From the reviews "This is a reprint of the original edition of Lang’s ‘A First Course in Calculus’, which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish it’....[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging....There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." --Mathematical Gazette
This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.
This book, modern in its writing style as well as in its applications, contains numerous exercises--both skill oriented and applications--, real data problems, and a problem solving method.The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes, strategic checkpoints, interactive activities, section summaries and projects, and chapter openers and reviews.For anyone who wants to see and understand how mathematics are used in everyday life.
This is a textbook for an intermediate level course in microeconomics that uses calculus throughout. Most of the competition either uses no calculus or relegates the math to footnotes and appendices. The text also focuses on theory rather than empirical data. To motivate the analysis, the authors include references to real events and firms, with no distracting separate boxes.
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
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.
Two-dimensional calculus is vital to the mastery of the broader field, and this text presents an extensive treatment. Advantages include the thorough integration of linear algebra and development of geometric intuition. 1986 edition.
