Math 10550 is the first course of a two-semester sequence. In Math 10550, we explore the properties of functions and how to interpret and apply this theory to real world situations. We use the concept of limits and continuity to bridge the gap between average and instantaneous change (a.k.a. the derivative). We study methods of differentiation (caluclating the derivative) in detail.
Applications of differentiation studied include the analysis of motion in a straight line, linear approximation, related rates, exponential growth and decay, techniques of graphing and optimization.
In the last part of the course, we turn our attention to approximating the area under a curve and use limits to find that area for continuous functions. This process is called integration and the aptly named Fundamental Theorem of Calculus shows how differentiation and integration are inverse operations. This simplifies calculation of the area under a curve for many well known curves. As examples of applications, we will look at how to use the process of integration to calculate areas and volumes.
The tutorial Math 12550/12350 is a corequisite for this class