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A Problem Text in Advanced Calculus
From the Preface:
In American universities two distinct types of courses are often called “Advanced Calculus”: one, largely for engineers, emphasizes advanced computational techniques in calculus; the other, a more “theoretical” course, usually taken by majors in mathematics and physical sciences (and often called elementary analysis or intermediate analysis), concentrates on conceptual development and proofs. This ProblemText is a book of the latter type. It is not a place to look for post-calculus material on Fourier series, Laplace transforms, and the like. It is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from.
In American universities two distinct types of courses are often called “Advanced Calculus”: one, largely for engineers, emphasizes advanced computational techniques in calculus; the other, a more “theoretical” course, usually taken by majors in mathematics and physical sciences (and often called elementary analysis or intermediate analysis), concentrates on conceptual development and proofs. This ProblemText is a book of the latter type. It is not a place to look for post-calculus material on Fourier series, Laplace transforms, and the like. It is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from.
381 pages, ebook
First published January 1, 2009
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February 9, 2010
Prof. Erdman made this book available online in PDF format, along with its LaTeX source code, for anyone to download and read.
It's probably more valuable if you're taking a class from him as you read through it and do the problems, but I really like the style of the book.
In class, we rushed quickly through all of the Appendices to fill in any gaps in our background knowledge before proceeding to Chapter 1. If you're going to go through the book on your own, I'd recommend that you at least skim the Appendices first to make sure you are using the same definitions.
There is very little in the way of repetitive problems. It is likely that if a problem looks very similar to the one immediately prior, there is some significant difference between them that will be worthwhile to track down and understand.
It's probably more valuable if you're taking a class from him as you read through it and do the problems, but I really like the style of the book.
In class, we rushed quickly through all of the Appendices to fill in any gaps in our background knowledge before proceeding to Chapter 1. If you're going to go through the book on your own, I'd recommend that you at least skim the Appendices first to make sure you are using the same definitions.
There is very little in the way of repetitive problems. It is likely that if a problem looks very similar to the one immediately prior, there is some significant difference between them that will be worthwhile to track down and understand.
Displaying 1 of 1 review