This is a first-year Introduction to Differential Calculus course containing some applications to the Sciences. In general, theorems will be stated precisely, mostly without proofs but with an indication of the mathematical ideas involved. The topics to be covered in this course include: Review of Trigonometry, Limits, Continuity, Rules of Differentiation, Implicit Differentiation, Higher Derivatives, Derivatives of Logarithmic, Exponential and Inverse Trigonometric Functions, Lâ€™Hospitalâ€™s Rule, Related Rates, Mean Value Theorem, Graphing, Optimization Problems, Exponential Growth and Decay Problems, Examples from Life and Physical Sciences Applications, Antiderivatives.