2016級復(fù)變函數(shù)教學(xué)大綱_第1頁
2016級復(fù)變函數(shù)教學(xué)大綱_第2頁
2016級復(fù)變函數(shù)教學(xué)大綱_第3頁
2016級復(fù)變函數(shù)教學(xué)大綱_第4頁
全文預(yù)覽已結(jié)束

下載本文檔

版權(quán)說明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權(quán),請進行舉報或認領(lǐng)

文檔簡介

FunctionsofaComplex總學(xué)時:64上機學(xué)時:0實驗學(xué)時:04畢業(yè)要求(專業(yè)課程培養(yǎng)學(xué)生的教學(xué)內(nèi)容與學(xué)時(一)復(fù)數(shù)及復(fù)平 4學(xué) 2學(xué) 2學(xué)程表示的幾何圖形掌握復(fù)數(shù)的乘冪與理解平面曲線,光滑曲線與平面區(qū)(二)復(fù)變函 8學(xué) 4學(xué) 4學(xué)C-RC-R及簡單映射性質(zhì)。掌握歐拉和復(fù)數(shù)的指數(shù)表示(三)復(fù)變函數(shù)的積 12學(xué) 8學(xué)柯西4學(xué)西積分定理和柯西積分。掌握柯西不等式、定理、莫勒拉定理。(四)級 16學(xué) 2學(xué) 6學(xué) 8學(xué)的求法。掌握泰勒級數(shù)的定義及常見函數(shù)的泰勒展開式。掌握洛朗級數(shù)的定(五)留 12學(xué) 4學(xué) 8學(xué)(六)保形映 12學(xué) 4學(xué) 4學(xué) 4學(xué)實驗教學(xué)(包括上機學(xué)時、實驗無現(xiàn)用:余家榮.復(fù)變函數(shù)[M].:高等教育方企勤.復(fù)變函數(shù)[M].:鐘玉泉.復(fù)變函數(shù)論[M].:高等教育制定人及制定時間,2017220“FunctionsofaComplexVariable”CourseCourseFunctionsofaComplexCourseDisciplinaryBasicCourseCompulsoryClass4SchoolofProgramMathematicsandApplied Withasolidmathematicalfoundationandtheabilityofrigorouslogicalthinkingandreasoning.Masteringthebasictheoryofmathematicsandmethods,withtheabilitytousetheknowledgeofmathematicsandcomputerstosolveproblems.SubjecttopreliminarytraininginscientificByteachingthiscoursetoenablestudentstograspandunderstandsomebasicconcepts,basictheoriesandbasicmethodsofyticfunctiontheory,tocultivatethebasicskillsofapplyingtheseconceptsandmethodstosolvepracticalproblems,andtoprovidethenecessarymathematicalbasisforthestudyfollow-upCourseThiscourseisabasiccourseofmathematics,includingthebasictheory:complexnumbers,yticfunctions,differential,integral,series,residueandconformalmapofyticfunctions,andthebasicoperation:complexintegral,thepowerseriesexpansionofyticfunctions,classificationofapplicationoftheresiduetheorem,conformalmapofsimpleTeachingContentand (I)Complexnumberandcomplex 4ClassComplexnumberanditsgeometric 2ClassTopologyofthecomplexne 2ClassHoursMastertheconceptofcomplexnumbers,theirsrepresentationsandoperations.Understandthegeometricmeaningofarithmeticoperationsofcomplexnumbersandthegeometricalrepresentationofcomplexequation.Masterthepowerandtherootsofacomplexnumber.Understandthenecurve,smoothcurveneregion.Understandthedefinitionofcomplexfunctionofavariable,masterthelimitandcontinuityofcomplexFunctionsofacomplex 8Classytic 4ClassElementary 4ClassUnderstandingthederivabilityandthedifferentiabilityandclarifytherelationshipbetweenthetwoconcepts.MastertheC-Rconditionanduseittodeterminethedifferentiabilityofcomplexfunctions.Masterthebasicrulesofdifferentiation.Masterthedefinition,basicpropertiesandbasicmappropertiesoftheexponentialfunction,powerfunction,trigonometricfunction.MasterEulerformulaandexponentialrepresentationofcomplexnumbers.(III)Complex 12ClassCauchy's 8ClassCauchy'sintegralformula 4ClassHoursMasterthedefinition,basicpropertiesandcalculationmethodsoftheintegrationofacomplexfunctionalongapiecewisesmoothcurve.MasteringCauchyintegraltheoremandCauchyintegralformula.MasterCauchyinequality,Liouville'stheorem,Morera'stheorem.(IV) 16ClassThebasicpropertiesoftheseriesand 2ClassTheTaylor 6ClassTheLaurent 8ClassUnderstandtheconceptofthelimitofasequenceofcomplexnumbers,theconceptofseriesofcomplexfunctions.Mastertheconcept,thepropertiesandtheconvergenceradiusofthepowerseries.MasterthedefinitionoftheTaylorseriesandtheTaylorexpansionofcommonfunctions.MasterthedefinitionofLaurentseriesandtheLaurentexpansionofsomeyticfunctionsinanannulus.Masterthedefinitionandclassificationofisolatedsingularities.(V) 12ClassGeneral 4ClassApplicationofresiduecalculation 8ClassHoursMasterthedefinitionandcalculationmethodofresidues.Mastertheresiduetheoremanditsapplications.(VI)Conformal 12ClassHoursMappropertiesofunivalentytic 4ClassFractionallinearfunctionanditsmap 4ClassTheRiemannmap 4ClassUnderstandthegeometricmeaningofthederivativeofyticfunctionsandtheconceptofconformalmap;mastertheconceptoflinearfractionaltransformationanditsproperties;mastertheummodulusprinciple,Schwarzlemma,Riemannmaptheorem;mastertheconformalmapbetweensomesimpleClassroom ,comprehensiveExaminationandclassroomperformance:Finalexamination: andReferenceBooksTeachingMaterials:Ji

溫馨提示

  • 1. 本站所有資源如無特殊說明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請下載最新的WinRAR軟件解壓。
  • 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
  • 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁內(nèi)容里面會有圖紙預(yù)覽,若沒有圖紙預(yù)覽就沒有圖紙。
  • 4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
  • 5. 人人文庫網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護處理,對用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對任何下載內(nèi)容負責。
  • 6. 下載文件中如有侵權(quán)或不適當內(nèi)容,請與我們聯(lián)系,我們立即糾正。
  • 7. 本站不保證下載資源的準確性、安全性和完整性, 同時也不承擔用戶因使用這些下載資源對自己和他人造成任何形式的傷害或損失。

最新文檔

評論

0/150

提交評論