This is a textbook for the second semester of calculus. The major topics are applications of integrals, methods of integration, the inverse trigonometric functions, elementary differential equations, calculus with polar coordinate functions and functions given by parametric equations, sequences and infinite series. The text has explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Topics are typically introduced by way of applications, and the text contains the usual theorems and techniques of a second semester of calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of calculus. The exposition and problem sets have been highly rated by reviewers.