Kurikulum 2024

Kode Mata KuliahSK5007 / 4 SKS
Penyelenggara209 - Computational Sciences / FMIPA
KategoriLecture
Bahasa IndonesiaEnglish
Nama Mata KuliahAnalisis Numerik LanjutAdvanced Numerical Analysis
Bahan Kajian
  1. Metode langsung untuk menyelesaikan sistem persamaan linear (SPL): eliminasi Gauss, faktorisasi LU, sistem positif definit, faktorisasi LDLt dan Choleski, SPL dengan matriks pita
  2. Metode iteratif untuk menyelesaikan SPL: norm vektor dan matriks, jari-jari spektral matriks, metode iterasi Jacobi, metode iterasi Gauss-Seidel dan Sor; metode conjugate gradient untuk SPL
  3. Metode untuk hampiran nilai eigen: metode power, metode deflasi
  4. Metode untuk menyelesaikan sistem persamaan tak linear: iterasi titik tetap, metode Newton dan quasi-Newton, metode steepest descent
  5. Optimasi numerik satu peubah tanpa kendala: golden section search, metode Newton
  6. Optimasi numerik banyak peubah tanpa kendala: metode Newton, metode quasi-Newton, metode conjugate gradient
  7. Optimasi numerik masalah kuadrat terkecil tak linear: metode Gauss-Newton, metode Levenberg-Marquard
  8. Masalah nilai awal untuk PDB, masalah nilai batas untuk PDB: metode Euler, metode deret Taylor berderajat-n, metode Runge-Kutta
  9. Metode numerik untuk PDP, metode beda hingga untuk PD linear dan tak linear
  10. Metode beda hingga untuk PDP eliptik, parabolik dan hiperbolik
  11. Pengantar metode elemen hingga
  1. Direct methods for solving systems of linear equations (SPL): Gaussian elimination, LU factorization, positive definite systems, LDLt and Choleski factorization, SPL with band matrices
  2. Iterative methods for solving SPL: vector and matrix norms, matrix spectral radius, Jacobi iteration method, Gauss-Seidel and Sor iteration methods; conjugate gradient method for SPL
  3. Methods for approximating eigenvalues: power method, deflation method
  4. Methods for solving systems of nonlinear equations: fixed point iteration, Newton's and quasi-Newton's methods, steepest descent method
  5. Unconstrained one-variable numerical optimization: golden section search, Newton's method
  6. Numerical optimization of many variables without constraints: Newton's method, quasi-Newton method, conjugate gradient method
  7. Numerical optimization of nonlinear least squares problems: Gauss-Newton method, Levenberg-Marquard method
  8. Initial value problem for GDP, boundary value problem for GDP: Euler's method, n-degree Taylor series method, Runge-Kutta method
  9. Numerical methods for PDP, finite difference methods for linear and nonlinear PD
  10. Finite difference methods for elliptic, parabolic and hyperbolic PDPs
  11. Introduction to the finite element method
Capaian Pembelajaran Mata Kuliah (CPMK)
  1. Mahasiswa memiliki wawasan dan pengetahuan mengenai berbagai metode numerik untuk menyelesaikan berbagai permasalahan penting dalam sains
  2. Mahasiswa menguasai dasar-dasar mengenai metode numerik untuk menyelesaikan persamaan linear dan tak linear, optimasi numerik, serta persamaan diferensial biasa dan parsial
  3. Mahasiswa memiliki gambaran mengenai berbagai teknik numerik untuk menyelesaikan persamaan linear dan tak linear, optimasi numerik, serta persamaan diferensial biasa dan parsial
  1. Students have insight and knowledge about various numerical methods to solve various important problems in science
  2. Students master the basics of numerical methods for solving linear and nonlinear equations, numerical optimization, and ordinary and partial differential equations
  3. Students have an overview of various numerical techniques for solving linear and nonlinear equations, numerical optimization, as well as ordinary and partial differential equations
Metode PembelajaranCeramah, diskusi, pembelajaran berbasis riset/masalah/studi kasus, studi literatur, kerja kelompok/mandiri,presentasi, praktekLectures, discussions, research/problem/case study based learning, literature studies, group/independent work, presentations, practice
Modalitas PembelajaranLuring/daring/hybrid, sinkronous dan asinkronousOffline/online/hybrid, synchronous and asynchronous
Jenis NilaiABCDE
Metode PenilaianPenilaian diberikan melalui PR / Tugas / Kuis / Praktikum / RBL / Laporan / Presentasi / UTS / UASAssessment is given through Homework / Assignments / Quizzes / Practicum / RBL / Reports / Presentations / UTS / UAS
Catatan Tambahan