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Further topics in Numerical Methods
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 18276
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Linear Algebra (Course 1 - Semester 1); Differential Calculus (Course 1 - Semester 1); Programming (Course 1 - Semester 1); Integral Calculus (Course 1 - Semester 2); Programming Techniques (Course 1 - Semester 2); Numerical Methods (Course 2 - Semester 1); Ordinary Differential Equations (Course 3 - Semester 1).
DESCRIPTION
1. Approximation
1.1 Uniform approximation
1.2 Approximation in the 2-norm
1.3 Orthogonal polynomials
1.4 Gaussian quadrature
1.5 Trigonometric interpolation and approximation
1.6 The Fast Fourier Transform (FFT)
2. Computation of eigenvalues and eigenvectors
2.1 The power method
2.2 Householder transformation; reduction to tridiagonal forms
2.3 The QR method
2.4 Singular Value Decomposition
3. Ordinary differential equations
3.1 Introduction: existence and uniqueness
3.2 One-step methods
3.3 Runge-kutta methods
3.4 Multistep methods
3.5 System of equations
3.6 Stiff problems
1.1 Uniform approximation
1.2 Approximation in the 2-norm
1.3 Orthogonal polynomials
1.4 Gaussian quadrature
1.5 Trigonometric interpolation and approximation
1.6 The Fast Fourier Transform (FFT)
2. Computation of eigenvalues and eigenvectors
2.1 The power method
2.2 Householder transformation; reduction to tridiagonal forms
2.3 The QR method
2.4 Singular Value Decomposition
3. Ordinary differential equations
3.1 Introduction: existence and uniqueness
3.2 One-step methods
3.3 Runge-kutta methods
3.4 Multistep methods
3.5 System of equations
3.6 Stiff problems
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