Master of Science in Mathematical Science
First Committee Member
Angel S. Muleshkov
Second Committee Member
Third Committee Member
Fourth Committee Member
Number of Pages
In this thesis, various generalizations to the n-dimension of the polar coordinates and spherical coordinates are introduced and compared with each other and the existent ones in the literature. The proof of the Jacobian of these coordinates is very often wrongfully claimed. Currently, prior to our proof, there are only two complete proofs of the Jacobian of these coordinates known to us. A friendlier definition of these coordinates is introduced and an original, direct, short, and elementary proof of the Jacobian of these coordinates is given. A method, which we call a perturbative (not perturbation) method, is introduced so that the approach in the general case is also valid in all special cases.
After the proof, the definitions of the n-dimensional quasiballs (hyperballs for n ≥ 4) and the n-dimensional quasispheres (hyperspheres for n ≥ 4) are given. The Jacobian is used to calculate the n-dimensional quasivolume of the n-dimensional quasiball and the n-dimensional quasi-surface area of the n-dimensional quasisphere directly. The formulas obtained afterwards are free of any special functions and could be introduced without any advanced mathematical knowledge. Numerical results are provided in a table followed by interpretations of these results.
Coordinates, Polar; Jacobians; N-dimensional Sphere; Sphere
Nguyen, Tan Mai, "N-Dimensional Quasipolar Coordinates - Theory and Application" (2014). UNLV Theses, Dissertations, Professional Papers, and Capstones. 2125.