电大工程数学复习资料（本）期末复习考试试题资料小抄.docx

电大工程数学复习资料（本）期末复习考试试题资料小抄电大工程数学复习资料 一、 线性代数 1、 矩阵的初等行变换：1）两行互换，2）某一行乘以一个非零常数，3）某一行的K倍加到另一行。2、 阶梯型矩阵：1）全为0的行写在最下面，2）首非零元的列标随行标的增大而增大。如 3、 行简化阶梯型矩阵：满意下列条件的阶梯型矩阵：1）首非零元全为1，2）首非零元所在列其余元素全为0。如： 4、 求矩阵A的秩：A阶梯型矩阵。阶梯型矩阵非零行的行数既为矩阵A的秩即r(A) 例： 设矩阵，求矩阵的秩 解：用初等行变换将矩阵化为阶梯形 由此可知矩阵的秩为2 5、 求矩阵方程AX=B：（A B）(I X)或X=B 求矩阵A的逆矩阵：（A I）（I ） 1. 例：设矩阵A=,B=,求AB. 或解矩阵方程AX=B 解：（AB）= 例：设矩阵，求： 解： 所以 6 、n元线性方程组解的判定 1）AX=b ：r(A b)=r(A)时，方程组有解 r(Ab)r(A)时，方程组无解 AX=0：方程组肯定有解 2）求齐次线性方程组AX=0的基础解系：将方程组中的自由未知量分别取（k，0，0）,(0,k,0),(0,0,k)形式所得到的解向量 3）求AX=0的一般解和全部解： 求AX=b的一般解和全部解： 例：设齐次线性方程组的系数矩阵经过初等行变换，得 求此齐次线性方程组的一个基础解系和通解 解： 因为 得一般解： （其中是自由元） 令，得； 令，得 所以，是方程组的一个基础解系 方程组的通解为：，其中是随意常数 例：2.线性方程组的全部解 解：（A b）=方程组的一般解将常数项视为零，取得 相应齐次方程组的一个基础解系，取原方程组的一个特解故方程组的全部解 X=+C 例：当取何值时，线性方程组 有解，在有解的状况下求方程组的全部解 解：将方程组的增广矩阵化为阶梯形 由此可知当时，方程组无解。当时，方程组有解。 此时齐次方程组化为 分别令及，得齐次方程组的一个基础解系 令，得非齐次方程组的一个特解 由此得原方程组的全部解为 （其中为随意常数） 二、 概率部分 1、假设为两事务，已知，求 解： 2、正态分布X , ,P(X>b)=1-P（X<b）=1- 例：.设XN(2,9),试求（1）P(X<11);(2)P（5<X<8）.（已知（1）=0.8413， （2）=0.9772，（3）=0.9987） 解：P(X<11)=()=(3)=0.9987 P(5<X<8)=()-()=(2)-(1)=0.1359 3、估计区间和假设检验：对于正态分布N（ 1）方差已知：统计量U=，其中 置信区间：,假设检验：若，则假设 成立 2）方差未知：统计量T= ， 置信区间：,假设检验：若 ，则假设 例：. 某车间生产滚珠，已知滚珠直径听从正态分布今从一批产品里随机取出9个，测得直径平均值为15.1mm，若已知这批滚珠直径的方差为，试找出滚珠直径均值的置信度为0.95的置信区间 解：由于已知，故选取样本函数 已知，经计算得 滚珠直径均值的置信度为0.95的置信区间为，又由已知条件，故此置信区间为 例：对某一距离进行4次独立测量，得到的数据为（单位：米）： 15.51, 15.47, 15.50, 15.52 由此计算出，已知测量无系统误差，求该距离的置信度为0.95的置信区间（测量值听从正态分布） 解：由于未知， 已知，经计算得 该距离的置信度为0.95的置信区间为，又由已知条件，故此置信区间为。例：.据资料分析，某厂生产的一批砖，其抗断强度XN(32.5,1.21),今从这批砖中随机地抽取了9块，测得抗断强度（单位：kg/cm）的平均值为31.12，问这批砖的抗断强度是否合格（=0.05，=1.96） 解：假设：32.5 已知9，31.121.1 =3.76>1.96 故认为这批砖的抗断强度不合格 例：某钢厂生产了一批管材，每根标准直径100mm,今对这批管材进行检验，随机取出9根，测得它们直径的平均值为99.9mm,样本标准差s=0.47,已知管材直径听从正态分布，问这批管材的质量是否合格（检验显著性水平=0.05，） 解：假设H:=100 已知：n=9 s=0.47 =99.9 故认为这批管材的质量是合格的 请您删除一下内容，O(_)O感谢！2015年中心电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄After earning his spurs in the kitchens of The Westin, The Sheraton, Sens on the Bund, and a sprinkling of other top-notch venues, Simpson Lu fi nally got the chance to become his own boss in November 2010. Sort of. The Shanghai-born chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof- house at this Sinan Mansionsstalwart.  “Its certainly a responsibility to be the head chef, and then to have to manage the rest of the restaurant as well,“ the 31-year-old tells Enjoy Shanghai. “In hotels, for example, these jobs are strictly demarcated, so its a great opportunity to learn how a business operates across the board.“  It was a task that management back in sunny California evidently felt he was ready for, and a vote of confi dence from a company that, to date, has opened 250 outlets in 11 countries. And for added pressure, the Shanghai branch was also CPKs China debut.  “For sure it was a big step, and unlike all their other Asia operations that are franchises, they decided to manage it directly to begin with,“ says Simpson.  Two years ago a private franchisee took over the lease, but the links to CPK headquarters are still strong, with a mainland-based brand ambassador on hand to ensure the business adheres to its ethos of creating “innovative, hearth-baked pizzas“, a slice of PR blurb that Simpson insists lives up to the hype.  “They are very innovative,“ he says. “The problem with most fast food places is that they use the same sauce on every pizza and just change the toppings. Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly.“  The largely local customer base evidently agrees and on Saturday and Sunday, at least, the place is teeming. The kids-eat-for-free policy at weekends is undoubtedly a big draw, as well as is the spacious second-fl oor layout overlooked by a canopy of green from Fuxing Park over the road.  The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week. Still, the sta are honest enough to admit that business could be better; as good, in fact, as in CPKs second outlet in the popular Kerry Parkside shopping mall in Pudong.  “Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened, and it hasnt been easy for any of the tenants here,“ adds Simpson. “Were planning a third outlet in the city in 2015, and we will probably choose a shopping mall again because of the better foot traffic.“ The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai, Xu Junqian visits the Parisian outpost with sweet treats. One thing the century-old Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food, pastries in particular. One of the most popular tearooms in Paris, Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust. Now Angelina has packed up its French ambience, efficient service, and beautiful, comforting desserts and flown them to Shanghai. At the flagship dine-in and take-out space in Shanghai, everything mimics the original tearoom designed from the beginning of the 20th century, in Paris, the height of “Belle Epoque“. The paintings on the wall, for example, are exactly the same as the one that depicts the landscape of southern France, the