This course is concerned with the study of limits of real functions of a single variable, continuity derivatives and their applications as mentioned in the topics below. 1. The Limit of a function. 2. Continuity and its Consequences, domain and range of functions, hyperbolic and inverse hyperbolic functions. 3. Derivatives. The Chain Rule, Derivatives of polynomial, Exponential and Logarithmic Functions, Trigonometric and Inverse Trigonometric Functions, hyperbolic and inverse hyperbolic functions, Implicit Differentiation. Higher Order Derivatives, 4. Applications of derivatives. Indeterminate Forms and, L’Hospital’s rule, local extrema, concavity, horizontal and vertical asymptotes. Graphing curves, applications of extrema, related rates, Rolle’s theorem, mean value theorem, Taylor and Maclurin’s series in one variable.