Born in Germany in 1928, George Rawitscher moved with his family to Sao Paulo, Brazil in 1934 in order to escape Nazi persecution. He studied Physics and Mathematics at the University of S. Paulo from 1945 to 1949, (with BA degrees), received his Ph.D. in Nuclear and Particle Physics in 1956 from Stanford University. After teaching at the University of Rochester and at Yale University, he went to the University of Connecticut in 1966 and rose to the rank of Full Professor in 1972. In 2009 he retired, and is now a Research Professor in UConn's physics department. His research specializations are in low energy nuclear physics and in computational methods. In addition to his continuing scientific physics involvements, his other interests are on World Order (UN transformation) and Climate Change.

Victo dos Santos Filho, born in 1967 in Lorena, São Paulo State, Brazil, studied Mathematics at the Universidade Salesiana de Lorena from 1985 to 1988, and in sequence he studied Physics at Universidade Estadual Paulista (UNESP) de Guaratinguetá from 1989 to 1992. He received his Master degree in Superconducting Technology in Fundação de Tecnologia Industrial (FTI) in 1994 and his Ph.D. in 2001 in Theoretical Physics at Instituto de Física Teórica (IFT) of UNESP, in the area of Bose-Einstein Condensates. After four years of post-doc in IFT concerning theoretical studies in Bose-Einstein Condensates with dissipative effects, he began to teach in private institutions of São Paulo. From 2015, he has worked in the H4D Scientific Laboratory Research as a scientific researcher in physics and technology. Among his recent scientific research interests are condensed matter physics, mathematical physics, general physics and computational physics.

Dedication.- Preface.- Numerical Errors.- Methods.- Galerkin and Collocation Methods.- Convergence Theorems.- Chebyshev Polynomials.- The Integral Equation Corresponding to a Differential Equation.- Spectral Finite Element Method.- The Phase-Amplitude Representation of a Wave Function.- The Vibrating String.- Iteratively Calculated Eigenvalues.- Sturmian Functions.- Index.