MODULE HANDBOOK MATHEMATICS 2 - Beranda
MODULE HANDBOOKMATHEMATICS 2Module nameModule levelCodeCourse (if applicable)SemesterPerson responsible forthe moduleLecturerLanguageRelation to curriculumType of teaching,contact hoursWorkloadCredit pointsMathematics 2UndergraduteKM184201Mathematics 2Second Semester (Genap)Dra. Rinurwati, M.Si.ITS Mathematics Lecturer TeamBahasa IndonesiaUndergradute degree program, mandatory, 2nd semester.Presentation, 60 students1. Presentation : 3 x 50 150 minutes per week.2. Exercises and Assignments : 2 x 60 120 minutes (2 hours) perweek.3. Private learning : 2 x 60 120 minutes (2 hours) per week.3 credit points (sks)Requirementsaccording to theexaminationregulationsA student must have attended at least 75% of the presentation to sitinthe exams.MandatoryprerequisitesLearning outcomesand theircorresponding PLOs-ContentCourse Learning Outcome (CLO) after completing thismodule,CLO 1 Students are able to apply basic concept ofmathematics related to transcendent functionsCLO 2 Students are able to apply integration techniquesCLO 3 Students are able to apply it in the form ofCartesian coordinate function, and polar coordinates andparametric equationsCLO 4 Students are able to determine the convergence ofinfinite sequences and infinite series and the number ofconvergent infinite seriesCLO 5 Students are able to transform functions into Taylorseries or the Mac Laurint seriesIn this course, students will study the following subjects:PLO1,2,4PLO 3PLO3,4,5PLO2,3,4PLO 4,5
1. Transcendent function, differential and integral.2. Integral and improper integral.3. Application of certain integral in a plane, volume of object, arclength and surface area, center of mass, application of Guldintheorem.4. Polar coordinate systems and parametric equations, graphicalsketches, and their applications.5. Convergences of infinite sequences and series, and calculate thenumber of convergence infinite series, Taylor series or Mac LaurintseriesStudy andexaminationrequirements andforms of examinationMedia employedReading listIndependent Assignments, Written Exams (Quiz, ETS, EAS).LCD, whiteboard, websites (myITS Classroom), zoom.Main :1. Tim Dosen Jurusan Matematika ITS, Buku Ajar Kalkulus 2 ,Edisi ke-4 Jurusan Matematika ITS, 20122. Anton, H. dkk, Calculus, 10-th edition, John Wiley & Sons, NewYork, 2012Supporting :1. Kreyzig, E, Advanced Engineering Mathematics, 10-th edition,John Wiley & Sons, Singapore, 20112. Purcell, J, E, Rigdon, S., E., Calculus, 9-th edition, Prentice-Hall,New Jersey, 20063. James Stewart , Calculus, ed.7, Brooks/cole-Cengage Learning,Canada,2012
I.Rencana Pembelajaran Semester / Semester Learning PlanINSTITUT TEKNOLOGI SEPULUH NOPEMBER (ITS)DocumentCodeFACULTY OF INTELLIGENT ELECTRICAL AND INFORMATICS TECHNOLOGYDEPARTMENT OF BIOMEDICAL ENGINEERINGSEMESTER LEARNING PLANMATA KULIAH (MK)COURSEMatematika 2Mathematics 2KODECODEKM184201Rumpun MKCourse ClusterIlmu Dasar TeknikBasic EngineeringOTORISASI / PENGESAHANAUTHORIZATION / ENDORSEMENTDosen Pengembang RPSDeveloper Lecturer of Semester Learning Plan(Dra. Rinurwati, M.Si.)CapaianPembelajaranLearningOutcomesBOBOT (sks)CreditsT 3SEMESTERP 0Koordinator RMKCourse Cluster Coordinator(Dimas Anton Asfani, ST.,MT., Ph.D)IITgl PenyusunanCompilation Date15 Juli 2020July 15th, 2020Ka DEPARTEMENHead of Department(Dedet Candra Riawan, ST.,M.Eng., Ph.D.)CPL-PRODI yang dibebankan pada MKPLO Program Charged to The CourseCPL-01Mampu menginterpertasikan konsep dasar matematika dan menyusun pembuktian secara langsung, tidak langsung,PLO-01maupun dengan induksi matematika.Able to interpret the basic concepts of mathematics and establish direct, indirect or induced mathematics proofCPL-02Mampu melakukan identifikasi permasalahan sederhana, membentuk model matematika dan menyelesaikannyaPLO-02Able to identify simple problems, form mathematical models and solve themCPL-03Menguasai metode-metode standar dalam bidang matematikaPLO-03Mastering standard methods in mathematicsCPL-04Mampu menguasai teori fundamental matematika yang meliputi konsep himpunan, fungsi, diferensial, integral, ruang dan strukturPLO-04matematika.Able to master the fundamental theory of mathematics including the concepts of sets, functions, differentials, integrals, geometry andstructure of mathematics.CPL-05Mampu melakukan identifikasi permasalahan, membentuk model matematika dan menyelesaikannyaPLO-05Able to identify problems, form mathematical models and solve them
