Syllabus for Scientific Computing KF

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;
• explain simple programming code in MATLAB and write small size programs by means of script files and self-written functions;
• in a student group write programming code that use fundamental programming structures (if, while, for);
• in a student group structure and divide a computational problem into sub-problems, formulate an algorithm and implement the algorithm in MATLAB;
• in a short report explain and summarise solution methods and results in a lucid way

Content

MATLAB and programming in MATLAB: fundamental programming structures (if statements, for, while), functions, parameter passing. Programming structure. Problem solving methodology. Given a problem, divide it into sub-problems, write an algorithm and transform the algorithm to a MATLAB program.

Basic matrix and vector operations. Expressing linear systems of equations in matrix vector form. Matrices and vectors as mathematical objects and data structures. 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, complexity, discretisation och discretisation error, machine epsilon, floating point numbers, round off error, accuracy and order of accuracy, stable and unstable algorithm, iteration and iterative method, condition and condition number, efficiency, adaptivity and adaptive methods, convergence, convergence rate, fix point iteration.

Instruction

Lectures, workouts (problem classes), laboratory work, mini projects.

Assessment

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