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Numerical Analysis II
University of Galway - Direct Enroll Program
Galway, Ireland
Dates: 1/7/25 - 5/11/25
Numerical Analysis II
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Instruction in: English
Course Code: MA378
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
Polynomial interpolation and its applications in numerical integration, numerical differentiation, splines, and finite element methods for ODEs.
Learning Outcomes
1. Construct Lagrange and Hermite interpolating polynomials to a function/set of points
2. Bound the error in polynomial interpolation
3. Derive Cauchy's theorem
4. Construct piecewise linear and cubic splines
5. Derive formulas for Newton-Cotes quadrature in low degrees
6. Derive formulas for Gaussian quadrature in low degrees
7. Bound the error in Newton-Cotes and Gaussian quadrature
8. Use the FEM to approximately solve ODEs
9. Derive the system of equations of the FEM solution with piecewise linear basis functions
Learning Outcomes
1. Construct Lagrange and Hermite interpolating polynomials to a function/set of points
2. Bound the error in polynomial interpolation
3. Derive Cauchy's theorem
4. Construct piecewise linear and cubic splines
5. Derive formulas for Newton-Cotes quadrature in low degrees
6. Derive formulas for Gaussian quadrature in low degrees
7. Bound the error in Newton-Cotes and Gaussian quadrature
8. Use the FEM to approximately solve ODEs
9. Derive the system of equations of the FEM solution with piecewise linear basis functions