Peta CPL – CP MKMap of PLO - CLOBahan KajianCapaian Pembelajaran Mata Kuliah (CPMK)Course Learning Outcome (CLO) - If CLO as description capability ofeach Learning Stage in the course, then CLO LLOCP MK 1Mahasiswa mampu menerapkan konsep-konsep Dasar Matematika yang terkait dengan fungsi transendenCLO 1Students are able to apply basic concept of mathematis related to transcendent functionsCP MK 2Mahasiswa mampu menerapkan teknik integrasiCLO 2Students are able to apply integration techniquesCP MK 3Mahasiswa mampu mengaplikasikannya baik dalam bentuk fungsi koordinat kartesius, maupun koordinat kutub danCLO 3persamaan parametrikStudents are able to apply it in the form of Cartesian coordinate function, and polar coordinates andparametric equationsCP MK 4Mahasiswa mampu menentukan kekonvergenan barisan dan deret tak hingga dan jumlah deret tak hingga yangCLO 4KonvergenStudents are able to determine the convergences of infinite sequence and infinite series and the number of convergent infinite seriesCP MK 5Mahasiswa mampu mentransformasikan fungsi ke dalam bentuk deret Taylor atau deret Mac LaurintCLO 5Students are able to transform functions into Taylor series or Mac Laurint seriesCPL 1CPL 2CPL 3CPL 4CPL 5PLO 1PLO 2PLO 3PLO 4PLO 5 CPMK 1CLO 1 CPMK 2CLO 2 CPMK 3CLO 3 CPMK 4CLO 4 CPMK 5CLO 5Fungsi Transenden, diferensial dan integralnyaTeknik Integrasi, Integral tak wajar
Course Materials:Pokok BahasanSubjectAplikasi IntegralFungsi bentuk Kutub, fungsi Parametrik, diferensial dan integralnyaBarisan dan DeretTranscendent functions, differential and integralIntegration Technique, improper IntegralApplication of integralPolar form functions, Parametric functions, differential and integralSequence and seriesDalam Mata Kuliah ini mahasiswa akan mempelajari Pokok bahasan pokok bahasan sebagai berikut:1. Fungsi Transenden, diferensial dan integralnya.2. Teknik integrasi dan Integral tak wajar.3. Aplikasikan integral tertentu pada luas bidang datar, volume benda, Panjang busur dan luas kulit benda putar, pusat massa, penerapan teoremaGuldin.4. Sistem koordinat kutub dan persamaan parametrik, sketsa grafiknya, dan aplikasinya.5. Kekonvergenan barisan dan deret tak hingga, dan menghitung jumlah deret tak hingga yang konvergen, deret Taylor atau deretMac LaurintIn this course students will study the following subjects:1. Transcendent function, differential and integral.2. Integration techniques and improper integral.3. Application of certain integral in plane, volume of object, length of arc and surface area, center of mass, application of Guldin theorem.4. Polar coordinate systems and parametric equations, graphical sketches, and their applications.5. Convergences of infinite sequences and series, and calcuating the number of convergent infinite series, Taylor series or Mac Laurint seriesPustakaReferencesUtama / Main:1.Tim Dosen Jurusan Matematika ITS, Buku Ajar Kalkulus 2 , Edisi ke-4 Jurusan Matematika ITS, 20122.Anton, H. dkk, Calculus, 10-th edition, John Wiley & Sons, New York, 2012
