An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

It is a known fact that there is no substitute for hard work - However hard work must be done smartly to get the desired result. Keeping Smart Hard Work philosophy in mind, we have designed this book. As time plays an important factor & is limited in competitive exams hence the magic to score high in such examination is to solve questions accurately with speed. The ability to solve lengthy questions accurately in the shortest possible time will fetch you lead over other students resulting not only into good marks but also top rank. And the Short Tricks is sure to make it happen. For this purpose, we are elated to present a compilation of Short Tricks of Mathematics in a book form. These tricks have the edge which can make any aspirant solve questions accurately & quickly.

This book contains theory and a large collection of about 7500 questions. In each chapter, theory is divided into Sections and questions are divided into Question Categories. For each Section there are one or more corresponding Question Category/ Categories in order to make this book more readable and more useful for the readers and students. This book is useful for students and learners of IIT-JEE, Higher and Technical Mathematics; and also for the students who are preparing for Standardized Tests, Achievement Tests, Aptitude Tests and other competitive examinations all over the world.