Bassein, An Infinite Series Approach to Calculus
xvi + 361 pages.   Clothbound.  1993

 Click on cover picture for more detailed image     

Contents:

PART 1    Making sense of infinity
                     1 Discrete models
                     2  Functions and continuity of the line
                     3  Infinite series
                     4  Functions and power series

PART 2    Differentiation: rate of change
                     5  Linear and quadratic functions
                     6  Derivatives of Polynomials
                     7  Power series and differentiability
                     8  Differential equations
                     9  Compositions and quotients of functions
                    10  Inverse functions
                    11  Extreme values
                    12  Graphing
                    13 Functions of two variables

PART 3    Integration
                    14  Anti-derivatives
                    15  Areas
                    16  Techniques of integration
                    17  Lengths
                    18  Volumes and surface areas
                    19 Approximation of integrals
                    20 Improper integrals
                    21 Analytic functions
                    22 Techniques in solving differential equations

From the Acknowledgements:

Despite the single authorship indicated, this textbook could not have been written without the help of many people. The most important of these are the many students, primarily the women undergraduates at Mills College to whom I have taught calculus during the past 23 years:  by balking at the apparently paradoxical definitions and concepts that I accepted so glibly when I was a student, they pushed me to search for the deeper directions of the path along which I wanted to lead them through the mathematics.  Over the years, I began to see that when the students did not seem to understand some concept, it was less the result of any inherent difficulty in that concept than of my failure to demonstrate the necessity of introducing the complications.

Two books have significantly influenced my approach to teaching, which is reflected in this text. Evelyn Fox Keller's insightful and inspiring book, "Reflections on Gender and Science" (Yale University Press, 1985), made me aware of my persistent but unrecognized discomfort with the Baconian paradigm of mathematics, science, and technology as a battle to subdue nature, and gave voice to my unspoken feeling that these pursuits can be, instead, an expression of one's love of the world.  i believe that an important factor in my increasing success in reaching students is my newly acquired awareness of this latter point of view, in which we and the world we experience become completely intertwined, in which we are influenced by that world as much as we influence it, and in which we are guided by our feelings and desires, tested by reason. Belenenky, Clinchy, Goldberger, and Tarule's "Women's Ways of Knowing" (Basic Books, 1986) helped me recognize the simple but effective pedagogical truth that new information is best assimilated by students when it is presented as an extension of what they already know in a way which validates and confirms that previous knowledge.
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About the author:

Susan Bassein, formerly Richard Bassein, has published papers in the Journal of Algebra, Mathematische Annalen, The American Mathematical Monthly, and the Journal of Music Theory; illustrated several mathematics books; taught at Princeton University; and has been a professor of Mathematics and Computer Science at Mills College for 16 years.
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