This mathematically challenging and precise text covers trigonometric and logarithmic functions, and differential equations early, with Numerical methods gathered in a single chapter. Applications of the integral precede techniques of integration and include probability distributions, areas, volumes and length, areas of surfaces of rotation, work and fluid pressure. Problem sets are large, well-graded and cover a wide range of applications, including optional computer exercises. Coverage of moments of continuously distributed masses is delayed until the multivariable chapter, where multivariable differential calculus is divided into two and three variables, and one primarily with differentiability and its consequences. Tables of integration and their use has a special section in the coverage of techniques of integration, and the coverage of vector field theory is thoroughly and carefully presented. This book should be of interest to degree and diploma students on calculus courses in departments of mathematics, engineering or physical sciences; a background in algebra and trigonometry is a prerequisite.