Numerical Analysis

(3 Credit Hours) · Undergraduate

Polynomial interpolation and its applications in numerical integration, numerical differentiation, splines, and finite element methods for ODEs. Implementation of methods. (Language of instruction: English) Learning Outcomes Construct Lagrange and Hermite interpolating polynomials to a function/set of points Bound the error in polynomial interpolation Derive Cauchy's theorem Construct piecewise linear and cubic splines Derive formulas for Newton-Cotes quadrature in low degrees Derive formulas for Gaussian quadrature in low degrees Bound the error in Newton-Cotes and Gaussian quadrature Use the FEM to approximately solve ODEs Derive the system of equations of the FEM solution with piecewise linear basis functions Implementation of methods in MATLAB and/or Octave