Numerical Analysis 2 | MA | Course

Brief Information
  • Name : Numerical Analysis 2
  • Lecturer : 이진우
  • Semester : 2015 Spring
  • Course : BS, Mathematics
  • Textbook
    • Sauer, T. (2011) Numerical Analysis. 2nd Ed. Pearson
  • Syllabus : Syllabus_2015-4-1__Numerical Analysis 2
  • In short
    • Numerical Analysis with implementation using MATLAB
    • Numerical Differentiation and Integration, Ordinary Differential Equations, Boundary Value Problems, Partial Differential Equations, Random Numbers and Applications
Trace lectures
  • Numerical Differentiation Methods (ND)
    • two-point forward-difference formula (ND 1)
    • three-point centered-difference formula (ND 2)
    • three-point centered-difference formula for second derivative
    • rounding error
    • extrapolation
  • Numerical Integration Methods (NI)
    • Newton-Cotes formulas for numerical integration
    • trapezoid rule
    • Simpson’s rule
    • degree of precision
    • composite trapezoid rule (NI 1)
    • composite Simpson’s rule (NI 2)
    • midpoint rule
    • composite midpoint rule (NI 3)
    • adaptive quadrature (NI 4)
    • Gaussian quadrature (NI 5)
  • ODE Solvers (ODE)
    • Euler’s method (ODE 1)
    • Lipschitz continuity
    • local truncation error
    • global truncation error
    • the explicit trapezoid method (ODE 2)
    • Conversion from the nth-order differential equation into a system of first-order equations
    • midterm exam         
    • midpoint method
    • Runge-Kutta Method of order four (RK4)
  • BVP Solvers (BVP)
    • shooting method
  • PDE Solvers (PDE)
    • stability of methods
Assignments
Summarize themes
  • A
  • B
  • C

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