Calculus

高斯積分

前情提要: 數值積分初探 前情提要: 以內插多項式來做數值積分 我們想要找到一些插值點使得以內插多項式來做數值積分會最準. 這就是高斯積分. Goal: 任意給定

Sec.13.4 - Kepler’s Laws

Applied Project in Sec.13.4, Calculus by Stewart Chinese version 克卜勒定律 Johannes Kepler stated the following three laws of planetary motion on the basis of massive amounts of data on the positions of the planets at various times. Kepler’s Laws A planet revolves around the sun in an elliptical orbit with the sun at one focus. The line joining the

Sec.13.4 - 克卜勒定律

Applied Project in Sec.13.4, Calculus by Stewart 英文版請見 Kepler’s Laws 約翰尼斯‧克卜勒在有關不同時間行星位置的大量數據基礎上,提出了以下三個行星運動定律。 克卜勒定律 每一

Sec.14.4 - The speedo LZR razer

Applied Project in Sec.14.4, Calculus by Stewart Chinese version 速比濤鯊魚皮系列第四代泳裝 Many technological advances have occurred in sports that have contributed to increased athletic performance. One of the best known is the introduction, in 2008, of the Speedo LZR racer. It was claimed that this full-body swimsuit reduced a swimmer’s drag

Sec.14.4 - 速比濤鯊魚皮系列第四代泳裝

Applied Project in Sec.14.4, Calculus by Stewart 英文版請見 The speedo LZR razer 在體育運動中, 許多科技的進步讓運動員的表現更好. 最廣為人知的例子之一就是速比濤在2008年時推出鯊魚皮系列第

Sec.12.4 - The Geometry of a Tetrahedron

Discovery Project in Sec.12.4, Calculus by Stewart Chinese version 四面體的幾何學 A tetrahedron is a solid with four vertices, P ,Q , R and S ,and four triangular faces, as shown in the figure. Question 1: Let $v_1, v_2, v_3$ and $v_4$ be vectors with lengths equal to the areas of the faces opposite the vertices P, Q, R and S, respectively, and directions perpendicular

Sec.12.4 - 四面體的幾何學

Discovery Project in Sec.12.4, Calculus by Stewart 英文版請見 The Geometry of a Tetrahedron 如圖所示,四面體是一個擁有4個頂點(P,Q,R,S)和四個三角面的固體。 問題1: 令 $v_1, v_2, v_3$ 和 $v_4$ 為向量, 其長度

Sec.3.1 - 建造較佳的雲霄飛車

Applied Project in Sec.3.1, Calculus by Stewart 英文版請見 Building a better roller coaster 假設你被要求設計一架新的雲霄飛車的第一個上升與下降。在研究你最喜歡的雲霄飛車的圖片後,你決定新的雲霄飛車先

Sec.6.5 - Where to Sit at the Movies

Applied Project in Sec.6.5, Calculus by Stewart Chinese version 電影院要坐哪? A movie theater has a screen that is positioned $3$m off the floor and is $10$m high. The first row of seats is placed $3$m from the screen and the rows are set $1$m apart. The floor of the seating area is inclined at an angle of $\alpha=20^{\circ}$ above the horizontal and the distance

Sec.6.5 - 電影院要坐哪?

Applied Project in Sec.6.5, Calculus by Stewart English version Where to Sit at the Movies? 有家電影院的螢幕高10米且離地3公尺,第一排的位子距離螢幕3公尺且每排間隔1公尺,座位區的地板以與水平20度夾