Pendukung / Supporting:1. Kreyzig, E, Advanced Engineering Mathematics, 10-th edition, John Wiley & Sons, Singapore, 20112. Purcell, J, E, Rigdon, S., E., Calculus, 9-th edition, Prentice-Hall, New Jersey, 20063. James Stewart , Calculus, ed.7, Brooks/cole-Cengage Learning, Canada,2012Dosen PengampuLecturersMatakuliah syaratPrerequisiteITS Mathematics Team Lecturer-Kemampuan akhir tiapMgtahapan belajar (Sub-CPMK) /ke/Final ability of each learningWeekstage (LLO)(1)1(2)Pengantar KuliahIntroductionMampu menjelaskan:Sifat-sifat fungsi dan grafikyang melibatkan logaritma,dan eksponensialAble to explain:Bentuk Pembelajaran; MetodeMateri PembelajaranPembelajaran; Penugasan Mahasiswa;[Pustaka] /[ Estimasi Waktu] /Learning MaterialForm of Learning; Learning Method;Indikator /Kriteria & Teknik /[Reference]Student Assignment;IndicatorCriteria & Techniques[ Estimated Time](3)(4)Tatap Muka /Daring /(7)In-class (5)Online (6)Menyampaikan RPS, Kontrak Kuliah, dan Perjanjian macam Evaluasi dan Prosentase masing masing evaluasiPenilaian / AssessmentPresenting SLP, study contracts, and agreement about evaluation and persentages of each evaluationKetepatanKetajaman mensketsaKuliah, latihanKuliah, latihan soal- Ihtisar sifat logaritma,menjelaskan sifat2Grafik log & eksponen.soal-soal sertaeksponensial dansoal sertalog danmemberikan soalfungsi log &memberikan soalperpangkatan,Soal-soal latihantugaseksponensialtugas melaluimensketsa grafikserta tugas[1] hal: 1-40Sinkronus/dasar log &Waktu: 1.40 menit asinkronus di MyITSeksponensialAcuity in sketchingOverview ofClassroomgraphic of Log &logarithms properties,Accuracy inexponentialexponential and log &describing log andexponential functionsBobotPenilaian/AssessmentLoad (%)(8)5
The property of functions andgraphs involving logarithms,and exponentialsexponentialproperties, sketchingbasic graph of log &exponentialExercises andassignmentsPresentation,exercises andassignmentTime: 1.40minutes2-3Mampu menentukan turunan:fg invers trigonometri, FungsiHiperbolik & invers fshiperbolikAble to determine thederivative:fg inverse trigonometric,Hyperbolic Functions & fsinverse hyperbolicKetepatan:MemperolehTurunan, Inversfungsi transendendan inverstrigonometri dansketsa GrafiknyaKetajaman Sketsagrafik dan inversnya,diferensiasi danintegrasinyaKuliah, latihansoal-soal sertamemberikansoal tugasSoal-soal latihan sertatugasWaktu: 2 x 1.40MenitAccuracy:Obtain theDerivative, Inverse oftranscendentfunction and inverseof trigonometricfunctions andsketching the GraphsSharpness of thesketched graph and itsinverses, differentiationand integrationPresentation,exercises andassignment4Time: 2x1.40minutesExercises andassignmentsPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronnus di MyITSClassroomPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomASISTENSI KE 1ASSISTANCE 15EVALUASI 1KUIS 1, bahan Bab 11st EVALUATIONQUIZ 1, material inChapter 1Ketajamanmenyelesaikan soal-soalyang terkait denganmateri Bab 1TES TERTULISWaktu: 60 menitWritten TestTime: 60 minutesTES TERTULISWaktu: 50 menitmelalui MyITSClassroomWritten test[1] page: 1-40Grafik fs log & eks,fungsi inverstrigonometri, turunandan integralnya[1] hal: 4499Graph of fs log & ex,inverse functions oftrigonometry,derivatives and itsintegrals[1] p: 449910
6Mampu menyelesaikanIntegral parsial dan integralfungsi trigonometriAble to solve partial integralsand integral of al: parsial danfungsi trigonometriAccuracy in solvingintegrals: partialsand trigonometricfunctionsAcuity in solvingproblems related to thematerial in Chapter 1Ketajamanmenyelesaikan integraldengan metode IntegralParsial dan fungsiTrigonometriSoal-soal latihan sertatugasAcuity in solvingintegrals using PartialIntegral method andTrigonometric functionKuliah, latihansoal-soal sertamemberikan soaltugasWaktu: 1.40 menitPresentation,exercises andassignmentTime: 1.40minutesExercises andassignments7Mampu menyelesaikanIntegral fungsi rasional.Mampu pengaplikasikanTeknik teknik integral yanglainAble to solve integral ofrational functions.Able to apply other integraltechniquesKetepatanmenyelesaikan:Integral fungsirasionalKetepatan subtitusidalammenyelesaikanintegral menujubentuk integral fginvers trigonometriKetajamanmenyelesaikan Integralfungsi rasional.Soal-soal latihan sertatugas Ketajamanmengaplikasikan Teknikteknik integral yang