Kurikulum 2024

Kode Mata KuliahMA5031 / 4 SKS
Penyelenggara201 - Matematika / FMIPA
KategoriKuliah
Bahasa IndonesiaEnglish
Nama Mata KuliahAnalisis Real LanjutAdvanced Real Analysis
Bahan Kajian
  1. Konstruksi Sistem Bilangan Real
  2. Topologi pada Bilangan Real
  3. Fungsi Kontinu
  4. Kalkulus Diferensial dan Integral
  5. Barisan Fungsi
  6. Ruang Metrik
  7. Kalkulus pada Ruang Euklides
  8. Persamaan Diferensial Biasa
  9. Deret Fourier
  10. Teorema Fungsi Implisit
  11. Integral Lebesgue
  1. Construction of Real Number Systems
  2. Topology of the Real Numbers
  3. Continuous Functions
  4. Differential and Integral Calculus
  5. Sequence of Functions
  6. Metric Space
  7. Calculus on Euclidean Spaces
  8. Ordinary Differential Equations
  9. Fourier Series
  10. Implicit Function Theorem
  11. Lebesgue Integral
Capaian Pembelajaran Mata Kuliah (CPMK)
  1. Memiliki pengetahuan yang memadai mengenai konsep-konsep matematika dalam analisis real
  2. Menunjukkan kemampuan menyelesaikan masalah dalam analisis real
  3. Menggunakan notasi formal secara tepat dan juga dalam kaitannya dengan pernyataan matematika dalam bahasa Indonesia
  4. Membangun argumen untuk membuktikan pernyataan matematika dan memformulasikan secara akurat konsep dalam bentuk pernyataan matematika
  1. Have adequate knowledge of mathematical concepts in real analysis
  2. Demonstrate the ability to solve problems in real analysis
  3. Use formal notation appropriately and also in relation to mathematical statements in Indonesian
  4. Build arguments to prove mathematical statements and accurately formulate concepts in the form of mathematical statements
Metode PembelajaranKombinasi ceramah dan diskusiCombination of lecture and discussion
Modalitas PembelajaranLuring, BauranOffline, Blended
Jenis NilaiABCDE
Metode PenilaianKuis, Tugas, UjianQuiz, Assignments, Exams
Catatan TambahanReferensi: [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.