Advanced Calculus

by David Vernon Widder

This classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text in both applied mathematics and engineering.Believing that clarity of exposition depends largely on precision of statement, the author has taken pains to state exactly what is to be proved in every case. Each section consists of definitions, theorems, proofs, examples and exercises. An effort has been made to make the statement of each theorem so concise that the student can see at a glance the essential hypotheses and conclusions.For this second edition, the author has improved the treatment of Stieltjes integrals to make it more useful to the reader less than familiar with the basic facts about theRiemann integral. In addition the material on series has been augmented by the inclusion of the method of partial summation of the Schwarz-Holder inequalities, and of 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 a final section.

Genres: Mathematics, Reference, Textbooks, Calculus, Science, Nonfiction

520 pages, Hardcover

First published January 1, 1989

Reviews

[Ayush Bhat · Rating 5 out of 5]

He has explained Fourier Series so beautifully, He explained Fourier Integrals just by turning discrete indexes of Fourier Series into continuous which technically becomes frequency in Physics.

[William Schram · Rating 4 out of 5]

Advanced Calculus is a textbook written by David V Widder. It contains problems to solve and proofs to complete. Professor Widder does an excellent job of explaining the subject.

I assume that people reading this know what calculus is. Advanced Calculus begins with Partial Derivatives and focuses on multivariable problems.

Since the book is a Dover reprint, some of the text is faint. I don't have any other problems with the book.

The book has fourteen chapters, a list of selected answers, and a glossary of symbols used, and is user-friendly, considering it is a book. It builds on itself but expects you to know the basics of Calculus.

The farthest I have gotten in Calculus is the second semester, so I am ill-equipped to understand a lot of this. However, much of it is familiar to me. The book mentions Rolle's Theorem and others that I remember from my time in Calculus class. The only difference is in the leap required from one variable to two or more.

[Tom Ritman-Meer · Rating 5 out of 5]

Excellent calculus text. Improved my understanding considerably.

[Thomas Dubium · Rating 4 out of 5]

very much missing in school. this book helped many things

[Matthieu · Rating 5 out of 5]

Changed everything. One of the most beautiful and satisfying textbooks ever printed. The 'vibrating string' section (Fourier Series) is breathtaking. I can't even begin to say how important this book is (to me).

[Sanjay]

this is stupid website..

[Ashiqul Dip · Rating 4 out of 5]

Mathematically rigorous, but difficult to digest. I liked the chapter on Fourier specially.

[Kumar Mayank]

good