In this chapter we use ideas based on the elementary definition of derivative to define derivatives of a vector function of a Euclidean vector variable. We relate these new derivatives to the elementary ones, and generalize an important result from the real-variable case....
How to prove whether or not a multivariable function is continuous or differentiable at a point? Suppose f and g are differentiable on (a, b). Prove that T (x) = F (x) - g (x) is differentiable on (a, b). Let f(x, y) be any differentiable function of x and y and let x...
Vector-valued functions 01:40:59 MTH008 W6L1 11.6 Lines and tangent lines in 3-space 01:40:30 MTH008 W6L2 11.8 Surfaces in 3-space. Supplementray problems 01:38:55 MTH008 W8L1 12.1-12.2 Functions of two or more variables, partial derivatives 01:42:32 MTH008 W8L2 12.3 Limits ...
How Do We Understand Differentiability and Gradients in Multivariable Calculus? For a function ƒ defined on an open set U having the point X:(x1,x2,...,xn) and the point ||H|| such that the point X + H lies in the set we try to define the meaning of the derivative. \frac{f...
The foundation of the concepts of fuzzy fractional integral and Caputo gH-partial for fuzzy-valued multivariable functions is defined. As a result, fuzzy fractional partial differential equations are considered and the appropriateness of local boundary value problems for hyperbolic equations is proved. ...
In addition, the notion of granular partial derivative of a multivariable fuzzy function whose variables are fuzzy functions with uncertain domains is presented. Then, we propose a theorem which is proved to be applicable to the FBB control problem. Moreover, taking the relative-distance-measure ...