Akademik Dersler - İçerik

express the fundamental properties of n-dimensional eucledian space.
explain the n-dimensional euclidean space.
calculate the norm of a vector.
express the properties of norm.
calculate the distance between two points in n-dimensional eucledian space.
express the Cauchy-Schwarz inequality.
exemplify open and closed subsets of n-dimensional euclidean space.
express the fundamental concepts of functions of several variables.
define the graph of a function.
determine the level set of a function.
sketch the graph of a real valued function of two variables.
explain the limit and continuity of a function of several variables.
define limit at a point of a function.
characterize the limit by sequences.
express the properties of limit.
define continuity at a point of a function.
explain the differences between limit and continuity.
express the properties of continuous functions.
define uniformly continuous function.
use derivative to determine the properties of a function.
express the differentiability of a multivariable function at a point.
express the properties of the derivative.
determine the partial derivatives of a multivariable function.
express the chain rule.
calculate the directional derivative of a multivariable function.
find the gradient of a multivariable function.
find the equation for the tangent plane through a point of the graph of a multivariable function.
express the higher order derivatives.
express the Taylor's theorem for multivariable functions.
investigate the maxima and minima for multivariable functions.
determine the critical points of a multivariable function using partial derivatives.
identify a critical point of a multivariable function using the second partial derivative test.
solve optimization problems using the concept of critical points.
explain the method of Lagrange multipliers.
express the implicit and inverse function theorems.