Math 115, Calculus I

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


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