復變函數(shù)與積分變換復習提綱第一章復變函數(shù)一、復變數(shù)和復變函數(shù)YXIVUZFW,二、復變函數(shù)的極限與連續(xù)極限連續(xù)AFZLIM0LIM00ZFZ第二章解析函數(shù)一、復變函數(shù)可導與解析的概念。,YXIVUFW二、柯西黎曼方程掌握利用CR方程判別復變函數(shù)的可導性與解析性。XYV掌握復變函數(shù)的導數(shù)YXYXVIIUFVFZF1三、初等函數(shù)重點掌握初等函數(shù)的計算和復數(shù)方程的求解。1、冪函數(shù)與根式函數(shù)單值函數(shù)INNNERIRIRZWSCOSCOK0、1、2、N1N多值函數(shù)NKZIE2AG12、指數(shù)函數(shù)SINCYXZ性質(zhì)（1）單值（2）復平面上處處解析，（3）以為周期ZEI23、對數(shù)函數(shù)（K0、1、2）KIZKZILNZW2LN2ARGL性質(zhì)（1）多值函數(shù),（2）除原點及負實軸處外解析,（3）在單值解析分枝上。KZ1LN4、三角函數(shù)2COSIZIEZIEIZI2SIN性質(zhì)（1）單值（2）復平面上處處解析（3）周期性（4）無界5、反三角函數(shù)（了解）反正弦函數(shù)1SIN2ZILZARCW反余弦函數(shù)O2I性質(zhì)與對數(shù)函數(shù)的性質(zhì)相同。6、一般冪函數(shù)（K0、1）ARG2LNIZKZSSLZE四、調(diào)和函數(shù)與共軛調(diào)和函數(shù)1調(diào)和函數(shù)0,2YXU2已知解析函數(shù)的實部（虛部），求其虛部（實部）有三種方法A）全微分法B）利用CR方程C）不定積分法第三章解析函數(shù)的積分一、復變函數(shù)的積分存在的條件。LLLUDYVXIDYUXFDZ二、復變函數(shù)積分的計算方法1、沿路徑積分利用參數(shù)法積分，關鍵是寫出路徑的參數(shù)方程。CF2、閉路積分A利用留數(shù)定理，柯西積分公式，高階導數(shù)公式。DZB利用參數(shù)積分方法ZYXIVUC,三、柯西積分定理0CDZF推論1積分與路徑無關DZFFZC21推論2利用原函數(shù)計算積分1221FZFZ推論3二連通區(qū)域上的柯西定理21CCDZFF推論4復連通區(qū)域上的柯西定理KCNCZFZF1四、柯西積分公式DZFIZFC2002CFZDIFZA五、高階導數(shù)公式FINFCNN1解析函數(shù)的兩個重要性質(zhì)解析函數(shù)在任一點的值可以通過函數(shù)沿包圍點的任一簡單閉合回路的積分表示。ZFZZ解析函數(shù)有任意階導數(shù)。本章重點掌握復變函數(shù)積分的計算方法沿路徑積分1）利用參數(shù)法積分2）利用原函數(shù)計算積分。CDZF閉路積分利用留數(shù)定理計算積分。第四章解析函數(shù)的級數(shù)一、冪級數(shù)及收斂半徑0NNBZA1、一個收斂半徑為R（0）的冪級數(shù)，在收斂圓內(nèi)的和函數(shù)是解析函數(shù)，在這個收斂圓內(nèi)，這個展開式ZF可以逐項積分和逐項求導，即有1NNBZAZFRBZ1000NNZLNZADDFRBZ2、收斂半徑的計算方法1）比值法1/LIMNNR2）根值法A二、泰勒（TAYLOR）級數(shù)1、如函數(shù)在圓域內(nèi)解析，那么在此圓域內(nèi)可以展開成TAYLOR級數(shù)ZFRBZFFNNNBZFA001）展開式是唯一的。故將函數(shù)在解析點的鄰域中展開冪級數(shù)一定是TAYLOR級數(shù)。2收斂半徑是展開點到的所有奇點的最短距離。ZF3）展開式的系數(shù)可以微分計算NBFA4）解析函數(shù)可以用TAYLOR級數(shù)表示。2、記住一些重要的泰勒級數(shù)1）2）0NZ0NZE3）4）012SINN021COSNNZZ三、羅蘭（LAURENT）級數(shù)如果函數(shù)在圓環(huán)城內(nèi)解析，則ZF21RBZZFXNNBCDZBFICLNN12（N0、1、2）1、展開式是唯一的，即只要把函數(shù)在圓環(huán)城內(nèi)展開為冪級數(shù)即為LAURENT級數(shù)。2、展開式的系數(shù)是不可以利用積分計算。利用已知的冪級數(shù)，通過代數(shù)運算把函數(shù)展開成LAURENT級數(shù)。3、注意展開的區(qū)域，在展開點的所有解析區(qū)域展開。四、孤立奇點1、定義若B是的孤立奇點，則在內(nèi)解析。在此點可展開為羅蘭級數(shù)，ZFZFB0ZFZF10NNNNCBCZC2、分類孤立奇點1,RE,CBZFSF無窮多負冪項本性奇點有限負冪項極點無負冪項可去奇點把函數(shù)在奇點的去心鄰域中展開為羅蘭級數(shù)，求解C13、極點留數(shù)計算A如果B是的一階極點，則ZFLIM,EZFZFSBZB如果B是的M階極點，則LI1,RE1ZFBDZZFSMBC如B是的一階極點，且PB0，那么ZQPFBS,RED0,1E,2ZFSZFE若是的可去奇點，并且，0LIMZFZCZFSZLI,RE1關系全平面留數(shù)之和為零。0,RE,1FSBZFSKK本章重點函數(shù)展開成TAYLOR級數(shù)，并能寫出收斂半徑。函數(shù)在解析圓環(huán)城內(nèi)展開成LAURENT級數(shù)。孤立奇點（包含點）的判定及其留數(shù)的計算。Z第五章留數(shù)定理的應用一、DR20COS,IN條件（1）RSIN，COS為COS與SIN的有理函數(shù)（2）R在0，2或者，上連續(xù)。令，則，。IEZIZSIN12COS1ZIZDZFIIZRDZZ1120,CO,INKKFSI1,E2K注意留數(shù)是計算單位圓中的奇點。