hometown of the owner; and the small tables are intentional imitations of the ones that Coco Chanel once sat at every afternoon for hot chocolate. The famous hot chocolate, known as LAfricain, is a luxurious mixture of four types of cocoa beans imported from Africa, blended in Paris and then shipped to Shanghai. Its sinfully sweet, rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped cream on the side makes a light, but equally gratifying contrast. It is also sold in glass bottles as takeaway. The signature Mont-Blanc chestnut cake consists of three parts: the pureed chestnut on top, the vanilla cream like stuffing, and the meringue as base. Get all three layers in one scoop, not only for the different textures but also various flavors of sweetness. The dessert has maintained its popularity for a century, even in a country like France, perhaps the worlds most competitive place for desserts. A much overlooked pairing, is the Paris-New York choux pastry and N226 chocolate flavored tea. The choux pastry is a mouthful of airy pecan-flavored whipped cream, while the tea, a blend of black teas from China and Ceylon, cocoa and rose petals, offers a more subtle fragrance of flowers and chocolate. Ordering these two items, featuring a muted sweetness, makes it easier for you to fit into your little black dress. Breakfast, brunch, lunch and light supper are also served at the tearoom, “a hub of many cultures“ and takes in “a mix of different styles of French cuisines“, according to the management team. The semi-cooked foie gras terrine, is seductive and deceptive. Its generously served at the size and shape of a toast, while the actual brioche toast is baked into a curved slice dipped with fig chutney. The flavor, however, is honest: strong, smooth and sublime. And you dont actually need the toast for crunchiness. This is the season for high teas, with dainty cups of fine china and little pastries that appeal to both visual and physical appetites. But there is one high tea with a difference, and Pauline D. Loh finds out just exactly why it is special. Earl Grey tea and macarons are all very well for the crucial recuperative break in-between intensive bouts of holiday season shopping. And for those who prefer savory to sweet, there is still the selection of classic Chinese snacks called dim sum to satisfy and satiate. High tea is a meal to eat with eye and mouth, an in-between indulgence that should be light enough not to spoil dinner, but sufficiently robust to take the edge off the hunger that strikes hours after lunch. The afternoon tea special at Shang-Xi at the Four Seasons Hotel Pudong has just the right elements. It is a pampering meal, with touches of luxury that make the high tea session a treat in itself. Whole baby abalones are braised and then topped on a shortcrust pastry shell, a sort of Chinese version of the Western vol-au-vent, but classier. Even classier is the dim sum staple shrimp dumpling or hargow, upgraded with the addition of slivers of midnight dark truffles. This is a master touch, and chef Simon Choi, who presides unchallenged at Shang-Xi, has scored a winner again. Sweet prawns and aromatic truffles whats not to love? His masterful craftsmanship is exhibited in yet another pastry a sweet pastry that is shaped to look like a walnut, but which you can put straight into the mouth. It crumbles immediately, and the slightly sweet, nutty morsel is so easy to eat youll probably reach straight for another. My favorite is the dessert that goes by the name yangzhi ganlu, or ambrosia from the gods. The hotel calls it chilled mango cream with sago, pomelo and birds nest made with ingredients that resonate with every female soul. It does taste like ambrosia, with the sweet-sour fragrance of the mango forming the first layer of taste and sensation, and the pomelo sacs and sago pearls providing the tactile contrast. The birds nest its the ingredient that gilds the lily, since it is supposed to nourish and nurture a perfect complexion. For those unfamiliar with this exotic ingredient, the birds nest is not a bundle of twigs, but is, instead, the dried secretion that cave swifts use to build their nest. Technically, its bird saliva, but the Chinese believe that it has collagen-boosting properties essential to beauty. To me, it just tastes good, adding a slight gelatinous crunch to the back of the teeth. There is also a baked mushroom puff pastry that includes the highly prized Matsutake or pine mushroom. You also get a choice of teas, but I strongly recommend the aged Puer from Yunnan province. It is a mellow tea that will go perfectly with the rich little nuggets, and will warm you up on a cold afternoon. Incidentally, the general guide is green tea such as Longjing or Dragonwell for the hot season, semi-fermented teas like Wu-long or Iron Buddha for autumn, and more warming teas like Puer for winter. The Shang-Xi afternoon tea costs 228 yuan ($37) per person, and 388 yuan for the more opule