lainsoal-soal latihan sertatugasKuliah, latihansoal-soal sertamemberikan soaltugasWaktu: 50 menitPresentation,exercises andassignmentTime: 50 minutesTime: 50 minutesvia MyITSClassroomKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomTeknik Integrasi[1] hal: 107-1255Integration Technique[1] page: 107-125Presentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomKuliah, latihan soalsoal sertamemberikan soaltugas di MyITSClassroomTeknik Integrasi[1] hal: 127-138Presentation,exercises andprovide assignmentquestions throughSynchronus /Integration Technique[1] pp: 127-138Teknik Integrasi[1] hal: 139-150Integration Technique[1] p: 139-1505
Accuracy incompleting:Integral of rationalfunctionsThe precision of thesubstitution insolving the integralinto integral form ofinverse trigonometryAcuity in resolvingIntegral of rationalfunctions.Exercises andassignment to measureacuity in applying otherintegration techniquesExercises andassignments89ASISTENSI KE 2ASSISTANCE 2Mampu menyelesaikan Limitbentuk tak tentu,Mampu menghitung Integraltak wajarAble to solve indefinite formLimit,Able to calaculate improperIntegral10asynchronous inMyITS ClassroomEVALUASI 2EVALUATION 2Ketepatanmenghitung Limitbentuk tak tentu &Integral tak wajarAccuracy incalculating indefiniteform Limit &improper integralKuis 2, Bahan Bab 2dan 3Ketajaman menghitungLimit bentuk tak tentu &Integral tak wajarKuliah, latihansoal-soal sertamemberikan soaltugassoal-soal latihan sertatugasWaktu: 1.40 menitAcuity in calculatingindefinite form Limit &improper integralPresentation,exercises andassignmentexercisess andassignmentsTime: 1.40minutesKetajamanmenyelesaikan soal-soalyang terkait denganmateri Bab 2 dan 3TES TERTULISWaktu: 60 menitWritten testKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomTES TERTULISWaktu: 50 menitmelalui MyITSClassroomLimit bentuk tak tentu& Integral tak wajar[1] hal: 171-180indefinite form Limit &improper Integral[1] pp: 171-18010
Quiz 2, Materials InChapter 2 And 3Time: 60 minutesTES TERTULISWritten testTime: 50 minutesvia MyITSClassroomAcuity in solvingproblems related tomaterials in Chapters 2and 311Mampu menghitung Luasbidang datarAble to calculate plane areaKetepatanmenghitung Luasbidang datarAccuracy incalculating the areaof a planeWRITTEN TESTKetajaman menghitungLuas bidang datarSoal-soal latihan sertatugasKuliah, latihansoal-soal sertamemberikan soaltugasWaktu: 1.40 menitAcuity to calculates thearea of planeExercises andassignmentsPresentation,exercises andassignmentTime: 1.40minutes1213Kuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomAplikasi integral[1] hal: 183-1915Application of integral[1] pp: 183-191Presentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomASISTENSI KE 3ASSISTANCE 3Mampu menghitung volumebenda putar dengan metodeCakramKetepatanmenghitung volumebenda putar metodecakramKetajaman menghitungvolume benda putarsoal-soal latihan sertatugasKuliah, latihansoal-soal sertamemberikan soaltugasWaktu: 50 menitKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronVolume benda putar[1] hal: 192-203Volume benda putar[1] hal: 204-2115
Mampu menghitung volumebenda putar dengan metodeCincin SilinderAble to calculate the volumeof rotating objects using thedisc methodAble to calculate the volumeof rotary objects using theCylinder Ring method14Mampu menghitung Panjangkurva dan luas permukaanbenda putarAble to calculate curve lengthand surface area of rotatingobjectsKetepatanmenghitung volumebenda putar metodecincin silinderThe accuracy ofcalculating thevolume of the discrotating objectThe accuracy ofcalculating thevolume of the rotaryobject with thecylinder ring methodKetepatanmenghitung Panjangkurva dan luaspermukaan bendaputarAccuracy ofcalculating curvelength and surfacearea of rotary objectKetajaman menghitungvolume benda putarsoal-soal latihan sertatugasSharpness calculates thevolume of rotatingobjects for exercisessand assignmentsPresentation,exercises