KONTRAK PERKULIAHAN

Mata Kuliah

ANALISIS REAL II(REAL ANALYSIS II)

oleh

Dr. Bornok Sinaga, M.PdMangaratua Simanjorang, M.Pd.

PRODI PENDIDIKAN MATEMATIKAFMIPA – UNIMED

2 0 1 0KONTRAK PERKULIAHAN

A. IDENTITAS MATA KULIAH

1. Nama Mata Kuliah : Analisis Real II (Real Analysis)

2. Kode Mata Kuliah :

3. Jumlah SKS : 3 SKS

B. DESKRIPSI MATA KULIAH

Mata kuliah ini membahas tentang Limit dan Kekontinuan serta Diferensiasi. Sebagai

lanjutan dari kuliah Analisis Real I, kuliah ini memberi kesempatan mahasiswa untuk

berlatih bernalar dan membuktikan pernyataan matematika secara formal.

C. KOMPETENSI DASAR

Setelah mengikuti perkuliahan ini mahasiswa diharapkan dapat meningkatkan

wawasannya untuk mampu berpikir secara deduktif dalam memahami konsep-konsep

dasar matematika.

D. INDIKATOR

Setelah selesai mengikuti program pembelajaran pada mata kuliah ini, mahasiswa

mampu:

1. Menguasai berbagai konsep terkait dengan Limit dan Kekontinuan serta

Diferensiasi.

2. Membuktikan berbagai teorema terkait dengan Limit dan Kekontinuan

serta Diferensiasi.

3. Mengaplikasikan Aksioma, Definisi dan Teorema dalam pemecahan

masalah, yang berhubungan dengan Limit dan Kekontinuan serta Diferensiasi.

4. Melakukan critical book report terkait Aksioma, Definisi dan Teorema

dalam Analisis Real, khususnya tentang Limit dan Kekontinuan serta Diferensiasi.

5. Melakukan mini research dalam pemecahan masalah dalam bidang

Analisis Real, yang terkait dengan Limit dan Kekontinuan serta Diferensiasi.

E. MATERI KULIAH

Pertemuan 1 A Glimpse at Real Analysis IIPertemuan 2 Limit of FunctionPertemuan 3 Limit TheoremsPertemuan 4 Some Extensions of Limit ConceptsPertemuan 5 Continuous FunctionsPertemuan 6 Combinations of Continuous FunctionsPertemuan 7 Continuous Functions on IntervalsPertemuan 8 Uniform Continuity and ApproximationPertemuan 9 TestPertemuan 10 Monotone and Inverse FunctionsPertemuan 11 Compact SetsPertemuan 12 The DerivativePertemuan 13 The Mean Value TheoremPertemuan 14 L’Hospital’s RulePertemuan 15 Taylor’s TheoremPertemuan 16 Test

F. STRATEGI/METODE PEMBELAJARAN

Strategi pembelajaran yang diterapkan dalam perkuliahan ini adalah melibatkan

partisipasi aktif mahasiswa melalui pemberian tugas terstruktur, yaitu: mengerjakan

soal latihan dari buku referensi yang diberikan dosen, mendownload berbagai

informasi tentang Analisis Real.

Metode pembelajaran yang diterapkan dalam perkuliahan ini adalah metode

ekspositori, diskusi, tanya jawab, penugasan dan presentasi.

G. TAGIHAN

1. Laporan dan Presentasi hasil kerja kelompok mengenai materi Analisis

Real

2. Makalah tentang topik Analisis Real baru atau yang tidak dibahas dalam

pertemuan (hasil pencarian di buku lain atau internet)

3. Hasil ujian midsemester

4. Hasil ujian semester

H. PENILAIAN

Penilaian akhir diperoleh dari hasil rata-rata NF1, NF2, NF3 dan NF4.

Definisi:

NF1 adalah penilaian laporan dan presentasi tentang topik Analisis Real

NF2 adalah penilaian makalah topik Analisis Real baru

NF3 adalah penilaian mid semester

NF4 adalah penilaian akhir semester

Skor Akhir (SA) = 4

NF4 NF3 NF2 1 +++NF

Nilai Mahasiswa

Nilai A, Jika 90 ≤ SA ≤ 100

Nilai B, Jika 80 ≤ SA ≤ 89

Nilai C, Jika 70 ≤ SA ≤ 79

Nilai D, Jika 60 ≤ SA ≤ 69

Nilai E, Jika 0 ≤ SA ≤ 59

I. REFERENSI/SUMBER BACAAN

1. Bartle, Robert G., Donald R., Sherbert., 1982, Introduction to real analysis – 1st ed., New York: John Wiley & Sons, Inc.

