Modern mathematical analysis - Protter, Murray H. (Addison-Wesley, 1964)
This book is designed for students who have already completed a one-year course in calculus and analytic geometry devoted to the study of functions of one variable. We assume that the student has learned prerequisite "Calculus and Analytic Geometry, A first Course" or equivalent text which covers approximately the same body of knowledge. Throughout this book we shall refer to theorems and examples in previous text, using the term First Course in making such references. For most students the step up is an abrupt and difficult one. By including in this book the more advanced portions of elementary calculus and the beginning portions of advanced calculus, we have attempted to make the transfer as smooth as possible.