Lectures in Integral Calculus

This book is a complete course in integral calculus of one variable, based on lectures given by the author at UC San Diego over the past several years. It starts with defining antiderivatives and indefinite integrals, discusses the construction of the definite integral, and then connects these ideas with the fundamental theorem of calculus. We demonstrate integration using the method of substitution, integration by parts, and the method of partial fractions. We also look at areas, volumes, improper integrals, and separable ... Read More

This book is a complete course in integral calculus of one variable, based on lectures given by the author at UC San Diego over the past several years. It starts with defining antiderivatives and indefinite integrals, discusses the construction of the definite integral, and then connects these ideas with the fundamental theorem of calculus. We demonstrate integration using the method of substitution, integration by parts, and the method of partial fractions. We also look at areas, volumes, improper integrals, and separable differential equations. These lectures form a detailed first look at integral calculus, as one might see in a ten-week quarter at UC San Diego. In addition to a complete collection of lectures, each lecture is accompanied by exercises (with answers!) that are intended to help students develop mastery of the skills needed for this fascinating topic. Read Less