Originally published in 1962, as the second edition of a 1930 original, 'the main purpose of the book is to give a logical connected account of the subject, by starting with the definition of 'Number' and proceeding in what appears ... to be a natural sequence of steps'. The chapters cover all of the cornerstones of complex mathematical analyses; chapters include, 'Bounds and limits of sequences', 'Integral calculus' and 'Functions of more than one variable'. Multiple examples are included at the end of every chapter to support and illustrate the fundamental concepts; 'I have aimed at presenting the subject in such a way as to make every important concept clearly understood'. Primarily aimed at undergraduates with a background in advanced calculus for study and practice, this comprehensive and dynamic textbook will be of considerable value to scholars of mathematics as well as to anyone with an interest in the history of education.