Learning outcomes

To pass, the student should be able to

• describe and perform tasks in connection to the key concepts covered in the course;
• explain the idea behind and apply the algorithms covered in the course;
• explore properties for numerical methods and mathematical models by using the analysis methods covered in the course;
• in a student group structure and divide a computational problem into sub-problems, formulate an algorithm and implement the algorithm in MATLAB and in MATLAB connected to other programming languages (such as C);
• in a short report explain and summarise solution methods and results in a lucid way

Content

MATLAB and programming in MATLAB. MEX-files as an interface between MATLAB and the programming language C. Problem solving methodology. Given a problem, divide it into sub-problems, write an algorithm and transform the algorithm to a computer program.

Solution to linear equation systems using LU-factorisation with pivoting. Norms for matrices and vectors. Sensitivity and condition number, stable/unstable algorithm. Numerical solution to integrals. Simpsons metod and Trapezoid rule. Solution to non-linear equations and iterative methods. Bisection, Newton-Raphon method and hybrid algorithms. Floating point representation and the IEEE-standard for floating point arithmetic, machine epsilon and round-off error.

Key concepts covered in the course: algorithm, numerical method, discretisation och discretisation error, accuracy and order of accuracy, stable and unstable algorithm, machine epsilon, iteration, condition and condition number, efficiency, adaptivity, convergence.

Instruction

Lectures, problem classes/workouts, laboratory work, compulsory assignments.

Assessment

Written examination (3 credits) and approved mini projects (2 credits).