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Papers On Lagrange's Differential Calculus
As the pieces below are rather old, I recently summarized my thinking on the matter in the following which is also available from Research Gate.
To Calculate In Calculus
1. The following, presented at the instigation of a well-meaning Dean, Dr. Judith Toman, at the third National Science, Technology and Society (STS) Conference, February 6, 1988, appeared in the Bulletin of Science, Technology & Society, 01/1988; 8(4):411-418, and eventually led to NSF grant USE-8814000.
The Differential Calculus As Language
2. The following were published in connection with NSF grant USE-8814000.
Integrated Precalculus-Differential Calculus, A Lagrangian Approach
In The AMATYC Review, Volume 11, Number 1 (Part 2) - Fall 1989.
An Introduction to Lagrangian Differential Calculus
Editor's Note: This article extends the mathematical ideas presented by the authors in their article Integrated Precalculus and Differential Calculus: A Lagrangian Approach that appeared in the Fall, 1989 (Part 2) issue of this journal.
In The AMATYC Review, Volume 11, Number 2 - Spring 1990.
3. The following, which appeared in 2013 in the Notices of the American Mathematical Society, Volume 60, Number 3, page 340, describes a preparation to the Lagrangian View.
How Content Matters
4. The following were presented at national conferences in connection with NSF grant USE-8814000.
A Lagrangian Approach to the Differential Calculus
Presented at the What is happening with calculus revision session of the
Joint AMS/MAA Phoenix Meeting, January 1989.
A Post-Cauchy View of Lagrange's Calculus
Adapted from the Lecture Notes of a Minicourse given at the Joint Mathematics Meetings in Louisville,
5. We urged the Lagrangian View at many regional conferences but I do not remember where the following were presented or appeared, if at all.
In Defense of Differential Calculations
Elementary Differential Calculus
Differential Calculus of Equationally Defined Functions By Way of Polynomial Approximations
A Post-Lagrange/Poincaré Look At Calculus