TE4485 Engineering Mathematics II

Deskripsi Mata Kuliah / Course Description

Mata kuliah ini membahas metode analitis dan numerik untuk menyelesaikan Persamaan Diferensial Biasa (PDB) dan Persamaan Diferensial Parsial (PDP). Materi mencakup teknik penyelesaian PDB dengan pendekatan numerik yaitu, metode Euler, Heun, dan Runge-Kutta serta penerapan metode beda hingga untuk PDP. Fokus utamanya adalah penerapan analitik dan numerik dalam pemodelan fenomena fisis dan sistem melalui studi kasus yang relevan dengan Teknik Elektro.

This course discusses analytical and numerical methods for solving Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE). The material includes techniques for solving ODE using a numerical approach, namely, the Euler, Heun, and Runge-Kutta methods, and applying finite difference methods for PDE. The main focus is analytical and numerical applications in modeling physical phenomena and systems through case studies relevant to Electrical Engineering.

Materi Pembelajaran / Learning Materials

  • Pengantar persamaan diferensial (PD) (slide)
    Introduction to differential equation (DE)
  • PDB tingkat 1 (slide 1) (slide 2) (slide 3)
    1st order ODE
    • Aplikasi PDB tingkat 1 dan visualisasi dengan MATLAB (slide)
  • PDB linier tingkat 2 homogen (slide)
    Homogeneous 2nd order linear ODE
  • PDB linier tingkat 2 tak-homogen (slide)
    Non-homogeneous 2nd order linear ODE
  • Transformasi Laplace untuk solusi PDB (slide)
    Laplace transform for solving ODE
  • Aplikasi PDB
    Applications of ODE
  • Sistem PDB
    Systems of ODE
  • Metode numerik untuk solusi PDB
    Numerical methods for solving ODE
  • PDP and aplikasinya
    PDE and its applications
  • Metode numerik untuk solusi PDP
    Numerical methods for solving PDE

Evaluasi / Evaluation : Quiz 1, Ujian Tengah Semester (UTS), Quiz 2, Ujian Akhir Semester (UAS)

Referensi / References

Utama / Primaries :

  1. Boyce, W. E. and DiPrima, R. C., (2012), Elementary Differential Equations and Boundary Value Problems, 10th ed., Wiley.
  2. Evans, L. C., (2010), Partial Differential Equations, 2nd ed., American Mathematical Society.
  3. Strikwerda, J. C., (2004), Finite Difference Schemes and Partial Differential Equations, SIAM.
  4. Lambert, J. D., (1991), Numerical Methods for Ordinary Differential Systems, Wiley.

Pendukung / Supplementaries :

  1. Nagy, G., (2021), Ordinary Differential Equations, Mathematics Department, Michigan State University.
  2. Burden, R.C., Faires J.D., and Reynolds, A.C., (2010), Numerical Analysis, 9th ed., Brooks/Cole Cengage Learning, Boston.
  3. Chapra, S.C., and Canale, R.P., (2015), Numerical Methods for Engineers, 7th ed., McGraw-Hill Education.

Rencana Pembelajaran Semester (RPS) dapat diunduh melalui link berikut : RPS