Norsk
Course MAT260

# Scientific Computing 2

## Course offered:

### Course offered by

 Number of credits 10 Course offered (semester) Spring Schedule Schedule Reading list Reading list

English

None

### Learning Outcomes

After completed course, the students are expected to be able to

• explain and use the power method to find the smallest and the biggest eigenvalue of a matrix
• show Schur's and Gershgorin's theorem for matrices
• explain and use iterative methods for nonlinear systems like fix point method and Newton's method
• explain the least square method for determining the best approximation
• explain the Gauss-quadrature for approximating integrals
• describe and use the Runge-Kutta methods and the multistep methods for solving numerically ordinary differential equations

Spring

English

### Aim and Content

The course gives an introduction to algorithms and theory for numerical solution of systems of ordinary differential equations, iterative solution of systems of non-linear equations and basic methods for calculating eigenvalues. Computation of the best approximation in the least square theory with focus on orthogonal polynomials and trigonometric approximation are also treated. In addition one looks at special problems in numerical integration and Gauss quadrature.The course also deals with differential methods for initial value problems, Runge Kuta and multistep methods for time integration.

### Learning Outcomes

After completed course, the students are expected to be able to

• explain and use the power method to find the smallest and the biggest eigenvalue of a matrix
• show Schur's and Gershgorin's theorem for matrices
• explain and use iterative methods for nonlinear systems like fix point method and Newton's method
• explain the least square method for determining the best approximation
• explain the Gauss-quadrature for approximating integrals
• describe and use the Runge-Kutta methods and the multistep methods for solving numerically ordinary differential equations

None

### Recommended previous knowledge

MAT160 Scientific computing I

### Assessment methods

Written exam. It is opportunity for grades on exercises, which can be included in the final grade. If less than 20 students are taking the course, it can be oral exam.