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CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Biomedical Engineering
Instruction in: English
Course Code: 15543
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Calculus I, Calculus II, Linear Algebra, Differential Equations, Computer Programming
DESCRIPTION
PROGRAMME
1- PRINCIPLES OF NUMERICAL MATHEMATICS. Well-Posedness and Condition Number of a Problem Stability of Numerical Methods. The Floating-Point Number System.
2- ROOTFINDING OF NONLINEAR EQUATIONS. Conditioning of a Nonlinear Equation. The Newton-Raphson Method. Newton's Methods for Simultaneous Nonlinear Equations.
3- UNCONSTRAINED OPTIMIZATION. Necessary and Sufficient conditions for Optimality. Convexity. Optimization Methods.
4- FINITE DIFFERENCE METHODS: INTERPOLATION, DIFFERENTIATION AND INTEGRATION. Backward, Forward, and Central Differences. Interpolation and Extrapolation methods.
5- NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS (ODEs). ODEs and Lipschitz Condition. One Step Numerical Methods. Zero-Stability, Convergence Analysis and Absolute Stability. Consistency. Numerical methods for ODEs. Systems of ODEs. Stiff Problems.
6- APROXIMATION THEORY. Fourier Transform.
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