Discusses the direction in which the field of differential equations, and its teaching, is going.

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

The book is intended to serve as as a textbook for undergraduate and honors students. It will be useful to the engineering and management students, and other applied areas. It will also be helpful in preparing for competitive examinations like IAS, IES, NET, PCS, and other higher education exams. Key Features: Basic concepts presented in an easy to understand style, Notes and remarks given at appropriate places, clean and clear figures given for better understanding, includes a large number of solved examples, Exercise questions at the end of each chapter, Presentation of the subject in a natural way.

A method of analysis is developed for two dimensional flow on general surfaces of revolution in turbomachines with arbitrary blade shapes. The method of analysis is developed for steady, compressible, nonviscous, irrotational flow that is assumed uniform normal to the surfaces of revolution. Incompressible solutions on a mean surface of revolution between the hub and shroud are presented for four rates through each of two centrifugal impellers with the same hub-shroud contours but with different blade spacings. In addition, correlation equations are developed whereby the velocity components and the stream function distribution can be predicted for compressible or incompressible flow in straight-blade impellers only, with any tip speed, flow rate, area variation, blade spacing, and for any flow surface of revolution.

This authoritative text concentrates on the derivation of simple but reasonably accurate mathematical solutions, and the actual presentation of closed-form results for quantities that are of interest to the designer of shell structures.