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## TANA09 Course Information

In Computational mathematics we develop and analyze numerical methods for solving commonly occuring mathematical problems, mainly originating from applications. Important aspects of the methods are robustness, accuracy and efficiency. Since the methods are intended to be implemented on computers it is important to understand how a computer process numerical information. After completing the course the student should be able to
• explain basic concepts from computational mathematics, how a computer stores numbers, and the accuracy with which arithmetic operations are carried out.
• use a selection of numerical methods for solving mathematical problems from applications using a calculator or computer.
• discuss potential error sources in numerical calculations and estimate the accuracy in a computed result.
• use standard software for solvign practical problems from applications.

## TANA09 Organisation

The course consists of lectures, lessons and computer laborations. During the lectures the theory is presented. The numerical methods are introduced and analyzed. During the lessons both theoretical and practical problems are solved using a pocket calculator. During the computer laborations mathematical software is used to solve larger problems from applications.

## TANA09 Course contents

• Error analysis and floting point numbers. The IEEE floating points standard and the machine precision. Error propagation. Catastrophic cancellation.
• Linear systems of equations. LU-decomposition. Pivoting. Triangular systems. The condition number. Artihmetic complexity.
• Interpolation and Approximation. Error estimates. Polynomials. Splines. Overdetermined systems. The least squares method.
• Non-linear equations. The Newton-Raphson method. Fixed point iteration. Order of convergence. Error estimates.

Sidansvarig: Fredrik Berntsson