A short plea for such a sequence appeared in the

It all started after the publication by the Office of Instutional Research at my school of a

It immediately struck me that the mere length of the squence had to have had an impact and, based on my experience teaching Arithmetic and Basic Algebra, and since the only prerequisite for Lagrange Differential Calculus had been polynomial algebra, I had no doubt that it should be possible to design a prequel to Lagrange Differential Calculus that "developmental students" could reasonably cope with in one four-hour semester and which would then result in a three four-hour semester sequence as opposed to the "traditional sequence": five three-hour semesters followed by one four-hour semester.

And so the first thing I did was a "what if" spreadsheet to see what the likely

So, I started to work on a detailed table of contents for the "prequel"with the idea that the second and third semester would just be a rewrite of Lagrange Differential Calculus. However, it became quickly painfully obvious that the rewrite would have to be a total one if the conceptual flow was to be smooth and efficient.

Given the size of the undertaking, though, I thought that I would just write a

However, I soon had to bow to the wisdom of the Hestenes dictum and started to work on a Text for A2DC.

But then, I started using parts of the

The prequel was specified through a kind of reverse engineering, namely as what was strictly necessary for Lagrange Differential Calculus. Here are a few examples:

- In order to define, say, the exponential function as
solution of the Initial
Value Problem f
'(x) = f(x), f(0) = 1, it is
necessary to see an
*equation*as an a priori specification of something that may or may not exist—as opposed to being a "question" to be answered—and the idea needs to be introduced a long time before this point so as to give students the time to get completely used to it. So the idea is developed in the middle part of RBA as the investigation of Basic Problems,*Affine Problems*, etc. - In order to feel comfortable with the idea of (locally)
*approximating*a function, it is necessary to see*approximation*as a natural thing to do—as opposed to finding "the" (exact) answer to the given question. The idea is thus introduced in RDA where, for instance, 1/3 = 0.3 + (...) or 1/3 = 0.33 + (...) or 1/3 = 0.334 + (...), etc with (...) standing for "a little bit of no significance in the present situation". - In order to realize that the + in 3x
^{5}+ 4x^{2}is not the symbol for*addition*but for a (linear) combination—and thus we really ought to use &, it helps to have already seen that this is the exact same situation as in 3 Apples + 4 Bananas, 3 Hundreds + 4 Tens, 3 Halves + 4 Thirds, 3f + 4g, etc—And of course as in 3e_{1}+ 4e_{2}= (3, 4) in linear algebra.

Part
I. Decimal-Metric Arithmetic, Arithmetic
Functions, Comparisons
and Operations, Equations/Inequations Problems, Laurent Polynomial
Algebra.

Part II. Algebraic Functions: Power Functions, Polynomial Functions, Rational Functions.

Part III. Transcendental Functions as solution of Initial Value Problems: Exponential Functions, Logarithmic Functions, Circular Functions, Hyperbolic Functions.

Part II. Algebraic Functions: Power Functions, Polynomial Functions, Rational Functions.

Part III. Transcendental Functions as solution of Initial Value Problems: Exponential Functions, Logarithmic Functions, Circular Functions, Hyperbolic Functions.

and the corresponding standalones:

- Reasonable Decimal Arithmetic. (RDA) Essentially the arithmetic part of Part I of A2DC.
- Decimal-Metric Number-phrases
- Approximation
- Arithmetic Functions
- Comparisons and Operations

- Reasonable Basic Algebra. (RBA) A reduction of RDA with the algebra necessary for Lagrange Differential Calculus.
- Decimal Arithmetic
- Equations/Inequations
- Polynomial Algebra

- Reasonable
Arithmetic and Algebra. (RAA) An assembly of RDA and RBA
that corresponds to a reduction of Part
I of A2DC.
- Decimal-Metric Number-phrases
- Comparisons and Operations
- Equations/Inequations
- Polynomial Algebra

- Reasonable
Algebraic Functions. (RAF) A reduction of Part II of A2DC that
de-emphasizes
*derivatives*. - Power Functions
- Polynomial Functions
- Rational Functions

- Reasonable
Transcendental Functions. (RTF) A reduction of Part III of A2DC
that de-emphasizes
*derivatives*. - Exponential Functions
- Logarithmic Functions
- Box Functions
- Circular Functions
- Hyperbolic Functions

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