Integral Calculus

2013 ◽  
pp. 87-115
Author(s):  
John Vince
Keyword(s):  
Integral Calculus

The method of sweeping tangents

2008 ◽  
Vol 92 (525) ◽  
pp. 396-417 ◽  
Author(s):  
Tom M. Apostol ◽  
Mamikon A. Mnatsakanian
Keyword(s):  
Integral Calculus ◽  
Visual Approach

What is the area of the shaded region between the tyre tracks of a moving bicycle such as that depicted in Figure 1 ? If the tracks are specified, and equations for them are known, the area can be calculated using integral calculus. Surprisingly, the area can be obtained more easily without calculus, regardless of the bike’s path, using a dynamic visual approach called the method of sweeping tangents that does not require equations for the curves.

Addressing common errors and misconceptions in integral calculus with clickers and classroom voting

2019 ◽  
Vol 39 (2) ◽  
pp. 71-85
Author(s):  
Kelly Cline ◽  
Holly Zullo ◽  
David A Huckaby
Keyword(s):  
Correct Answer ◽  
Group Discussion ◽  
Multiple Choice ◽  
Small Group Discussion ◽  
Multiple Choice Questions ◽  
Integral Calculus ◽  
Common Features ◽  
Incorrect Answer ◽  
The Common ◽  
The Mean

Abstract Common student errors and misconceptions can be addressed through the method of classroom voting, in which the instructor presents a multiple-choice question to the class, and after a few minutes for consideration and small-group discussion, each student votes on the correct answer, using a clicker or a phone. If a large number of students have voted for one particular incorrect answer, the instructor can recognize and address the issue. In order to identify multiple-choice questions that are especially effective at provoking common errors and misconceptions, we recorded the percentages of students voting for each option on each question used in 25 sections of integral calculus, taught by 7 instructors, at 4 institutions, over the course of 12 years, on a collection of 172 questions. We restricted our analysis to the 115 questions which were voted on by at least 5 different classes. We present the six questions that caused the largest percentages of students to vote for a particular incorrect answer, discuss how we used these questions in the classroom, and examine the common features of these questions. Further, we look for correlations between question characteristics and the mean percentage of students voting for common errors on these questions, and we find that questions based on general cases have higher percentages of students voting for common errors.

scholarly journals Integral calculus on quantum exterior algebras

2014 ◽  
Vol 11 (04) ◽  
pp. 1450026 ◽  
Author(s):  
Serkan Karaçuha ◽  
Christian Lomp
Keyword(s):  
Differential Calculus ◽  
Polynomial Algebra ◽  
Exterior Algebra ◽  
Integral Calculus ◽  
De Rham Complex ◽  
Integral Forms ◽  
Rham Complex ◽  
De Rham ◽  
Quantum Polynomial

Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

Integral Calculus

1966 ◽  
Vol 50 (372) ◽  
pp. 204
Author(s):  
R. P. Gillespie ◽  
Walter Ledermann
Keyword(s):  
Integral Calculus

Differential and Integral Calculus.

1961 ◽  
Vol 68 (4) ◽  
pp. 391
Author(s):  
E. H. Crisler ◽  
J. R. F. Kent
Keyword(s):  
Integral Calculus

Finding the optimum layout for cable-stayed bridge in conceptual design

2021 ◽  
Author(s):  
Sami Soppela ◽  
Esko Järvenpää
Keyword(s):  
Longitudinal Direction ◽  
Simple Calculation ◽  
Integral Calculus ◽  
Bearing Material ◽  
Load Bearing ◽  
Permanent Load ◽  
Early Design Stages ◽  
Cable Forces ◽  
The Cost ◽  
Cable Stayed Bridges

<p>In the cable-stayed bridges the primary cost components of the load-bearing material, in the longitudinal direction of the bridge, are the cables. The longer the bridge, the higher the share of the costs of the load-bearing material. The quantity of the cables and the cost optimized cable and tower topology can be reliably solved, already in very early design stages, using a simple calculation method proposed in this article. The cables are considered as a curtain structure and the cable forces are calculated for the permanent load balance. The solutions are performed mathematically by using integral calculus based on a force length method and a unit bridge concept. The results provide a good idea of the optimum pylon height for both one-pylon and two-pylon bridges. The optimum pylon height depends on the span ratio and the chosen cable system.</p>

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