andassignmentTime: 50 minutesus di MyITSClassroomPresentation,exercisess andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomVolume of rotaryobjects[1] page: 192-203Volume of rotaryobjects[1] p: 204-211Sharpness calculates thevolume of a rotatingobjectexercisess andassignmentsKetajaman menghitungPanjang kurva dan Luaspermukaan benda putarKuliah, latihansoal-soal sertamemberikan soaltugasSoal-soal latihan sertatugasWaktu: 1.40 menitAcuivity in calculatingcurve length and surfacearea of rotary objectPresentation,exercisess andassignmentExercises andassignmentsTime: 1.40minutesKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asi nkronus di MyITSClassroomPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomPanjang kurva danluas permukaan[1] hal: 211-220Curve length andsurface area[1] p: 211-2205
15,16 EVALUASI KE 3EVALUATION 3UJIAN TENGAHSEMESTERMID-TERM EXAM17,18 Mampu menentukan Pusatmassa dan menerapkan dalilGuldinAble to determine the centerof mass and applying Guldin'stheoremKetepatanmenerapkan dalilGuldin untukmenghitung pusatmassa dan luas,Volume,panjangbusur dan luas KulitAccuracy in applyingGuldin's theorem tocalculate the centerof mass and area,volume, arc lengthand surface areaKetajamanmenyelesaikan soal-soalyang terkait denganfungsi trensenden,teknik integrasi luasbidang dan volumebenda putarTES TERTULISAcuity in solvingproblems related to thetransendent function,integration technique forplane area and rotaryobject volumeWRITTEN TESTKetajaman menerapkandalil pada aplikasiintegralSoal-soal latihan sertatugasAcuity in applyingtheorems for applicationof integralExercises andassignmentTERJADWALUjian tertulisWaktu: 100 menitTERJADWALDaring asinkronusWaktu: 90 menitSchedulesWritten testTime: 100 minutesScheduledOnlineasynchronousTime: 90 minutesKuliah, latihansoal-soal sertamemberikan soaltugas Waktu: 2 x1.40 menitKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomPresentation,exercises andassignmentTime: 2x1.40minutesPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomKOMPREHENSIFComprehensivePusat massa dan dalilGuldin[1] hal: 221-231Center of mass andGuldin’s theorem[1]page: 221-23110
19Mampu menggambar Grafikdalam koordinat kutubAble to draw a graph in polarcoordinateKetepatanmenggambar grafikfs bentuk kutubKetajaman menggambarGrafik dalam koordinatkutubKuliah, latihansoal-soal sertamemberikan soaltugasAccuracy in drawingfs graph in polarformsoal-soal latihan sertatugasWaktu: 1.40 menitAcuity in drawing agraph in polarcoordinatePresentation,exercises andassignmentTime: 1.40minutes2021Kuliah, latihan soalsoal sertamemberikan soaltugas melaluimelaluiSinkronus/asinkronus di MyITSClassroomGrafik fungsi dalamKoordinat kutub[1] hal: 233-2525Graph of function inpolar coordinate[1]page: 233-252Presentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomASISTENSI KE 4ASSISTANCE 4Mampu Menghitung Luasdalam sistem koordinat KutubAble to calculate area in polarcoordinate systemKetepatanmenghitung luasdalam kutubAccuracy incalculating area inpolarKetajaman menghitungLuas dalam koord kutubsoal-soal latihan sertatugasKuliah, latihansoal-soal sertamemberikan soaltugasWaktu: 1.40 menitAcuity in calculatingarea in polar coordinateExercises andassignmentPresentation,exercises andassignmentTime: 1.40minutesKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomPresentation,exercises andprovide assignmentquestions throughSynchronus /Koordinat kutub[1] hal: 254-262Polar coordinate[1]page: 254-2627,5
