chapter 1 Constrained coordinate system -- chapter 2 Generation of the coordinate system -- chapter 3 Natural coordinates -- chapter 4 Computation of the number of elements -- chapter 5 An ordering relation -- chapter 6 Application to symbolic computation of derivatives -- chapter 7 Multivariate Hermite Interpolating Polynomial -- chapter 8 Generation of the Hermite Interpolating Polynomials -- chapter 9 Hermite Interpolating Polynomials -- chapter 10 Normalized symmetric square domain -- chapter 11 Rectangular nonsymmetric domain -- chapter 12 Generic domains -- chapter 13 Extensions of the constrained numbers -- chapter 14 Field of the complex numbers -- chapter 15 Analysis of the behavior of the Hermite Interpolating Polynomials -- chapter 16 Construction of the approximate solution -- chapter 17 One-dimensional two-point boundary value problems -- chapter 18 Application to problems with several variables -- chapter 19 Thermal analysis of the surface of the space shuttle.