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e-Book Short Calculus: The Original Edition of “A First Course in Calculus” (Undergraduate Texts in Mathematics) epub download

e-Book Short Calculus: The Original Edition of “A First Course in Calculus” (Undergraduate Texts in Mathematics) epub download

Author: Serge Lang
ISBN: 0387953272
Pages: 260 pages
Publisher: Springer; Reprint of the 1st ed. Addison-Wesley, 1964. edition (November 29, 2001)
Language: English
Category: Mathematics
Size ePUB: 1459 kb
Size Fb2: 1117 kb
Size DJVU: 1278 kb
Rating: 4.1
Votes: 746
Format: lit lrf docx lrf
Subcategory: Science

e-Book Short Calculus: The Original Edition of “A First Course in Calculus” (Undergraduate Texts in Mathematics) epub download

by Serge Lang



But even Lang's full First Course is shorter than most calculus texts; and the First Course goes beyond the Short Calculus by the addition of four extra chapters, concerned with functions of several variables.

Covers everything in my college calculus course and thensome. Lots of problems to do, often too much to do in a single sitting

Only 10 left in stock (more on the way). Covers everything in my college calculus course and thensome. Lots of problems to do, often too much to do in a single sitting. Makes basic calculus very easy to understand.

Undergraduate Texts in Mathematics (UTM) is a series of. .

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. There is no Springer-Verlag numbering of the books like in the Graduate Texts in Mathematics series. The books are numbered here by year of publication. ISBN 978-0-387-95327-4. Estep, Donald (2002).

The advantage of this book is that you can get a first look at calculus in the span of 240 pages.

I was fortunate to come across a copy of the Short Calculus at a cost of even less. The advantage of this book is that you can get a first look at calculus in the span of 240 pages.

A First Course in Calculus book Original Title. A First Course in Calculus (Undergraduate Texts in Mathematics).

A First Course in Calculus book. Details (if other): Cancel. 0387962018 (ISBN13: 9780387962016).

The audience consists of those taking the first calculus course, in high school or college.

This is a reprint of A First Course in Calculus, which has gone through . There are no epsilon-deltas, but this does not imply that the book is not rigorous.

It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students¿ background was not as substantial as it might be. We are now back to those times, so it¿s time to start over again. Lang learned this attitude from Emil Artin, around 1950.

File: PDF, . 6 MB. Save for later

It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students'background was not as substantial as it might be. We are now back to those times, so it's time to start over again. Series: Undergraduate Texts in Mathematics. File: PDF, . Save for later.

transitorykris · 2017-04-21 · Original thread. This is an incredible book. I'm a visual thinker, and while this book lacks all the glossy pages of illustration found in a modern Calculus textbook, the writing style helps develop that visual intuition. In the same vein of concise Calculus books, Serge Lang's Short Calculus is also great (if you need a refresher, or if you're just starting out). Get dozens of book recommendations delivered straight to your inbox every Thursday.

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

Bajinn
Very succinct, has a small amount of problems. It is less intimidating than those huge calculus textbooks, but I think that if you really want to master the subject you need a source of more problems to work out, because this book does not have enough.
Buzatus
This is a reprint of the first edition of what was given its final form by Serge Lang in the 5th edition of his A First Course in Calculus. Both are published by Springer, so it's tempting to make page number comparisons and point out that it takes 500 pages to reach the appendix on epsilon and delta in the 5th edition "First Course" and it takes only 226 pages in the 1st edition "Short Calculus". But the fonts differ, and sometimes Lang broke a paragraph into more than one, and he often added more exercises. Sometimes the extra text is additional examples. He also added graphs and diagrams. The page layout sometimes differs, so occasionally graphs or diagrams take up more space in the 5th edition. It's not the case, then, that the final edition is really twice as long in content as the first.

I have a copy of the 4th edition (Addison Wesley, pub.s) and also a copy of the Short Calculus. As soon as I got this Short Calculus home, I opened the 4th edition and started to compare page-by-page the two books. It's interesting to see what Lang kept and how he revised the chapters from their first edition form. Changes show up already in section 1 of chapter 1, where he adds what amounts to a half-page in the 4th edition within what is page 2 of the 1st edition. But then he's also deleted text from this section: text which amounts to a page and a quarter from the 1st edition version of this section is gone by the 4th edition. Sometimes the changes expand and clarify the text, sometimes they tighten it and make it move quicker. Interestingly, in the section on sums, products, and quotients (Ch 3: The Derivative), he lists the rules at the end of the section of the 1st edition, and in the 4th they aren't there. Chapter 4, on sine and cosine, is significantly expanded from the 1st edition. The appendix on epsilon and delta is also expanded.

From comparing my copy of the 4th edition to what I can see of the 5th through the amazon page-view feature, Lang expanded on the 4th in making the 5th and moving to Springer as his publisher; so the 5th is one more revision removed from the Short Calculus.

Another example of expansion in later editions is the section on rate of change, in chapter 3. In the 1st edition it is a single page long, and in the 4th around 6 pages longer. This is Lang's initial nod to physical applications. This 1st edition has a second appendix following the one on epsilon and delta. In the 4th edition, the content of that second appendix occurs as an introduction to chapter 12, on applications of integration. The appendix is entitled "Physics and Mathematics" and Lang there remarks: "For psychological reasons, it is impossible (for most people) to learn certain mathematical theories without seeing first a geometric or physical interpretation. ... These two [i.e. mathematical theories and the interpretations of them], however, should not be confused." (p. 239) Most calculus textbooks that are currently published mix together the mathematical concepts and scientific applications in which those mathematical concepts are used to model and interpret scientific concepts (or even other mathematical concepts). As Lang points out: "Nevertheless, it is important to keep in mind that the derivative (as the limit of f(x+h)-f(x) / h) and the integral (as a unique number between upper and lower sums), are not to be confused with a slope or an area respectively. It is simply our mind which interprets the mathematical notion in physical or geometric terms. Besides, we frequently assign several such interpretations to the same mathematical notion (viz. the integral being interpreted as an area, or as the work done by a force)." (p. 240)

This book, especially in its 1st edition, is about the mathematics of calculus. It is not a book on "calculus and its applications", as most current calculus textbooks are.

The retail prices for the Short Calculus (paperback) and for the 5th edition of A First Course in Calculus (hardcover) differ by $20 but currently they sell through amazon for essentially equivalent prices. I was fortunate to come across a copy of the Short Calculus at a cost of even less. The advantage of this book is that you can get a first look at calculus in the span of 240 pages. But even Lang's full First Course is shorter than most calculus texts; and the First Course goes beyond the Short Calculus by the addition of four extra chapters, concerned with functions of several variables. Followups to this book (in any edition) are Lang's Calculus of Several Variables, from which the four additional chapters of the First Course are taken (the added chapters are the first chapters of the Calculus of Several Variables), and his Undergraduate Analysis.