22Mampu:- Menjelaskan fs parametrik,turunannya dan luas luasnya.- Menghitung panjang busurdalam koordinat kutubAble to:Ketepatanmenghitung panjangbusur dalam bentukparametric danbentuk kutubAccuracy incalculating arclength in parametricand polar form-Explain fs parametric, itsderivation and areaKetajaman menghitungpanjang busur dandalam koordinat kutubdan bentuk parametrikKuliah, latihansoalsoal sertamemberikan soaltugassoal-soal latihan sertatugasWaktu: 1.40 menitAcuity in calculating arclength in polarcoordinate andparametric formPresentation,exercises andassignmentTime: 1.40minutes- Calculate arc length in polarcoordinate2324asynchronous inMyITS ClassroomKuliah, latihansoalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomASISTENSI KE-5ASSISTANCE 5EVALUASI KE-4EVALUATION 4KUIS KE-3: BahanDalil Guldin dan Bab5QUIZ 3: Material ofGuldin’s theoremand chapter 5Ketajamanmenyelesaikan soal soalyang terkait Dalil Guldin& Bab 5TES TERTULISAcuity in solvingproblems related toGuldin’s theorem andchapter 5Written testTES TERTULISWaktu: 60 menitWritten testTime: 60 minutesTES TERTULISWaktu: 50 menitmelalui MyITSClassroomWRITTEN TESTTime: 50 minutesvia MyITSClassroomKoordinat kutub[1] hal: 262-282Polar coordinate[1]page:262-2827,5
25Mampu menjelaskan barisan,kekonvergenan derettakhingga dengan Ujikonvergenan Deret.Able to explain sequence,infinite series convergencesusing the test of seriesconvergency26Mampu mentransformasikanfungsi ke dalam bentuk deretTaylor atau deret MacLaurintAble to transform a functioninto Taylor series orMaclaurint series formKetepatanmenentukankekonvergenanBarisan, mengujikekonvergenanDeret tak hingga danmenghitungjumlahnyaAccuracy indeterminingconvergencies ofsequence, intiniteseries convergencytest and calculate itsnumberKetepatanmendapatkan deretTayloy dan MacLaurin dari fungsikontinuAccuracy inobtaining Taylorseries and MacLaurin series from acontinue functionKetajaman : mengujikekonvergenan deret takhingga dan menghitungjumlahnyaKuliah, latihansoal-soal sertamemberikan soaltugassoal-soal latihan sertatugasWaktu: 1.40 menitAcuity in:Testing infinite seriesconvergencies andcalculating its nuberExercises andassignmentPresentation,exercises andassignmentTime: 1.40minutesKetajamanmentransformasi kanfungsi ke dalam bentukderet PolinomialKuliah, latihansoal-soal sertamemberikan soaltugassoal-soal latihan sertatugasWaktu: 1.40 menitAcuity in transforming afunction into polinomialseries formPresentation,exercisess andassignmentTime: 1.40minutesKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomPresentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomKuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomPresentation,exercisess andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomBarisan dan DeretUji konvergensi derettak hingga[1] hal: 285-30710Sequence and seriesInfinite seriesconvergency test[1]page: 285-307Deret Taylor dan DeretMac Laurint[1] hal: 327-330Taylor series and MacLaurint series[1]page: 327-3305
27Diferensiasi dan integrasideret pangkatDifferentiation andintegration of power seriesKetepatanmendeferensilkandan integral deretpangkatAccuracy indifferentiating andintegrating powerseriesKetajamanmendapatkan deret danderet fungsi Logaritma.Kuliah, latihansoal-soal sertamemberikan soaltugasSoal-soal latihan sertatugasWaktu: 1.40 menitAcuity in obtaining seriesand logarithm functionseriesPresentation,exercisess andassignmentExercises andassignmentTime: 1.40minutes28Kuliah, latihan soalsoal sertamemberikan soaltugas melaluiSinkronus/asinkronus di MyITSClassroomDeret Taylor dan DeretMac Laurint5[1] hal: 352-362Taylor series and MacLaurint series[1]page: 352-362Presentation,exercises andprovide assignmentquestions throughSynchronus /asynchronous inMyITS ClassroomASISTENSI KE 6ASSISTANCE29-32 EVALUASI KE-5EVALUATION 5UJIAN AKHIRSEMESTERFINAL-TERM EXAMKetajamanmenyelesaikan soal-soalyang terkait denganfungsi trensenden,teknik integrasi luasbidang dan volumebenda putarTES TERTULISAcuity in solvingproblems related totransdecent function,integration technique forTERJADWALUjian tertulisWaktu: 100 menitTERJADWALDaring asinkron usWaktu: 90 menitScheduledWritten testTime: 100 minutesSCHEDULEDOnlineasyncrhonousTime: 90 minutesKOMPREHENSIFCOMPREHENSIVE100
plane area and volumeof rotary objectTM Tatap Muka, PT Penugasan Terstuktur, BM Belajar Mandiri.FF Face to Face, SA Structured Assignment, SS Self Study.
