Problems: Multivariable Functions

In this chapter, the basic and advanced problems of multivariable functions are presented. The subjects include domain and range of multivariable functions, Jacobian determinant, gradient, directional derivative, unit vector, tangent plane, curl, divergence, Laplacian, critical point, type of critical point, relative maximum and minimum points, and saddle point. In this chapter, the problems are categorized in different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large). Additionally, the problems are ordered from the easiest problem with the smallest computations to the most difficult problems with the largest calculations.