Aims

The student should acquire insight into the way in which numerical calculations are made on a computer.
For that purpose concepts like rounding error, numerical stability, condition, robustness,... are important. The student learns about existing numerical software and elementary solution methods for numerical standard problems like: systems linear and non-linear comparisons, polynomial interpolation, numerical differentiation and integration, simple differential comparisons, zero points of functions, and optimilization problems, especially (non) linear smallest square problems.
Pursued skills:

• To recognize numerical partial problems within a greater complex problem
• To recognize difficult numerical problems (condition) and distinguish from a bad result obtained by unstable algorithms
• To describe a numerical solution method accurately through a number of algorithmic steps (high level and dependent of language)
• To read simple matlab programmes and apply modifications
• To interpret the numerical results of a computer programme on their accuracy, and be able to explain possible anomalies
• To conceive creative numerical and theoretical solutions for problems which are variants on topics discussed

Attitudes:

• Apart from the analytical solution of solving a problem with paper and pencil or with maple, also consider the possibility of a numerical solution
• A numerical common sense regarding numerical results obtained after long or even relatively brief calculations
• Attention to efficiency, robustness and accuracy in designing a numerical solution method
• Searching for good available software while tackling a numerical problem, before making a self-written programme.

Previous knowledge

Linear algebra and principles of analysis, notions of programming in matlab and maple.

Order of Enrolment

Mixed prerequisite:
You may only take this course if you comply with the prerequisites. Prerequisites can be strict or flexible, or can imply simultaneity. A degree level can be also be a prerequisite.
Explanation:
STRICT: You may only take this course if you have passed or applied tolerance for the courses for which this condition is set.
FLEXIBLE: You may only take this course if you have previously taken the courses for which this condition is set.
SIMULTANEOUS: You may only take this course if you also take the courses for which this condition is set (or have taken them previously).
DEGREE: You may only take this course if you have obtained this degree level.


(FLEXIBLE(H01A2B) OR FLEXIBLE(X0E02A)) AND (FLEXIBLE(H01A4B) OR FLEXIBLE(X0A02C)) AND FLEXIBLE(H01A0B) AND FLEXIBLE(H01B6B)

The codes of the course units mentioned above correspond to the following course descriptions:
H01A2B : Analysis, Part 2
X0E02A : Techniques for Mathematical Analysis
H01A4B : Applied Algebra
X0A02C : Linear Algebra
H01A0B : Analysis, Part 1
H01B6B : Fundamentals of Computer Science

Is included in these courses of study

• Preparatory Programme: Master of Mathematical Engineering (Leuven) 29 ects.
• Preparatory Programme: Master of Computer Science Engineering (Leuven) 61 ects.
• Bachelor of Engineering (Leuven) 180 ects.