The objective of this course is to familiarize students with important concepts coming under the branch “Differential Calculus” and to develop strong foundations on these concepts. Upon successful completion of this course, the students are expected to: 1. Familiarize with the concept of Limit and Continuity (Both informal and ε- δ definition) 2. Learn through examples Successive differentiation and Leibniz’s theorem. 3. Study Rolle’s theorem, Mean Value theorems through examples. 4. Study the concepts tangents and normals. 5. Familiarize with methods of finding Curvature, Asymptotes and Singular points. 6. Learn methods of Tracing of curves in Cartesian, Parametric and Polar forms 7. A study on sequences and series 8. A detailed study on Taylor’s theorem, Taylor’s series and Maclaurin’s series through examples. 9. Familiarise with functions of several variable. 10. Study Euler’s theorem on homogeneous functions and some of its mathematical applications.