MAPLE THROUGH EXAMPLES: ALGEBRAIC EXPRESSIONS, POLYNOMIALS, EQUATIONS, AND SYSTEMS

Maple is a scientific software that offers numerous possibilities for working in the field of algebra, and specifically in the manipulation of algebraic expressions. This book presents a wide variety of examples and exercises solved using Maple related to algebraic expressions. It delves into the elements of algebraic expressions, such as operators, variables, and functions, as well as operations with algebraic expressions, including factoring, simplification, expansion, combining like terms, and ordering. It also demonstrates working with algebraic fractions and subexpressions. Furthermore, it covers the manipulation of polynomials, interpolation, and algebraic extensions in depth. Algebraic expressions are also explored through power series expansions using Taylor, Laurent, Padé, and Chebyshev series, as well as formal power series. Finally, it considers conditional, recursive, nested, and flow control algebraic expressions through procedures. Finally, the text covers working with linear transformations, quadratic forms, equations, and systems. The subsequent chapters present the topics covered, always illustrated with representative examples solved step-by-step using Maple. At the end of each chapter, exercises are provided to reinforce the concepts studied.