| Kode Mata Kuliah | MA5031 / 4 SKS |
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| Penyelenggara | 201 - Mathematics / FMIPA |
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| Kategori | Lecture |
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| Bahasa Indonesia | English |
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| Nama Mata Kuliah | Analisis Real Lanjut | Advanced Real Analysis |
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| Bahan Kajian | - Konstruksi Sistem Bilangan Real
- Topologi pada Bilangan Real
- Fungsi Kontinu
- Kalkulus Diferensial dan Integral
- Barisan Fungsi
- Ruang Metrik
- Kalkulus pada Ruang Euklides
- Persamaan Diferensial Biasa
- Deret Fourier
- Teorema Fungsi Implisit
- Integral Lebesgue
| - Construction of Real Number Systems
- Topology of the Real Numbers
- Continuous Functions
- Differential and Integral Calculus
- Sequence of Functions
- Metric Space
- Calculus on Euclidean Spaces
- Ordinary Differential Equations
- Fourier Series
- Implicit Function Theorem
- Lebesgue Integral
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| Capaian Pembelajaran Mata Kuliah (CPMK) | - Memiliki pengetahuan yang memadai mengenai konsep-konsep matematika dalam analisis real
- Menunjukkan kemampuan menyelesaikan masalah dalam analisis real
- Menggunakan notasi formal secara tepat dan juga dalam kaitannya dengan pernyataan matematika dalam bahasa Indonesia
- Membangun argumen untuk membuktikan pernyataan matematika dan memformulasikan secara akurat konsep dalam bentuk pernyataan matematika
| - Have adequate knowledge of mathematical concepts in real analysis
- Demonstrate the ability to solve problems in real analysis
- Use formal notation appropriately and also in relation to mathematical statements in Indonesian
- Build arguments to prove mathematical statements and accurately formulate concepts in the form of mathematical statements
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| Metode Pembelajaran | Kombinasi ceramah dan diskusi | Combination of lecture and discussion |
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| Modalitas Pembelajaran | Luring, Bauran | Offline, Blended |
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| Jenis Nilai | ABCDE |
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| Metode Penilaian | Kuis, Tugas, Ujian | Quiz, Assignments, Exams |
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| Catatan Tambahan | Referensi:
[1] J. E. Marsden and M.J. Hoffman, Elementary Classical Analysis 2nd Edition, MacMillan, 1993.
[2] R. S. Strichartz, The way of analysis, Revised Edition, Jones & Bartlett, Boston, 2000.
[3] W. Rudin, Principle of Mathematical Analysis, International Series in Pure and Applied Mathematics. McGraw-Hill, 1976.
[4] A. W. Knapp, Basic Real Analysis, Birkhauser, Cambridge, 2005.
[5] T. Tao, Analysis II, 4th Edition, Hindustan Book Agency and Springer, 2022. | |
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