Taken from Syllabus:
This course covers polynomial, trigonometric, exponential, and logarithmic functions; first and second derivatives and their interpretations; definition and interpretation of the integral; differentiation rules; implicit differentiation; applications of the derivative; anti-derivatives; fundamental theorem of calculus.
There are as many reasons to learn calculus as there are students taking this class. Calculus is applied in every area of science. Traditionally, Calculus is a way of mathematically formalizing concepts that involve change or motion. In particular, one of the standard applications discussed in calculus is the relationship between position, velocity, and acceleration of an object. Sir Isaac Newton used calculus to describe how gravity acts and to describe the motion of planets.
Another application discussed in calculus is the relationship between areas of regions and the curves on the boundary of those regions. This is later expanded to the relationships between volume and the surface on the boundary of a shape. These topics in calculus were foreshadowed in ancient times by Archimedes in his methods of calculating areas and volumes.
The ideas of an "infinitesimal" and "limits" were necessary to develop both of the above applications, which is where the Calculus sequence begins. From there the relationships between position, velocity, and acceleration may be described formally via the derivative. Then the relationship between area and boundary curves may be developed using integrals. All of these topics are introduced in the first course in the Calculus sequence. The second and third courses in the sequence develop further all three of limits, derivatives, and integrals, as well as their applications.