MATH-251(a) / 3 credits

Teacher: Kressner Daniel

Language: English

## Summary

This course presents numerical methods for the solution of mathematical problems such as systems of linear and non-linear equations, functions approximation, integration and differentiation, and differential equations.

## Content

• Polynomial approximation: interpolation and least squares
• Numerical differentiation and integration
• Direct methods for solving systems of linear equations
• Iterative methods for solving systems of linear and non-linear equations
• Numerical approximation of differential equations.

In the exercise the students will implement and test the studied methods using Python.

## Keywords

Numerical algorithms, polynomial interpolation, numerical integration, numerical linear algebra, numerical solution of ODEs, iterative methods.

## Required courses

• Analyse
• Algèbre linéaire

Programmation

## Learning Outcomes

By the end of the course, the student must be able to:

• Choose a method for solving a specific problem
• Interpret in the light of theory the results obtained from a computation
• Estimate numerical errors
• Prove theoretical properties of numerical methods
• Implement numerical algorithms
• Apply numerical algorithms to specific problems
• Describe numerical methods
• State the theoretical properties of mathematical problems and numerical methods

## Transversal skills

• Use both general and domain specific IT resources and tools
• Access and evaluate appropriate sources of information.

## Teaching methods

Ex cathedra lectures, exercices in class and with computers

## Expected student activities

• Attendance to lectures
• Exercises resolution
• Resolution of elementary problem with computers

## Assessment methods

Written exam. The exam may require the resolution of problems in a computer using Python.

## Supervision

 Office hours Yes Assistants Yes Forum Yes

Yes

## Notes/Handbook

Available on the Moodle (English and French versions).

## In the programs

• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Numerical analysis
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 1 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Numerical analysis
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 1 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Numerical analysis
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 1 Hour(s) per week x 14 weeks
• Type: mandatory

## Reference week

Thursday, 8h - 10h: Lecture SG0211

Thursday, 10h - 11h: Exercise, TP INF3

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