Welcome to Calc I! In this course, we will study the foundations of calculus, the study of functions and their rates of change. We want you to learn how to model situations in order to solve problems. If you have already taken calculus before, we want you to gain an even deeper understanding of this fascinating subject. The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two ideas form the basis for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. The importance of calculus can not be overstated! In physical and biological sciences, economics, and even social sciences, the transition from qualitative or descriptive understanding to a more quantitative understanding is invariably achieved through mathematics and calculus in particular. This is because in all of these natural systems, one studies quantities that change with time or parameter values and inter-relations between such variables. This is the reason why a strong foundation in calculus is necessary in order to understand your chosen field of study at a deeper level. |