Calculus Made Easy

Thompson, Silvanus P.; Gardner, Martin

doi:10.1007/978-1-349-15058-8

Cited by 20 publications

(17 citation statements)

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“…The digitized flight track data points were smoothed using a rectangular sliding window 125 ms long. Flight velocities were obtained using Newton's difference quotient method (Thompson, 1919) to compute time derivatives of position for each time step.…”

Section: Flight Path Analysismentioning

confidence: 99%

Behavioral responses of big brown bats to dives by praying mantises

Ghose

Triblehorn

Bohn

et al. 2009

Journal of Experimental Biology

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SUMMARYInsectivorous echolocating bats face a formidable array of defenses employed by their airborne prey. One such insect defense is the ultrasound-triggered dive, which is a sudden, rapid drop in altitude, sometimes all the way to the ground. Although many previous studies have investigated the dynamics of such dives and their effect on insect survival rate, there has been little work on how bats may adapt to such an insect defense employed in the middle of pursuit. In this study we investigated how big brown bats (Eptesicus fuscus) adjust their pursuit strategy when flying praying mantises (Parasphendale agrionina) execute evasive, ultrasound-triggered dives. Although the mantis dive occasionally forced the bat to completely abort its chase (25% trials), in a number of cases (75% trials) the bat followed the mantis into the dive. In such cases the bat kept its sonar beam locked onto the target and maneuvered to maintain the same time efficient strategy it adopted during level flight pursuit, though it was ultimately defeated by the dive. This study suggests that although the mantis dive can be effective in evading the bat, it does not always deter the bat from continuing pursuit and, given enough altitude, the bat can potentially capture diving prey using the same flight strategy it employs to intercept prey in level flight.

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Section: Flight Path Analysismentioning

confidence: 99%

Behavioral responses of big brown bats to dives by praying mantises

Ghose

Triblehorn

Bohn

et al. 2009

Journal of Experimental Biology

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show abstract

“…In addition to the basic summary of calculus presented below, I recommend Thompson 1946, a classic, condensed calculus text. In this appendix, I summarize the basic concepts from calculus and matrix algebra that are necessary to understand mathematical statistics.…”

Section: A Background Mathematicsmentioning

confidence: 99%

Introduction to Applied Bayesian Statistics and Estimation for Social Scientists

2007

330

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“…For example, Sylvanus P. Thompson's 100-year-old calculus text [26] -which has never been out of print -uses differentials throughout, treating them as intuitive objects which anyone can master. However, the most recent edition of this text [27] contains a lengthy introduction by Martin Gardner, who effectively undoes this approach by providing modern definitions of functions, limits, and derivatives, alleged prerequisites which the original author clearly chose to do without.…”

Section: Historymentioning

confidence: 99%

“…However, the most recent edition of this text [27] contains a lengthy introduction by Martin Gardner, who effectively undoes this approach by providing modern definitions of functions, limits, and derivatives, alleged prerequisites which the original author clearly chose to do without.…”

Section: Historymentioning

confidence: 99%