Partial Differentation engineering mathematics complete course cover
Partial Differentation is one of the most important and fundamental chapter of engineering mathematics, we have cover complete module for you
Table of Content
- Direct Partial Differentiation.
- Partial Differentiation of composite Function.
- Euler’s theorem
- Homogeneous Function
- Euler’s Theorem For Homogeneous Function in Two Variables.
- Application Of Partial Differentiation
- Jacobian
- Maxima and Minima
List of all lecture
Theory of partial differentation
In engineering mathematics, partial differentiation is a mathematical operation used to find the rate of change of a function with respect to one of its variables, while holding all other variables constant. It is an extension of ordinary differentiation, which deals with functions of a single variable.
When dealing with functions of multiple variables, partial differentiation allows us to determine the rate at which a function changes with respect to one variable while keeping the other variables fixed. It is particularly useful in the study of fields such as physics, engineering, and economics, where multiple variables are often involved in complex systems.
The partial derivative of a function f(x,y) with respect to x is denoted as ∂f/∂x and is defined as the limit of the difference quotient as Δx approaches zero while y is held constant. Similarly, the partial derivative of f(x,y) with respect to y is denoted as ∂f/∂y and is defined as the limit of the difference quotient as Δy approaches zero while x is held constant.
Partial differentiation is useful in a variety of applications, including optimization problems, where it is used to find critical points of a function, and in the study of differential equations, where it is used to find solutions to partial differential equations. Additionally, partial differentiation is used in the analysis of physical systems, such as fluid dynamics and thermodynamics, where it is used to model and predict the behavior of complex systems.