The subject of integration of functions of a single variable is treated in the first eight chapters. Emphasis is here laid upon the fundamental processes, and the conception of the definite integral and its numerous applications are early introduced. Only after the student is well grounded in these matters are the more special methods of evaluating integrals discussed. In this way the student's interest is early aroused in the use of the subject, and he is drilled in those processes which occur in subsequent practice. A new feature of this part of the book is a chapter on simple differential equations in close connection with integration and long before the formal study of differential equations.