This course
discusses differential and integral calculus. The heart of calculus
is the study of rates of change. Differential calculus concerns the
process of finding the rate at which a quantity is changing (the
"derivative") and applying this information. As a student in Math
115, you will learn to calculate derivatives for a library of
standard functions (including polynomials, trigonometric functions,
logarithms, and exponentials). In this course derivatives are also
discussed for functions that are described by graphs or tables
(rather than by formulas). Such functions occur in many of the
applications of calculus to other fields. Seeing concepts in multiple
contexts also helps your understanding. Once you know how to find the
derivatives, you then learn how to apply this information to a
variety of problems.
Integral calculus reverses this process. Information is given about
the derivative (the rate of change). Then you use the process of
"integration" to find the "integral," which gives the accumulated
change over some period. Integration is closely connected to
antidifferentiation, which gives all functions having the given rate
of change. Given information about the rate at which a population is
growing, for example, integral calculus describes how the population
size will evolve.
This course aims to have you understand differentiation and the
concept of integration thoroughly and to learn a little about
techniques and applications of integration. Integration techniques
and applications are explored more thoroughly in 116.
Calculus is a beautiful subject that is universally recognized as one
of the triumphs of the human intellect. It arose for the purpose of
being able to answer questions in other fields. This course aims both
to have you appreciate the beauty of calculus, and to be comfortable
understanding and applying the concepts of calculus when you
encounter them in other courses. Many of the examples and homework
problems are based on realistic applications to fields such as
economics, physics, chemistry, biology, astronomy, population
dynamics, and medicine.
Open by permission of the department, based on the results of the
departmental placement exam. Intended for all students who have not
taken an equivalent course.
Distribution: Mathematical Modeling