Textbook in PDF format

This unique volume covers two fundamental elements of computational methods - numbers and functions. It provides an in-depth discussion of the behaviors of numbers, including both real and complex numbers. The discussion leads to the important closure properties of numbers, ensuring solution consistence and existence, and also possible failure in numerical computations in science and engineering. This text then introduces types of functions that take numbers as independent variables and produce a single number. Approaches for constructing inverse functions are also provided. Frequently used basis functions are introduced, with detailed studies on their properties and behaviors. Techniques are presented for constructing basis functions and their use in function approximation in computational methods. This book is Volume 1 of the Series in Computational Methods. The book series aims to provide theoretically essential and practically important basic theory, formulation, and applications on computational methods. It covers general computational methods and techniques used in STEM education, as well as various fields in science and engineering