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Mat 131
This presentation summarizes applications of differential equations in electrical and electronics engineering. It was prepared by three students for their Mathematics III course at Daffodil International University in Bangladesh. The presentation defines ordinary and partial differential equations, provides examples of each, and discusses the history and invention of differential equations by Newton, Leibniz, and others. It then outlines several applications of differential equations in areas like software, games, artificial intelligence, and physics concepts like electric circuits, cooling, decay, electromagnetism, fluids, heat, and waves. One application example calculates current in an RL circuit over time.
Mat 131
- 1. Welcome To OurPresentation Prepared for: Md. Mosfiqur Rahman Senior Lecturer in Mathematics Department of GED Daffodil International University, Bangladesh. Prepared By: Md. Jannatul Nayim Giyem Md. Arifur Rahman Md. Arafat Sarkar Course Title: Mathematics III Course Code: MAT 131 Department Of EEE Daffodil International University, Bangladesh.
- 2. Application Of DifferentialEquation’s in Electrical & electronics Engineering
- 3. Invention Of DifferentialEquations In mathematics, the history of Differential Equations traces the development of "differential equations" from calculus, which itself was independently invented by English physicist Isaac Newton and German mathematician Gottfried Leibniz. The history of the subject of differential equations, in concise form a synopsis of the recent article “The History Of Differential Equations,1670-1950” “Differential Equations began with Leibniz, the Bernoulli Brothers, and others from the 1680s, not long after Newton’s ‘Fluxional Equations’ in the 1670s.” Sir Isaac Newton Gottfried Leibniz
- 4. A Differential Equationis an equation containing the derivative of one or more dependent variables with respect to one or more independent variables. For Example ODE (Ordinary Differential Equation): An equation contains only ordinary derivatives of one or more dependent variables of a single independent variable. For example: 𝑑𝑦 𝑑𝑥 + 5𝑦 = 𝑒 𝑥, 𝑑𝑥 𝑑𝑡 + 𝑑𝑦 𝑑𝑡 = 2𝑥 + 𝑦 PDE (Partial Differential Equation): An equation contains partial derivatives of one or more dependent variables of two or more independent variables. For example: 𝜕2 𝑢 𝜕𝑥2 + 𝜕2 𝑢 𝜕𝑡2 = 2 𝜕𝑢 𝜕𝑡 , 𝜕𝑢 𝜕𝑦 = − 𝜕𝑣 𝜕𝑥 Differential Equation’s 𝒅𝒚 𝒅𝒙 = 𝟐𝒙𝒚 𝒙 𝒅𝒚 𝒅𝒙 = 𝐲 − 𝟏 𝒅 𝟐 𝒚 𝒅𝒙 𝟐 + 𝒅𝒚 𝒅𝒙 + 𝒚 = 𝟎 𝝏𝒖 𝝏𝒚 = − 𝝏𝒗 𝝏𝒙 𝝏𝒙 𝝏𝒚 + 𝝏𝒚 𝝏𝒙 + 𝟐 = 𝟎 Types Of Differential Equation:
- 5. Application Of DifferentialEquation’s in EEE ❖Creating Software ❖Constraint Logic Programming ❖Creating games , Aspects Of Algorithms ❖Mother Nature ❖Artificial Intelligence ❖Networking ❖in Theories & explanations: ►Electric R-L Series Circuit ► Newton’s law of Cooling ► Radio Active Decay ► Gauss’s law In Electrostatics, Magnetism & Gravity Continuity Equations- In Fluid Dynamics, Electromagnetism, Quantum Mechanics, Relativity Theory. ►Heat equation ►Wave equation
- 6. Application ( movementof electricity) Simple analog circuit Calculate the inductor current and voltage, move switch, calculate the inductance total current store in the circuit
- 7. Applied mathematics AnRL circuit has an emf of 5 V, a resistance of 50 Ω, an inductance of 1 H, and no initial current. Find the current in the circuit at any time t. Distinguish between the transient and steady- state current.
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