II.Rencana Asesmen & Evaluasi (RAE) / Assessment & Evaluation PlanASSESSMENT & EVALUATION PLANBACHELOR DEGREE PROGRAM OF BIOMEDICALENGINEERING - FTEIC ITSRA&EWriteCourse : Mathematics 2Doc CodeKode/code:KM184201Bobot sks/credits (T/P): 3/0Rumpun MK: Ilmu Dasar TeknikCourse Cluster: Basic EngineeringSmt: IIOTORISASIPenyusun RA & EKoordinator RMKKa DEPAUTHORIZATIONCompiler A&EPCourse Cluster CoordinatorHead of DEPDimas Anton Asfani, ST.,MT., Ph.DDedet CandraDra. Rinurwati, M.Si.Riawan, ST.,M.Eng., Ph.D.Mgke/Week(1)1Sub CP-MK /Bentuk Asesmen (Penilaian)Bobot /Form of AssessmentLoad (%)(3)(4)Lesson LearningOutcomes (LLO)(2)Pengantar KuliahTidak ada penilaianIntroductionNo assessmentMampumenjelaskan:Menyelesaikan persoalan yang melibatkan sifat-sifatfungsi logaritma dan eksponensial danmenggambarkan grafiknyaSifat-sifat fungsi dangrafik yangmelibatkanlogaritma, daneksponensialAble to explain:The property offunctions and graphsinvolving logarithms,and exponentialsSolving problems related to logarithm and exponentialsproperties and drawing its graph5
2-3Mampu menentukanturunan:fg inverstrigonometri, FungsiHiperbolik & inversfs hiperbolikMengerjakan tugas untuk menentukan turunan darifungssi trigonometri dan fungsi hiperbolik10Doing assignment to determine the derivative oftrigonometric and hyperbolic functionAble to determinethe derivative:fg inversetrigonometric,Hyperbolic Functions& fs inversehyperbolic56EVALUASI 1Kuis Bab 11st EVALUATIONQuiz Chapter 1MampumenyelesaikanIntegral parsial danintegral fungsitrigonometriMelakukan perhitungan matematis denganmenerapkan Teknik integrasi yang telah dipelajari55Doing mathematical calculation using integrationtechniqueAble to solve partialintegrals andintegral l fungsirasional.MampupengaplikasikanTeknik teknikintegral yang lainAble to solve integralof rational functions.Able to apply otherintegral techniquesMengerjakan soal integral fungsi rasionalSolving problems related to integral of rational functions5
9Mampumenyelesaikan Limitbentuk tak tentu,Menghitung limit bentuk tak tentu dan integral takwajar10Calculate indefinite form of limit and improper integralMampu menghitungIntegral tak wajarAble to solveindefinite form Limit,101113Able to calaculateimproper IntegralEVALUASI 2Kuis Bab 2 dan Bab 3EVALUATION 2Quiz Chapter 2 and 3Mampu menghitungLuas bidang datarMengerjakan soal terkait perhitungan luas bidang datardengan menerapkan Teknik integrasiAble to calculateplane areaSolving problems related to area of a plane usingintegration techniqueMampu menghitungvolume benda putardengan metodeCakramMenggunakan Teknik integrasi untuk menghitungvolume benda putar55Using integration technique to calculate volume ofrotary objectMampu menghitungvolume benda putardengan metodeCincin SilinderAble to calculate thevolume of rotatingobjects using thedisc method14Able to calculate thevolume of rotaryobjects using theCylinder RingmethodMampu menghitungPanjang kurva danluas permukaanbenda putarMenggunakan Teknik integrasi untuk menghitungPanjang kurva dan luas permukaan benda putarUsing integration technique to calculate curve lengthand surface area of rotating objectAble to calculatecurve length andsurface area ofrotating objects15-16EVALUASI KE 3Evaluasi Tengah Semester5
