Calculus

Applied Project in Sec.11.11, Calculus by Stewart Chinese version 恆星的輻射 Any object emits radiation when heated. A blackbody is a system that absorbs all the radiation that falls on it. For instance, a matte black surface or a large cavity with a small hole in its wall (like a blastfurnace) is a blackbody and emits blackbody radiation. Even the radiation from the sun is close to

Applied Project in Sec.11.11, Calculus by Stewart 英文版請見 Radiation From The Stars 任何物件在被加熱時會散發輻射. 而 黑體 則是一個會吸收所有經過他的輻射的一個系統. 舉例來說, 一個表面黑色且沒有光

Applied Project in Sec.8.3, Calculus by Stewart 英文版請見 Complementary Coffee Cups 假設你選擇了兩種形狀的咖啡杯，一種向外彎曲，另一種向內彎曲，你會注意到它們具有相同的高度，並且形狀可以緊密地貼

Applied Project in Sec.9.3, Calculus by Stewart Chinese version: 上升快，還是下降快? Suppose you throw a ball into the air. Do you think it takes longer to reach its maximum height or to fall back to earth from its maximum height? We will solve the problem in this project, but before getting started, think about that situation and make a guess based on

Applied Project in Sec.9.3, Calculus by Stewart 英文版請見 Which is faster, going up or going down? 假設你在空氣中將一顆球向上拋。你認為球從地表到最高高度和從最高處落回地面哪一個所耗的時間較長? 我們將

Applied Project in Sec.4.1, Calculus by Stewart 英文版請見 The Calculus of ranbows 當陽光照射到半空中的雨滴，光線被散射就會形成彩虹。彩虹自古以來就被人類著迷著，且早在亞里士多德時代以來激發許

Applied Project in Sec.4.1, Calculus by Stewart Chinese version: 彩虹的微積分學 Rainbows are created when raindrops scatter sunlight. They have fascinated mankind since ancient times and have inspired attempts at scientific explanation since the time of Aristotle. In this project we use the ideas of Descartes and Newton to explain the shape, location, and colors of rainbows. Question 1: The figure shows a ray of

Applied Project 2 in Sec.4.7, Calculus by Stewart 英文版請見 Planes and birds: Minimizing energy 像雀科這樣的小鳥滑翔時，會在拍打翅膀和保持翅膀折疊之間進行交替。在這裡，我們觀察這種現象並試著找出鳥類拍

Laboratory Project in Sec.3.10, Calculus by Stewart Chinese version: 泰勒級數 The tangent line approximation $L(x)$ is the best first-degree (linear) approximation to $f(x)$ near $x=a$ because $f(x)$ and $L(x)$ have the same rate of change (derivative) at $x=a$. For a better approximation than a linear one, let’s try a second-degree (quadratic) approximation $P(x)$. In other words, we approximate a curve by a parabola instead of a straight

Applied Project in Sec.8.3, Calculus by Stewart Chinese version: Complementary Coffee Cups Suppose you have a choice of two coffee cups of the type shown, one that bends outward and one inward, and you notice that they have the same height and their shapes fit together snugly. You wonder which cup holds more coffee. Of corse you could fill one cup with water and pour it into the other one