ENGINEERING MATHEMATICS -APPLCATION OF D.E
- 1. Subject: Engineering Mathematics III Topic: Application of Differential Equation to R-L Circuit Guided by: Ms. Chaitali Wadaskar Group No : 06 (SCOB48) Uttam Singh
- 2. Introduction to D.E A differential equation is a mathematical equation that relates some function with its derivatives. Differential equations first came into existence with the invention of calculus by Newton and Leibniz. Ordinary Differential Equation an ordinary differential equation(ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. Partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. Linear Differential Equation contains differential coefficient and dependent variable in the first degree and they are not multiplied together.
- 3. Applications of Differential Equations To Calculate the Exponential decay of Radioactive material in Nuclear Physics. To Calculate the heat equation in thermodynamics Laplace's equation, which defines harmonic functions In Electrodynamics to Calculate the Resistance, Inductance, Capacitance in Various circuits. Newton's law of cooling in thermodynamics.
- 4. D.E in Resistor-Inductor (RL) Circuit The RL circuit shown above has a resistor and an inductor connected in series. A constant voltage V is applied when the switch is closed. The (variable) voltage across the resistor is given by:
- 5. The (variable) voltage across the inductor is given by: Kirchhoff's voltage law says that the directed sum of the voltages around a circuit must be zero. This results in the following differential equation: The solution of the differential equation is: