MATH 115 Calculus I, fall '23

Most of the course will be devoted to the study of differential calculus, which is the study of the rate of change, followed by a brief introduction to integration.  Both concepts rely heavily on the notion of a limit, which is a way to handle things infinitely big or infinitely small, so that will be the central topic of the first part of the course from which we will build the rest of the theory. Calculus has many applications, some of them very cool and unexpected, so we'll try to cover as many of those as possible.

The general objective of this course is thus to provide you with an understanding and working knowledge of calculus, but in the process I hope to help you strengthen your analytical skills, increase your ability to communicate mathematics symbolically and orally, make you comfortable with reading and understanding mathematics on your own, and develop an appreciation for calculus as one of the greatest intellectual developments in history.

Here are some specific topics we will cover:

• Limits and limit laws

• Continutity

• Derivatives and rates of change

• Product, Quotient, and Chain Rule

• Implicit differentiation

• Derivatives of trigs, log, and exponential functions

• Applications of derivatives in the natural and social sciences

• Linear approximation

• Related rates

• Optimization problems

• Antiderivatives

• Areas

• Riemann sums

• Definite integrals

• Fundamental Theorem of Calculus

• Substitution