2015年電大工程數(shù)學復習資料(本）期末復習考試試題資料小抄

1、電大工程數(shù)學復習資料一、 線性代數(shù)1、 矩陣的初等行變換：1）兩行互換，2）某一行乘以一個非零常數(shù)，3）某一行的K倍加到另一行。2、 階梯型矩陣：1）全為0的行寫在最下面，2）首非零元的列標隨行標的增大而增大。如3、 行簡化階梯型矩陣：滿足下列條件的階梯型矩陣：1）首非零元全為1，2）首非零元所在列其余元素全為0。如：4、 求矩陣A的秩：A階梯型矩陣。階梯型矩陣非零行的行數(shù)既為矩陣A的秩即r(A)例： 設矩陣，求矩陣的秩解：用初等行變換將矩陣化為階梯形由此可知矩陣的秩為25、 求矩陣方程AX=B：（A B）(I X)或X=B求矩陣A的逆矩陣：（A I）（I ）1. 例：設矩陣A=,B=,求AB

2、. 或解矩陣方程AX=B解：（AB）=例：設矩陣，求： 解： 所以 6 、n元線性方程組解的判定1）AX=b ：r(A b)=r(A)時，方程組有解 r(Ab)r(A)時，方程組無解AX=0：方程組一定有解2）求齊次線性方程組AX=0的基礎解系：將方程組中的自由未知量分別?。╧，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：設齊次線性方程組的系數(shù)矩陣經(jīng)過初等行變換，得求此齊次線性方程組的一個基礎解系和通解解： 因為 得一般解： （其中是自由元） 令，得；令，得所以，是方程組的一個基礎解系 方程組的通解為：，其中是任意常

3、數(shù) 例：2.線性方程組的全部解解：（A b）=方程組的一般解將常數(shù)項視為零，取得相應齊次方程組的一個基礎解系，取原方程組的一個特解故方程組的全部解 X=+C例：當取何值時，線性方程組有解，在有解的情況下求方程組的全部解解：將方程組的增廣矩陣化為階梯形由此可知當時，方程組無解。當時，方程組有解。此時齊次方程組化為 分別令及，得齊次方程組的一個基礎解系令，得非齊次方程組的一個特解由此得原方程組的全部解為（其中為任意常數(shù)）二、 概率部分1、假設為兩事件，已知，求解： 2、正態(tài)分布X, ,P(X>b)=1-P（X<b）=1- 例：.設XN(2,9),試求（1）P(X<11);(2)P

4、（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)=0.13593、估計區(qū)間和假設檢驗：對于正態(tài)分布N（1）方差已知：統(tǒng)計量U=，其中置信區(qū)間：,假設檢驗：若，則假設成立2）方差未知：統(tǒng)計量T= ，置信區(qū)間：,假設檢驗：若 ，則假設例：. 某車間生產(chǎn)滾珠，已知滾珠直徑服從正態(tài)分布今從一批產(chǎn)品里隨機取出9個，測得直徑平均值為15.1mm，若已知這批滾珠直徑的方差為，試找出滾珠直徑均值的置信度為0.95的置信區(qū)間解：由于已知，故選取樣本函數(shù)

5、已知，經(jīng)計算得滾珠直徑均值的置信度為0.95的置信區(qū)間為，又由已知條件，故此置信區(qū)間為例：對某一距離進行4次獨立測量，得到的數(shù)據(jù)為（單位：米）： 15.51, 15.47, 15.50, 15.52由此計算出，已知測量無系統(tǒng)誤差，求該距離的置信度為0.95的置信區(qū)間（測量值服從正態(tài)分布）解：由于未知， 已知，經(jīng)計算得該距離的置信度為0.95的置信區(qū)間為，又由已知條件，故此置信區(qū)間為。例：.據(jù)資料分析，某廠生產(chǎn)的一批磚，其抗斷強度XN(32.5,1.21),今從這批磚中隨機地抽取了9塊，測得抗斷強度（單位：kg/cm）的平均值為31.12，問這批磚的抗斷強度是否合格（=0.05，=1.96）解：

6、假設：32.5已知9，31.121.1 =3.76>1.96故認為這批磚的抗斷強度不合格例：某鋼廠生產(chǎn)了一批管材，每根標準直徑100mm,今對這批管材進行檢驗，隨機取出9根，測得它們直徑的平均值為99.9mm,樣本標準差s=0.47,已知管材直徑服從正態(tài)分布，問這批管材的質(zhì)量是否合格（檢驗顯著性水平=0.05，）解：假設H:=100已知：n=9 s=0.47 =99.9故認為這批管材的質(zhì)量是合格的請您刪除一下內(nèi)容，O(_)O謝謝！2015年中央電大期末復習考試小抄大全，電大期末考試必備小抄，電大考試必過小抄After earning his spurs in the kitchens o

7、f 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 fro

8、ntof- house at this Sinan Mansions'stalwart.  "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

9、 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 bra

10、nch 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

11、 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 pr

12、oblem 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 Saturda

13、y 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

14、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 struggle

15、d 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 te

16、arooms 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 a

17、lso 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

18、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 o

19、ne 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 i

20、mported 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.

21、 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 popular

22、ity 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 blac

23、k 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,

24、"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 i

25、nto 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 th

26、ere 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 sele

27、ction 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 spe

28、cial 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-a

29、u-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 what

30、s 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.

31、 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 t