Outlines theory and techniques of calculus, emphasizing strong understanding of concepts, and the basic principles of analysis. Reviews elementary and intermediate calculus and features discussions of elementary-point set theory, and properties of continuous functions.

This classic text by a distinguished mathematician and former Harvard University Professor of Mathematics covers partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, and much more. Exercises and selected answers are included. Professor Widder’s classic math text takes students familiar with elementary calculus on a journey of mathematical discovery, introducing them to more theoretical problems and solutions that extend beyond elementary calculus. Not only does he guide students in mastering the material within this book, but he also offers insight into how these lessons can be applied to practical use in engineering and mathematics disciplines. The author states exactly what is to be proved in every case. Definitions, theorems, proofs, examples, and exercises are included in each section, and each theorem’s statement has been condensed so that the student can see the essential hypotheses and conclusions at a glance. In this second edition, the author has improved the treatment of Stieltjes integrals to make it more useful to readers who are unfamiliar with the basic facts about the Riemann integral. In addition, the material on series has been augmented by the inclusion of the method of partial summation of the Schwarz-Holder inequalities as well as additional results about power series. Carefully selected exercises, graded in difficulty, are found in abundance throughout the book; answers to many of them are contained in the final section. A COMPLETE, EXPANDED EDITION-Advanced Calculus: Second Edition provides a more in-depth exploration, delving into theoretical problems and solutions that go beyond elementary calculus. CLEARLY STATED THEOREMS-The author has made a point of stating each theorem concisely so that the student can see at a glance the essential hypotheses and conclusions. Each section consists of definitions, theorems, proofs, examples, and exercises. VARIETY OF EXERCISES-Graded in difficulty, exercises abound throughout the book to help students cement their understanding of the concepts being taught. Answers to many of them are contained in the final section. INCLUDES MATERIAL ON SERIES AND STIELTJES INTEGRALS-two key topics in calculus that often give students trouble. With this text, you’ll be able to overcome any challenges you may face with these concepts.