Differential Calculus

Abstract

These notes are intended to be used in first-semester calculus. Rather than having the structure of a typical textbook (narrative, examples, practice problems at home), each chapter consists of a carefully designed sequence of problems and questions that – if completely solved and understood in order – will deliberately lead each student to a full comprehension of differential calculus.

This student-centered (as opposed to instructor-centered) instruction has proven to be highly effective at all levels of learning. Commonly referred to as Inquiry- or Discovery-Based Learning, this method was pioneered several decades ago at UT-Austin by R. L. Moore. A controversial figure, Dr. Moore championed the philosophy that the level to which students can learn mathematics should not be damped by the knowledge of the instructor. In other words, it should be possible for a student to learn more than the instructor knows. This style of teaching (or rather that of learning) more than allows for this possibility.