Content (Syllabus outline)
1. Numerical computing. Representable numbers. Approximations, Error, Accuracy, Stability, Sensitivity.
2. Nonlinear equations solving: Bisection, Fixed point iteration, Newton's method, Secant method. Nonlinear sets of equations.
3. Solution of linear algebraic equations: Gaussian elimination. LU decomposition and its applications. Cholesky decomposition. Pivotting. Tridiagonal and diagonal dominant systems of equations.
4. Eigenvalues computation: Power method and its variants.
5. Approximations: Polynomial interpolation and extrapolation. Coefficients of the interpolating polynomial. Hermit interpolation. The method of least squares.
6. Numerical integration: Newton-Cotes quadratures. Method of undetermined coefficients.
Intended learning outcomes - knowledge and understanding
• Knowledge, understanding and application of the principles of symbolic calculation.
• Understand and be able to use, analyze and evaluate basic numerical methods and their useful value.
• To recognize practical problems and their modeling with numerical mathematics tools.
Intended learning outcomes - transferable/key skills and other attributes
• Critical Thinking Skills (problem solving): solving more demanding numerical tasks and practical problems.
• Communication skills: preparation of a written professional report, manner of expression at exams.
Readings
Z. Bohte, Numerično reševanje nelinearnih enačb, DMFA Slovenije, Ljubljana, 1993.
Z. Bohte, Numerično reševanje sistemov linearnih enačb, DMFA Slovenije, Ljubljana, 1994.
D. Kincaid, W. Cheney: Numerical Analysis, Brooks/Cole, Pacific Grove, 1996.
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling: Numerical Recipes in C, Cambridge University Press, New York, 2002.
E. Zakrajšek, Uvod v numerične metode, druga izdaja, DMFA Slovenije, Ljubljana, 2000.
J. Grasselli, A. Vadnal, Linearna algebra. Linearno programiranje, DMFA Slovenije, Ljubljana
S. Wolfram: The Mathematica Book, Wolfram Media, Inc. and Cambridge University Press 1996
