Partial derivatives are so called because they're the derivatives of multivariable functions. When a function is defined in terms of two or more variables, the function's derivative is actually a collection of partial derivative equations.
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. #Glogster #PartialDerivatives
Differential equations are those types of equations that have some derivatives of certain functions. The derivatives can either be ordinary derivatives or partial derivatives. If there are only ordinary derivatives in the equation then, the equation is defined as the ordinary type of differential equation and if the equation has all its terms as partial derivative then, such type of equation is called as partial differential equation.
Multivariable Calculus. This consists of 35 video lectures given by Professor Denis Auroux, covering vector and multi-variable calculus. Topics covered in this course include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
Multivariable Calculus by Professor Edward Frenkel. This course discusses essential topics in multivariable calculus, focusing on functions of two and three variables. Topics covered in this course include parametric curves, vectors in 2- and 3-dimensional spaces, partial derivatives, multiple integrals, vector calculus, Green's theorem, Stokes' theorem, and divergence theorem.