This book is designed to meet the requirements of students of Science and Engineering. This book offers the following chapters: Concepts of Limits and Continuity, Differentiability, Rolle's and Mean Value Theorem, Successive Differentiation (Leibnitz's Theorem), Expansion of Functions (Taylor's and Maclaurin's Series), Asymptotes, Curvature, Double Points and Curve Tracing. Each chapter is supplemented with a number of worked out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject.