The Autobiography from Benjamin Franklin内容赏析本杰明富兰克林自传赏析
Course: American Literature
Instructor: Ma Rui
Student Name: Liu Zirui from Mingde college of NWPU
Class Number: 082487
Date: Oct.29th, 2011
The Autobiography from Benjamin Franklin
The Autobiography was written by the great American writer Benjamin Franklin who was one of the American founders and the leader of the American independence movement, as well as the drafter of Declaration of independence. He was a politician, a scientist, a diplomat, a publisher, a writer and a social industrialist. He was praised as the second Prometheus who stole the fire from heaven to show his intelligent and contributions. He was the father of the modern civilization and a symbol of America.
This autobiography was written by Benjamin when he was in his old age according to his experiences which has a great influence to the world. In his autobiography, he wrote thirteen virtues: temperance, silence, order, resolution, frugality, industry, sincerity, justice, moderation, cleanliness, tranquility, chastity and humility which admonished people to try to be the best of yourself. By temperance he told us not to eat too dull and not to drink too much to be clear in mind. By silence he advised us not to say something that is meaningless but could benefit others or yourself. And by order he taught us that we need to take all our things in order so that we could have a tiny place to study, work and live. Resolution showed us what we decide to do need to be done with our consistency. He informed us to have a more comfortable life if we don’t waste our money in those empty and meaningful things by frugality. What’s more, industry showed us not to waste our time. Do something that is significant or good for you. Sincerity told us to be a loyal and honest people who could be trusted by others. And speak with accordingly. Justices informed us not to do things are negative to others and it’s our own duty to do things that are benefit to people. Moderation taught us not to do extreme things. Try to tolerate the injuries from others. And by cleanliness, he taught us to be a tidy person. In addition, he informed us to clam down when we come across some troubles. By chastity, he advised us to do things that could benefit or protect yourself, your family and friends’ reputation. Lastly, try to be humility as much as you can and imitate the great people like Socrates and Jesus.
Mostly, his writing is ironic, satire and meaningful. In his autobiography, he used plain but humorous words to tell his life experience and his reflections. He opened up a new autobiography writing style which was very frequently imitated by the latter.
I learned a lot from his autobiography not only from his intelligent but also his modesty. The way he treated people and the attitude he had when doing things that he made mind to do taught me to try my best to be the best of myself.
可降阶的高阶微分方程
可降阶的高阶微分方程解法 ①())(x f y n =型的微分方程 对())(x f y n =两边积分，有 ()?+=-11)()(C dx x f x y n ， ()()212])([C dx C dx x f x y n ++=??-， …… 依次进行n 次积分即得通解． ②()y x f y '='',型的微分方程 方程的特点是右端不显含y ，令p y ='，则p y '=''，于是原方程化为),(p x f p ='，是关于p 的一阶方程，若其解为),(1C x p ?=，即 ),(1C x dx dy ?=，积分求解即可． ③()y y f y '='',型的微分方程 方程的特点是右端不显含自变量x ，令p y ='，则dy dp p dx dy dy dp dx dp y =?==''，于是原方程化为),(p y f dy dp p =，是关于p 的一阶方程，若其解为),(1C y p p =，即),(1C y p dx dy =，再积分求解即可． 例题1求下列各微分方程的通解 （1）x x y x y e 1+'=''； （2）()221 12y y y y '+-='' 解 （1）原方程属于()y x f y '='',类型． 令p y ='，则p y '=''，原方程可化为 x x p x p e 1+= '， 此为P 的一阶线性方程，其通解为 () 1111e e e e C x C dx x p x dx x x dx x +=????????+???=???? ??-??? ??--，
所以 () 1e C x dx dy x +=， 分离变量后得 () dx C x dy x 1e +=， 两边积分，得原方程的通解为 2212 1e )1(C x C x y x ++-=． （2）原方程为属于()y y f y '='',类型． 令p y ='，则dy dp p y =''，代入原方程得 22112p y y dy dp p +-=， 当0=p 时，得0==dx dy p ，即C y =为原方程的解； 当0≠p 时，得 p y y dy dp 1 122+-=， 分离变量 dy y y p dp 1 122+-=， 两边积分 ()1 2ln arctan 1ln ln C y y p +-+=， 即 ()y y C p arctan 21e 1-+=， 从而 () y y C dx dy arctan 21e 1-+=， 分离变量，再两边积分后，得原方程通解为 2arctan 1e C x C y +=． 练习 练习1求方程222()0d y dy y dx dx -=的通解 练习2求方程1'''y y x = 的通解。