Claim up to $1,000 in flight credits!
Get up to $1,000 in flight credits or grants toward study or internship programs abroad when you apply by September 12, 2024. See our Official Rules for full details.
Numerical Methods in Biomedicine
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/18/24 - 6/5/24
Numerical Methods in Biomedicine
OVERVIEW
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.
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.