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The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described. The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described. |
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The aims of this unit are:
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A1 |
Deep understanding of analytical systems which are defined to predict and solve (and are also used to support) different mathematical problems in managerial contexts. |
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A2 |
Understanding of different types of numerical methods and comprehension of how they can be applied in operations management. |
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Detailed analysis of how numerical methods can, procedurally and methodologically, be applied for solving various problems in operations management. |
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Learning about computer-based frameworks and software that can be utilised for problem-solving in operations management. |
On satisfactory completion of the unit you will be able to:
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LO1 |
Identify, describe, and specify analytical systems to predict and solve different mathematical problems related to management. |
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LO2 |
Identify, describe, specify, and characterise numerical methods that are applicable in operations management. |
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LO3 |
Describe, specify, and analyse how numerical methods are applied for solving various problems in operations management. |
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LO4 |
Critically specify what computer-based frameworks can be utilised for real problems in operations management. |
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- Basic concepts of floating-point arithmetic. Conditioning of a problem. Numerical stability of an algorithm.
- Linear systems: direct methods (Gaussian eliminitations, LU-decomposition, Choleski) and iterative methods (Jacobi, Gauss-Seidel, SOR).
- Approximation of functions and data: polynomial and piecewise polynomial interpolation, splines, discrete least squares.
- Non-linear equations and systems: Newton's method and its discrete variants, fixed-point iteration.
- Numerical integration: Newton-Cotes formulas, Gaussian quadrature rules, composite rules.
- Initial value problems for ordinary differential equations: one-step methods (Runge-Kutta methods) and multistep (Adams) methods. Stiff problems.
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Essentials:
- Novek, K. (2022): Numerical Methods for Scientific Computing: The Definitive Manual for Math Geeks, Equal Share Press
Recommended:
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Barrett, Richard, Michael Berry, et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM: Society for Industrial and Applied Mathematics, 1987. ISBN: 9780898713282.
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Trefethen, Lloyd N. and David Bau III. Numerical Linear Algebra. SIAM: Society for Industrial and Applied Mathematics, 1997. ISBN: 9780898713619.
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Bai, Zhaojun, James Demmel, et al. Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide. SIAM: Society for Industrial and Applied Mathematics, 1987. ISBN: 9780898714715.
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Steven C. Chapra & Raymond P. Canale. Numerical Methods for Engineering
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J. Hoffman. Numerical Methods for Scientist and Engineering
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William Dorn & Daniel McCracken. Numerical Methods with Fortran IV Case Studies |
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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Giovanni Monegato
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