Robert G. Bartle & Donald R. Sherbert 
Introduction to Real Analysis [EPUB ebook] 

A strong foundation in real analysis gives students a broadly-applicable skill set in deductive reasoning and analytical math, strengthening the creative thought processes required to extend ideas to new situations. Now in its fourth edition, Introduction to Real Analysis provides a rigorous and comprehensive introduction to the fundamentals of this versatile area of mathematics. Acknowledging the field’s increasing importance across disciplinary boundaries, this text relates real analysis concepts and methods to applications in a variety of fields. Extensive use of examples and exercises underscores the necessity of hands-on learning and independent practice, while detailed appendices and early review chapters help students strengthen individual weaknesses to improve comprehension of new material. In-depth discussions surrounding sequences and series ensure a firm grasp of this fundamental topic, as these principles underlie much of the material that follows.