The present book having nine chapters offers a first course on calculus (of functions of real variables) for graduate and college students. It comprises of three segments: ‘differential calculus'' (dealing with the differentiation of functions), ‘integral calculus'' (giving integration of functions) and ‘ordinary linear differential equations'' involving two variables. The third segment offers an elementary course on differential equations and their applications mainly to the problems of rate of change (increase or decrease). In the end, 12 Tutorial sheets containing model questions, few Test Papers and a short bibliography of the subject are provided. The alphabetical index added in the end makes the faster access of the contents to the reader. More advanced topics of all above segments are kept away from the book. The contents of the exposition offered can be covered in one semester with four credit hours per week teaching.