Smith K.T. Power Series from a Computational Point of View

New York: Springer, 1987. - 132p.The purpose of this book is to explain the use of power series in performing concrete calculations, such as approximating definite integrals or solutions to differential equations. This focus may seem narrow but, in fact, such computations require the understanding and use of many of the important theorems of elementary analytic function theory, for example Cauchy's Integral Theorem, Cauchy's Inequalities, and Analytic Continuation and the Monodromy Theorem. These computations provide an effective motivation for learning the theorems, and a sound basis for understanding them.Taylor Polynomials
Sequences and Series
Power Series and Complex Differentiability
Local Analytic Functions
Analytic Continuation