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DD Calculus

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Samuel S.P. Shen, Qun Lin

History and Overview · Submitted 1 Apr 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The DD calculus, or simply direct calculus, makes many traditional notations and procedures unnecessary, a plus when introducing calculus to the non-mathematics majors.

how it is stated · asserted 0.99 read the record →

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arXiv ID1404.0070 (version 1)
Pith IDTBI4XWVF, Pith's permanent record of this paper and its review
CitationQun Lin, Samuel S.P. Shen. "DD Calculus." arXiv:1404.0070 (2014). https://pith.science/paper/TBI4XWVF
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,037 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.21 · human participants 0.04 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.31 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This paper introduces DD calculus and describes the basic calculus concepts of derivative and integral in a direct and non-traditional way, without limit definition: Derivative is computed from the point-slope equation of a tangent line and integral is defined as the height increment of a curve. This direct approach to calculus has three distinct features: (i) it defines derivative and (definite) integral without using limits, (ii) it defines derivative and antiderivative simultaneously via a derivative-antiderivative (DA) pair, and (iii) it posits the fundamental theorem of calculus as a natural corollary of the definitions of derivative and integral. The first D in DD calculus attributes to Descartes for his method of tangents and the second D to DA-pair. The DD calculus, or simply direct calculus, makes many traditional notations and procedures unnecessary, a plus when introducing calculus to the non-mathematics majors. It has few intermediate procedures, which can help dispel the mystery of calculus as perceived by the general public. The materials in this paper are intended for use in a two-hour introductory lecture on calculus.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper introduces DD calculus and describes the basic calculus concepts of derivative and integral in a direct and non-traditional way, without limit definition: Derivative is computed from the point-slope equation of a tangent line and integral is defined as the height increment of a curve. contribution 0.97 0.87 0.20 asserted 1.00
s1 This direct approach to calculus has three distinct features: (i) it defines derivative and (definite) integral without using limits, (ii) it defines derivative and antiderivative simultaneously via a derivative-antiderivative (DA) pair, and (iii) it posits the fundamental theorem of calculus as a natural corollary of the definitions of derivative and integral. contribution 0.91 0.80 0.26 asserted 1.00
s2 The first D in DD calculus attributes to Descartes for his method of tangents and the second D to DA-pair. background 0.53 0.30 0.05 asserted 1.00
s3 The DD calculus, or simply direct calculus, makes many traditional notations and procedures unnecessary, a plus when introducing calculus to the non-mathematics majors. interpretation 0.79 0.37 0.22 asserted 0.99
s4 It has few intermediate procedures, which can help dispel the mystery of calculus as perceived by the general public. interpretation 0.80 0.30 0.11 hedged possibility 0.70
s5 The materials in this paper are intended for use in a two-hour introductory lecture on calculus. future work 0.30 0.32 0.04 asserted 0.94

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from argument 0.68.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper introduces DD calculus and describes the basic calculus concepts of derivative and integral in a direct and non-traditional way, without limit definition: Derivative is computed from the point-slope equation of a tangent line and integral is defined as the height increment of a curve. This direct approach to calculus has three distinct features: (i) it defines derivative and (definite) integral without using limits, (ii) it defines derivative and antiderivative simultaneously via a derivative-antiderivative (DA) pair, and (iii) it posits the fundamental theorem of calculus as a natural corollary of the definitions of derivative and integral. The first D in DD calculus attributes to Descartes for his method of tangents and the second D to DA-pair. The DD calculus, or simply direct calculus, makes many traditional notations and procedures unnecessary, a plus when introducing calculus to the non-mathematics majors. It has few intermediate procedures, which can help dispel the mystery of calculus as perceived by the general public. The materials in this paper are intended for use in a two-hour introductory lecture on calculus.

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