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Numerical Analysis II University of Galway - Engineering & Computer Science Program Spring 2023 Semester - Galway

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Numerical Analysis II

Numerical Analysis II Course Overview

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

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