Numerical analysis - 3FMA1009

Goal(s)

Course learning outcomes

After completing the course the student is able to:
1)Present main ideas and features of basic numerical methods of
•solving linear and nonlinear equations,
•numerical differentiation and integration,
•approximation and interpolation,
•solving ordinary differential equations,
•numerical methods of linear algebra.
2)Weigh-up numerical calculations errors and influence of numerical method parameters on resulting errors.
3)Choose an adequate method for a given numerical problem.
4)Solve numerical problems unaided using Matlab environment.
5)Select and operate appropriate computer software.
6)Work effectively in a team, organizing the work properly according to the given time and the specific problem.

Content(s)

LECTURE:

• Floating point arithmetic, errors in numerical analysis. Round-off and truncation error. Error propagation. Conditioning of the numerical problem. Numerical stability and complexity.
• Systems of linear equations. LU factorization with applications.
• Interpolation and approximation. Several methods to construct interpolating polynomial, residual of interpolation, Runge phenomenon, piece-wise and spline interpolation. Linear mean-square approximation. Benefits of orthogonal basis functions. Uniform approximation.
• Richardson extrapolation, numerical differentiation and integration.
• Nonlinear eq. and systems of nonlinear eq. Roots of polynomials.
• Eigenvalues and eigenvectors. Singular values. Principal component analysis.
• Ordinary differential equations. Stability and convergence. Implicit and explicit methods. Single- and multi-step methods. Step control. - Selection of a proper method and parameters for a particular problem.

LABORATORY:
Numerical methods algorithmizing and programming in Matlab. Testing of Matlab procedures of scientific computing. Documentation of scientific computing.

Mathematics Course I.
In particular, matrix calculation is an essential basis. Ensure that the math I elements are mastered.
Polynomials are very important
To a lesser extent, Taylor, complex and rational fractions

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