fluid dynamics to model wave propagation. The document provides examples of these differential equations and notes their derivation from Maxwell's equations.
Application of differential equation in ETE
- 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