二、DXF條件（1）是X的多項式。XQP,（2）0X（3）分母階次比分子階次至少高二次則是在上半平面的奇點。NRKBZFSIDF1,EZF三、（）XEI0條件（1），且比至少高一階，XQPXP（2），（3）XNKKZIIBERSIDERI1,0IMK，IXCOSXDSIN重點關注第一和第三種類型第七章FOURIER變換一、傅立葉變換DTEXFFJFTJ21二、函數(shù)的傅立葉變換1DXEXJXDEXJ2三、一些傅立葉變換及逆變換IXH121四、性質(zhì)FXF1、相似性質(zhì)AF12、延遲性質(zhì)FEXXJ00位移性質(zhì)0FEJ3、微分性質(zhì)FJXFFXJFJFNNNNDFJ4、積分性質(zhì)10FJDXFX由FOURIER變換的微分和積分性質(zhì)，我們可以利用FOURIER變換求解微積分方程。四、卷積和卷積定理DXFXF2121F2211XF五、三維FOURIER變換及反演本章重點利用定義計算FOURIER變換第八章LAPLACE變換一、拉普拉斯變換PFDTEXFFP0二、幾個重要的拉普拉斯變換及逆變換PTH1TH1ETTEP12COSPTTCOS212SINPTTPSIN211MTT四、拉普拉斯變換的性質(zhì)1、PFETFT002、0TP3、FTF2FPFUNUNDTF4、PFTFT10DTF五、卷積TFTFT20121PF六、LAPLACE反演NNPTPTJESDETF1,R21七、LAPLACE逆變換（1）部分分式法（2）卷積定理（3）LAPLACE反演公式（留數(shù)定理）（4）利用LAPLACE變換的性質(zhì)八、利用LAPLACE變換求解微積分方程（1）對方程取LAPLACE變換，得到象函數(shù)的代數(shù)方程（2）解代數(shù)方程，得到像函數(shù)的表達式（3）求像函數(shù)的拉普拉斯逆變換拉氏變換解代數(shù)方程拉氏逆變換本章重點利用定義和性質(zhì)計算LAPLACE變換。微分方程像函數(shù)的代數(shù)方程像函數(shù)像原函數(shù)解函數(shù)計算LAPLACE逆變換。利用LAPLACE變換求解微積分方程。請您刪除一下內(nèi)容，O_O謝謝2016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BASKETBALLCANMAKEATRUECLAIMTOBEINGTHEONLYMAJORSPORTTHATISANAMERICANINVENTIONFROMHIGHSCHOOLTOTHEPROFESSIONALLEVEL,BASKETBALLATTRACTSALARGEFOLLOWINGFORLIVEGAMESASWELLASTELEVISIONCOVERAGEOFEVENTSLIKETHENATIONALCOLLEGIATEATHLETICASSOCIATIONNCAAANNUALTOURNAMENTANDTHENATIONALBASKETBALLASSOCIATIONNBAANDWOMENSNATIONALBASKETBALLASSOCIATIONWNBAPLAYOFFSANDITHASALSOMADEAMERICANHEROESOUTOFITSPLAYERANDCOACHLEGENDSLIKEMICHAELJORDAN,LARRYBIRD,EARVIN“MAGIC“JOHNSON,SHERYLSWOOPES,ANDOTHERGREATPLAYERSATTHEHEARTOFTHEGAMEISTHEPLAYINGSPACEANDTHEEQUIPMENTTHESPACEISARECTANGULAR,INDOORCOURTTHEPRINCIPALPIECESOFEQUIPMENTARETHETWOELEVATEDBASKETS,ONEATEACHENDINTHELONGDIRECTIONOFTHECOURT,ANDTHEBASKETBALLITSELFTHEBALLISSPHERICALINSHAPEANDISINFLATEDBASKETBALLSRANGEINSIZEFROM28530IN7276CMINCIRCUMFERENCE,ANDINWEIGHTFROM1822OZ510624GFORPLAYERSBELOWTHEHIGHSCHOOLLEVEL,ASMALLERBALLISUSED,BUTTHEBALLINMENSGAMESMEASURES29530IN7576CMINCIRCUMFERENCE,ANDAWOMENSBALLIS28529IN7274CMINCIRCUMFERENCETHECOVERINGOFTHEBALLISLEATHER,RUBBER,COMPOSITION,ORSYNTHETIC,ALTHOUGHLEATHERCOVERSONLYAREDICTATEDBYRULESFORCOLLEGEPLAY,UNLESSTHETEAMSAGREEOTHERWISEORANGEISTHEREGULATIONCOLORATALLLEVELSOFPLAY,THEHOMETEAMPROVIDESTHEBALLINFLATIONOFTHEBALLISBASEDONTHEHEIGHTOFTHEBALLSBOUNCEINSIDETHECOVERINGORCASING,ARUBBERBLADDERHOLDSAIRTHEBALLMUSTBEINFLATEDTOAPRESSURESUFFICIENTTOMAKEITREBOUNDTOAHEIGHTMEASUREDTOTHETOPOFTHEBALLOF4954IN1214MWHENITISDROPPEDONASOLIDWOODENFLOORFROMASTARTINGHEIGHTOF6FT180MMEASUREDFR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