In this calculus course, we shall start with the (quick) reviews of basic properties of certain elementary functions, for example, the sum to product identity of trigonometry functions. From this standing point, we look into the difference quotients and derive the derivatives of elementary functions. The technique of finding max and min of a function is one of the important ingredients. We then introduce how to plot graph and classify the asymptotic behaviors of functions. We explore several approximation methods and scientific models as well. In the second part of the semester, we introduce the series and integral. The useful convergence tests and different integral skills will be introduced.