Introduction to Calculus

MATH 1A Subject & Catalog Number

Description

Calculus stands as one of the great intellectual achievements of the last millennium, developed by Newton and Leibniz to understand motion, growth, and change. This single-variable course introduces you to that achievement by focusing on these central ideas: how differential calculus describes rates of change, how integral calculus describes accumulation, and how the Fundamental Theorem of Calculus connects them. Throughout, you will see these ideas at work in concrete problems drawn from the physical sciences, life sciences, economics, and everyday contexts.

A central theme of the course is understanding, describing, and calculating rates of change. You will learn to interpret derivatives graphically and numerically, connect derivatives to the shape and behavior of graphs, and use derivative techniques—including product, quotient, and chain rules, implicit and logarithmic differentiation—to solve optimization and related rates problems in context.

In the second part of the course, attention shifts from rates to accumulation. You will be introduced to the definite integral as a precise way to describe accumulated change over time—mathematically, a way of “adding up pieces” such as small changes, areas, or contributions to a total.

Throughout the semester, you will use algebraic reasoning—together with graphical, numerical, and symbolic representations of functions—to justify your conclusions, interpret situations, test ideas, and make sense of unfamiliar problems.