EVALUATION 317-18Mid-Term ExamMampu menentukan Aplikasi dalil Guldin untuk menentukan pusat massaPusat massa danApplication of Guldin theorem to determine center ofmenerapkan dalilmassGuldin10Able to determinethe center of massand applyingGuldin's theorem19Mampumenggambar Grafikdalam koordinatkutubMenggambarkan grafik dalam koordinat kutub5Drawing a graph in polar coordinateAble to draw a graphin polar coordinate20ASISTENSI KE 4ASSISTANCE 421Mampu MenghitungLuas dalam sistemkoordinat Kutub22Able to calculatearea in polarcoordinate systemMampu:- Menjelaskan fsparametrik,turunannya dan luasluasnya.- Menghitungpanjang busur dalamkoordinat kutubAble to:-Explain fsparametric, itsderivation and area- Calculate arclength in polarcoordinate23ASISTENSI KE-5Memberikan tugas untuk menghitung luas dalamsistem koordinat kutub7,5Giving assignment to calculate area in polar coordinatesystemMengerjakan Latihan untuk mengukur Panjang busurdalam koordinat kutubDoing exercises to calculate arc length in polarcoordinate7,5
ASSISTANCE 524EVALUASI KE-4Kuis 3EVALUATION 4Bahan Dalil Guldin dan Bab 5Quiz 3Material Guldin theorem and Chapter 525Mampu menjelaskanbarisan,kekonvergenanderet tak hinggadengan Ujikonvergenan Deret.Mengerjakan tugas berkaitan dengan barisan dan deret10Doing assignment related to sequence and seriesAble to explainsequence, infiniteseries convergencesusing the test ofseries convergency26Mampumentransformasikanfungsi ke dalambentuk deret Tayloratau deretMacLaurintMengerjakan Latihan soal untuk mentransformasikanfungsi kedalam bentuk deret Taylor5Doing exercises to transform a function into Taylorseries formAble to transform afunction into Taylorseries or Maclaurintseries form27Diferensiasi danintegrasi deretpangkatMengerjakan soal terkait integrasi deret pangkatSolving problem related to integration of power seriesDifferentiation andintegration of powerseries28ASISTENSI KE 6ASS
MODULE HANDBOOK MATHEMATICS 2. 1. Transcendent function, differential and integral. 2. Integral and improper integral. 3. Application of certain integral in a plane, volume of object, arc length and surface area, center of mass, application of Guldin theorem. 4. Polar coordinate systems and parametric equations, graphical
Teacher’s Book B LEVEL - English in school 6 Contents Prologue 8 Test paper answers 10 Practice Test 1 11 Module 1 11 Module 2 12 Module 3 15 Practice Test 2 16 Module 1 16 Module 2 17 Module 3 20 Practice Test 3 21 Module 1 21 Module 2 22 Module 3 25 Practice Test 4 26 Module 1 26 Module 2 27 Module 3 30 Practice Test 5 31 Module 1 31 Module .
WinDbg Commands . 0:000 k . Module!FunctionD Module!FunctionC 130 Module!FunctionB 220 Module!FunctionA 110 . User Stack for TID 102. Module!FunctionA Module!FunctionB Module!FunctionC Saves return address Module!FunctionA 110 Saves return address Module!FunctionB 220 Module!FunctionD Saves return address Module!FunctionC 130 Resumes from address
XBEE PRO S2C Wire XBEE Base Board (AADD) XBEE PRO S2C U.FL XBEE Pro S1 Wire RF & TRANSRECEIVER MODULE XBEE MODULE 2. SIM800A/800 Module SIM800C Module SIM868 Module SIM808 Module SIM7600EI MODULE SIM7600CE-L Module SIM7600I Module SIM800L With ESP32 Wrover B M590 MODULE GSM Card SIM800A LM2576
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
Approaches to Language Teaching: Foundations Module 1: Contextualizing Language Module 2: Building Language Awareness Module 3: Integrating Skills Module 4: Pairwork / Groupwork Module 5: Learner Feedback Approaches to Language Teaching: Extension Module 6: Managing Large Classes Module 7: Learning Strategies Module 8: Authentic Materials Module
Marxism is a highly complex subject, and that sector of it known as Marxist literary criticism is no less so. It would therefore be impossible in this short study to do more than broach a few basic issues and raise some fundamental questions. (The book is as short as it is, incidentally, because it was originally designed for a series of brief introductory studies.) The danger with books of .
