What do you think?
Rate this book
A First Course in Calculus
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.
746 pages, Hardcover
First published December 1, 1964
11 people are currently reading
235 people want to read
About the author
Serge Lang
175Ìýbooks53ÌýfollowersSerge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.
Librarian Note: There is more than one author in the GoodReads database with this name.
Librarian Note: There is more than one author in the GoodReads database with this name.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 5 of 5 reviews
December 12, 2019
4th edition.
Perfect book to review all the basic concepts of single variable calculus on field R.
If you need epsilon-delta based rigorous proofs on the notion of limit/least upper bound property etc, it is given in the appendix.
It serves as a good textbook companion to MIT's single variable calculus videos by Prof. Jerison. of which I am a big fan. Most chapters had right amount of appeal to geometry before proving the theorems. But the last chapter on power series unabashedly approaches epsilon-delta formalism therefore unsuitable for light reading/skimming.
Side note: This is a calculus book written by an algebraist! I hope to read an Algebra book written by a confirmed Analyst (It looks like "Linear algebra done wrong" might fit the bill).
Perfect book to review all the basic concepts of single variable calculus on field R.
If you need epsilon-delta based rigorous proofs on the notion of limit/least upper bound property etc, it is given in the appendix.
It serves as a good textbook companion to MIT's single variable calculus videos by Prof. Jerison. of which I am a big fan. Most chapters had right amount of appeal to geometry before proving the theorems. But the last chapter on power series unabashedly approaches epsilon-delta formalism therefore unsuitable for light reading/skimming.
Side note: This is a calculus book written by an algebraist! I hope to read an Algebra book written by a confirmed Analyst (It looks like "Linear algebra done wrong" might fit the bill).
July 18, 2015
This was an excellent text for self-studying the beginnings of calculus. It makes proofs accessible, and even taught me how to prove concepts that seemed obvious but were easy to forget when not used for a while. Learning how to derive and prove concepts like this is essential for someone who wants to study physics, which is the case for me.
I have reservations for recommending this book for Calculus II and beyond. Seeing second- and third-semester calculus topics listed in the table of contents raised my hopes for learning Calc II and III from Lang. Beginning with Taylor polynomials, however, Lang's calculus skipped explanations, became unnecessarily abstract when explaining relatively simple ideas, and yet did not cover the operations I needed in enough depth. This text was not sufficient for learning the calculus of vectors and volume integration.
If you understand pre-calculus and trigonometry, go with this text to learn derivative and integral calculus. Go elsewhere for series, vectors, and multivariable functions.
I have reservations for recommending this book for Calculus II and beyond. Seeing second- and third-semester calculus topics listed in the table of contents raised my hopes for learning Calc II and III from Lang. Beginning with Taylor polynomials, however, Lang's calculus skipped explanations, became unnecessarily abstract when explaining relatively simple ideas, and yet did not cover the operations I needed in enough depth. This text was not sufficient for learning the calculus of vectors and volume integration.
If you understand pre-calculus and trigonometry, go with this text to learn derivative and integral calculus. Go elsewhere for series, vectors, and multivariable functions.
September 20, 2012
This is a very good book for Calculus beginners. The new edition of the book has fully solved examples.
March 11, 2022
Nice and easy on basic topics from numbers and differentiation to Taylor polynomial and series, with easy-to-follow explanations. Good stepping stone for further studies.
March 13, 2024
Trivialement trivial
Displaying 1 - 5 of 5 reviews
Can't find what you're looking for?
Get help and learn more about the design.