# Numerical Analysis : Approximation, Interpolation, Integration

linma2171  2022-2023  Louvain-la-Neuve

Numerical Analysis : Approximation, Interpolation, Integration
5.00 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Language
Prerequisites
Basic skills in numerical methods, as covered, for example, within  LEPL1104 (Numerical methods).
Remark : LINMA2171 is the second part of a teaching programme in numerical analysis, of which LINMA1170 is the first part ; however, LINMA1170 is not a prerequisite for LINMA2171.
Main themes
• Interpolation
• Function approximation
• Numerical integration
Learning outcomes
 At the end of this learning unit, the student is able to : 1 AA1.1, AA1.2, AA1.3 At the end of the course, the student will be able to: Implement, in concrete problems, the basic knowledge required from an advanced user and a developer of numerical computing software; Analyze in depth various methods and algorithms for numerically solving scientific or technical problems, related in particular to interpolation, approximation, and integration of functions. Transversal learning outcomes : Use a reference book in English; Use programming languages for scientific computing.
Content
• Interpolation: polynomial, by spline functions, rational, trigonometric.
• Orthogonal polynomials: Legendre polynomials, Chebyshev polynomials.
• Approximation: uniform and in the least-square sense, by polynomials and by splines.
• Numerical integration: Newton--Cotes formulas, Gauss method.
• Other topics related to the course themes.
Teaching methods
• Lectures
• Homeworks, exercises, or laboratory work under the supervision of the teaching assistants
Evaluation methods
• Work carried out during the term: homework assignments, exercises, or laboratory work. These activities are thus organized (and evaluated) only once per academic year.
• Exam: written, or sometimes oral depending on the circumstances.
The final grade is min(2/5 D + 3/5 E, D+5, E+5), where D is the grade of the work carried out during the term and E is the grade of the exam.
Further information is provided in the "Course outline" document available on Moodle (see "Online resources" below).
Online resources
Bibliography
• Textbook
• Complementary documents posted on Moodle
Further information is provided in the "Course outline" document available on Moodle.
Faculty or entity

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