Basic Analysis I: Functions of a Real Variable by James K. Peterson instant download

Basic Analysis I: Functions of a Real Variable by James K. Peterson instant download

We will study basic analysis in this text. This is the analysis a mathematics major or a student from another discipline who needs this background should learn in their early years. Learning how to think in this way changes you for life. You will always know how to look carefully at assumptions and parse their consequences. That is a set of tools you can use for your own profit in your future. In this text, you learn a lot about how functions which map numbers to numbers behave in the context of the usual ideas from calculus such as limits, continuity, differentiation and integration. However, these ideas are firmly rooted in the special properties of the numbers themselves and we take great pains in this set of notes to place these ideas into the wider world of mappings on sets of objects. This is done anecdotally as we cannot study those things in careful detail yet but we want you exposed to more general things. The text also covers ideas from sequences of functions, series of functions and Fourier Series.