Numerical Methods
Course code
MLM6241.DT
old course code
Course title in Estonian
Arvutusmeetodid
Course title in English
Numerical Methods
ECTS credits
6.0
Assessment form
Examination
lecturer of 2025/2026 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2026/2027 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
Provide an overview of computational errors (absolute and relative) and error estimation techniques.
Introduce and apply key numerical methods: iterative solution of equations; interpolation (polynomials and splines); orthogonal polynomials; the least-squares method; numerical differentiation and integration; differential-equation solvers; and extremum problem-solving.
Develop the ability to derive, analyze and evaluate the convergence, stability and accuracy of numerical methods.
Cultivate practical programming skills in Mathematica for implementing numerical algorithms.
Promote the application of numerical methods in the modeling and simulation of scientific and engineering problems.
Introduce and apply key numerical methods: iterative solution of equations; interpolation (polynomials and splines); orthogonal polynomials; the least-squares method; numerical differentiation and integration; differential-equation solvers; and extremum problem-solving.
Develop the ability to derive, analyze and evaluate the convergence, stability and accuracy of numerical methods.
Cultivate practical programming skills in Mathematica for implementing numerical algorithms.
Promote the application of numerical methods in the modeling and simulation of scientific and engineering problems.
Brief description of the course
Approximate computation; absolute and relative errors. Using the total differential of a multivariable function to estimate absolute errors. Solving equations by iteration. Interpolation and splines. Orthogonal polynomials and their applications. The least squares method and its applications. Numerical differentiation and integration. Numerical solution of differential equations. Numerical methods for solving extremum problems.
Learning outcomes in the course
Upon completing the course the student:
- defines the concepts used in the course, derives key formulas, proves relevant theorems, and analyzes and assesses the accuracy of well-known numerical methods;
- evaluates the errors arising from indirect measurements in various expressions and applies numerical methods to obtain approximate solutions to a range of mathematical problems;
- solves equations using iterative methods;
- performs interpolation with polynomials and splines;
- carries out numerical differentiation and integration;
- solves numerically differential equations and finds extrema of single- and multi-variable functions;
- implements and applies numerical methods in the CAS Mathematica.
- defines the concepts used in the course, derives key formulas, proves relevant theorems, and analyzes and assesses the accuracy of well-known numerical methods;
- evaluates the errors arising from indirect measurements in various expressions and applies numerical methods to obtain approximate solutions to a range of mathematical problems;
- solves equations using iterative methods;
- performs interpolation with polynomials and splines;
- carries out numerical differentiation and integration;
- solves numerically differential equations and finds extrema of single- and multi-variable functions;
- implements and applies numerical methods in the CAS Mathematica.
Teacher
Tõnu Tõnso
Prerequisite course 1
Prerequisite course 2
Study programmes containing that course