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Calculus: A Computer Algebra Approach

I. Anshel and D. Goldfeld
International Press
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
, on

This is a very conventional calculus text, covering single-variable and multivariable calculus, series, and a lot of vector calculus including some differential forms. This is a 1996 text that was reissued in paperback in 2011.

Despite the subtitle, it is not a “computer algebra approach” but is a traditional approach. Computer algebra systems (CAS) make almost no appearance in the narrative, although many or most of the exercises in the first half of the book ask the student to use their CAS as an oracle to check results or do some of the drudge work. The CAS references almost disappear in the vector and multivariable parts, except for graphing. There are no experimental math or numerical math aspects to the book. It is not tied to a particular CAS and in fact does not give any instructions on how to use a CAS.

There are a large number of exercises, but nearly all are routine drill. There is an accompanying instructor’s manual with the answers to all exercises.

Bottom line: Although not a bad book, there is nothing special about it to distinguish it from hundreds of other freshman calculus books. One selling point may be that it is much less expensive than some (though not all) competing books.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at, a math help site that fosters inquiry learning.

1. What is Calculus?
2. Functions and their Graphs
3. The Algebra of Functions
4. Lines, Circles, and Curves: a Review
5. Limits and Continuity
6. The Derivative
7. Basic Applications of the Derivative
8. The Rules of Calculus
9. Implicitly Defined Functions and their Derivatives
10.The Maxima and Minima of Functions
11.Classical Optimization Theory
12.Graphing Functions
14.The Integral as Area
15.Sums, Induction, and Computation of Integrals
16.The Integral as an Antiderivative
17.Basic Applications of the Integral
18.Further Topics on Integration
19.Infinite Series
20.Taylor Series
21.Vectors in Two and Three Dimensions
22.Two and Three Dimensional Graphics
23.Calculus of Vector Valued Functions
24.Functions of Several Variables
25.Multidimensional Optimization
26.Double Integrals
27.Triple Integrals
28.Vector Fields and Line Integrals
29.Surface Integrals
30.Differential Forms: An Overview
31.Fourier Series