2. ________________, 2000, Introduction to real analysis - 3rd ed., New York: John Wiley & Sons, Inc.

3. Ghorpade, Sudhir R., Balmohan V. Limaye, 2006, A Course in Calculus and Real Analysis, New York: Springer.

4. Bressoud, David M., 2006, A Radical Approach to Real Analysis, 2nd edition, Washington DC: The Mathematical Association of America.

SYLLABI (LECTURE CONTRACT)

Subject Matter

REAL ANALYSIS II

By

Dr. Bornok Sinaga, M.PdMangaratua Simanjorang, M.Pd.

MATHEMATICS EDUCATION DEPARTMENTFACULTY OF MATHEMATIC AND NATURALE

SCIENCE STATE UNIVERSITY OF MEDAN

2 0 1 0

SYLLABI (LECTURE CONTRACT)

A. SUBJECT MATTER IDENTITY

1. Subject Matter : Real Analysis

2. Subject Matter Code :

3. SKS : 3 SKS

B. SUBJECT MATTER DESCRIPTION

This subject matter concerns on Limit and Continuity, and Differentiation. As an

advanced from Real Analysis I, this lesson give an opportunity for the students to

develop their reasoning and ability in proofing mathematical statement formally.

C. BASIC COMPETENCE

After finish this subject matter, students be able to improve their concept so they can

think deductively in understanding basic concepts in mathematic.

D. INDICATOR

After completing this course, students will be able to:

1. Mastering concepts about Limit and Continuity, and

Differentiation

2. Proving theorems about Limit and Continuity, and

Differentiation.

3. Applying axioms, definitions and theorems in Real Analysis,

especially about Limit and Continuity, and Differentiation

4. Making a critical book report about axioms, definitions and

theorems in Real Analysis, especially about Limit and Continuity, and

Differentiation

5. Make mini research about solving problems in Real Analysis,

connected with Limit and Continuity, and Differentiation.

E. MATERI KULIAH

Lesson 1 A Glimpse at Real Analysis II

Lesson 2 Limit of FunctionLesson 3 Limit TheoremsLesson 4 Some Extensions of Limit ConceptsLesson 5 Continuous FunctionsLesson 6 Combinations of Continuous FunctionsLesson 7 Continuous Functions on IntervalsLesson 8 Uniform Continuity and ApproximationLesson 9 TestLesson 10 Monotone and Inverse FunctionsLesson 11 Compact SetsLesson 12 The DerivativeLesson 13 The Mean Value TheoremLesson 14 L’Hospital’s RuleLesson 15 Taylor’s TheoremLesson 16 Test

F. INSTRUCTIONAL STRATEGY/METHOD

Instructional Strategies that are used in this subject matter involve student’s active

participation by giving task, i.e: solving some problem on reference that are gived,

downloading various information about Limit and Continuity, and Differentiation.

Instructional Methods that are applied in this lesson are expository, discussion,

dialogue, task and presentation. .

G. CLAIM

1. Report and presentation about topics in Limit and Continuity, and

Differentiation

2. Paper about new or undiscussed topic of Limit and Continuity, and

Differentiation

3. First Paper Test (Midsemester)

4. Second Paper Test (Semester)

H. ASSESMENT

Final score is determined by calculate the average of NF1, NF2, NF3 and NF4.

Definition:

NF1 is score of a Report and presentation about topics in Limit and Continuity, and

Differentiation

NF2 is score of paper about new topic of Limit and Continuity, and Differentiation

NF3 is score of mid semester test

NF2 is score of semester test

Final Score (FS) = 4

NF4 NF3 NF2 1 +++NF

Students Grade

A, Jika 90 ≤ FS ≤ 100

B, Jika 80 ≤ FS ≤ 89

C, Jika 70 ≤ FS ≤ 79

D, Jika 60 ≤ FS ≤ 69

E, Jika 0 ≤ FS ≤ 59

I. REFERENCE

1. Bartle, Robert G., Donald R., Sherbert., 1982, Introduction to real analysis – 1st ed., New York: John Wiley & Sons, Inc.

2. ________________, 2000, Introduction to real analysis - 3rd ed., New York: John Wiley & Sons, Inc.

3. Ghorpade, Sudhir R., Balmohan V. Limaye, 2006, A Course in Calculus and Real Analysis, New York: Springer.

4. Bressoud, David M., 2006, A Radical Approach to Real Analysis, 2nd edition, Washington DC: The Mathematical Association of America.