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We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical points. [ABSTRACT FROM PUBLISHER]

An overview is given of three conceptual lessons that can be incorporated into any first-semester calculus class. These lessons were developed to help promote calculus students' ability to think conceptually, in particular with regard to the role that infinity plays in the subject. A theoretical basis for the value of these lessons is provided, and both indirect and direct evidence, that demonstrates that these lessons were successful in beginning to achieve their goal, is described. Ideas for how to incorporate these lessons into the standard calculus curriculum are presented as well as thoughts on how to further improve the lessons' ability to promote students' conceptual understanding. [ABSTRACT FROM AUTHOR]

The article presents the solution for solving boundary value problems for fourth-order equation using fractional derivatives. It cites that the Caputo fractional derivative operator is expressed as a Riemann-Liouville fractional integral. It refers the theorem f(x,t) ∈ C1 [ 0,p], f(0,t) = f(p,t) = 0, ∂ f(x,t)/ ∂ x ∈ Lipϒ [0,p].

This article offers information on the distribution of relatively prime numbers. It also aims to prove that if one picks an ordered pair of integers at random, then the probability that these integers are relatively prime or approximately 60.8 percent. It also notes that this article will be useful for further reading in a probability or number theory course. The article also discusses some preliminary results starting with the recollection of the famous results of Leonard Euler using the formula, known as the Basel Problem.

The article discusses the author's formulation of the calculus course for honors college students. The author had used the historical approach inorder to create awareness and interest to students. It was used as a motivation to allow students to appreciate the subject more and pursue calculus in farther levels. The scrutinous study of the history of calculus generated a debate over the real father of calculus whether its Isaac Newton or Gottfried Leibniz. The author can not determine the success rate of the subject due to lack of evidential data but he is confident that it had created an active participation on his honors students.

We investigate one solvable subclass of quantified formulas in pure predicate calculus and obtain a necessary and sufficient condition for the satisfiability of formulas from this subclass. [ABSTRACT FROM AUTHOR]

We provide an easy argument, using the second fundamental theorem of calculus, for computing the area of the unit circle [ABSTRACT FROM AUTHOR]