111 Math

About this course

Math 111 is a course about the integral. Where the first calculus course asks how quantities change, this one asks how change accumulates — and the answer turns out to be one of the most useful ideas in mathematics.

We build the integral from the ground up, starting with sums of rectangles under a curve and arriving at the Fundamental Theorem of Calculus, the result that ties integration and differentiation together and makes both practical. From there the course divides into two halves. The first is technique: how to actually evaluate an integral, using substitution, integration by parts, trigonometric methods and partial fractions, along with the transcendental functions that arise naturally along the way. The second is application: using integration to find areas between curves, volumes of solids, arc lengths and surface areas, and to work in polar coordinates where the geometry calls for it.

The course rewards steady practice more than any other mathematics course you will take. Integration is a skill in pattern recognition — knowing which technique a given integral calls for — and that recognition comes only from working through problems. Attempt the exercises as each topic is covered rather than saving them, and please come to office hours early if something is not settling.

Course Description: Riemann Sums, Area, Fundamental Theorem of Calculus, Definite Integrals, Numerical Integration. Transcendental Functions with their Differentiation and Integration, Indeterminate Forms. Techniques of Integrations, Improper Integrals. Applications of integrations: Area, volume and Arc Lengths. Integrals in Polar Coordinates. Parametric Equations for Curves.

Course materials: the syllabus, section-wise exercises and textbook are attached below and on the Syllabus and Text Books pages.