## General information

Course type | AMUPIE |

Module title | Introduction To Numerical Analysis |

Language | English |

Module lecturer | dr Iwona Gulaczyk |

Lecturer's email | gulai@amu.edu.pl |

Lecturer position | Senior Lecturer |

Faculty | Faculty of Chemistry |

Semester | 2023/2024 (winter) |

Duration | 45 |

ECTS | 5 |

USOS code | 02-INAA |

## Timetable

Duration 45h (30h classes and 15h lecture)

## Module aim (aims)

Module aim (aims)

• to teach students to recognize the type of problems that require numerical techniques for their solution

• to show them some examples of the error propagation that can occur when numerical methods are applied

• to teach the students to approximate the solution to some problems that cannot be solved exactly.

• students are taught to use the numerical analysis methods in MS Excel.

## Pre-requisites in terms of knowledge, skills and social competences (where relevant)

The course is dedicated to students with some knowledge of mathematics and MS Excel.

## Syllabus

Week 1: Round-off errors: absolute error, relative error, significant digits.

Week 2: Solutions of nonlinear equations in one variable: the bisection algorithm.

Week 3: The Newton-Raphson method, the secant method. Fixed point iteration.

Week 4: Interpolation and polynomial approximation: Taylor polynomials and Lagrange polynomial.

Week 5: Divided differences method.

Week 6: Numerical differentiation: forward and backward-difference formula.

Week 7: Three-point formula of numerical differentiation. The Richardson’s extrapolation.

Week 8: Numerical integration: trapezoidal rule and Simpson’s rule.

Week 9: Initial value-problem for differential equations: Euler’s method, the Runge-Kutta methods.

Week 10: Methods for solving linear systems: linear systems of equations, Cramer’s rule, Gaussian elimination.

Week 11: Approximation theory: least-squares approximation.

Week 12: Linear algebra, matrix inversion and the determinant of a matrix.

Week 13: The similarity transformations. Eigenvalues and eigenvectors.

Week 14: Iterative techniques in matrix algebra: Jacobi iterative method.

Week 15: Optimization.

## Reading list

1) Numerical analysis, R. L. Burden, J. D. Faires

2) Fundamental numerical methods and data analysis, G. W. Collins