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Course content

An introduction to numerical methods which are used in solving problems in physics and chemistry, including solutions of differential equations, matrix operations and eigenvalue problems, interpolation and numerical integration, modeling of data and Monte Carlo methods.

Learning outcome

The course gives an introduction to several of the most used algorithms from numerical analysis to solve problems in the Sciences. These algorithms cover topics such as advanced numerical integration using Gaussian quadrature, Monte Carlo methods with applications to random processes, Markov chains, integration of multidimensional integrals and applications to problems in statistical physics and quantum mechanics. Advanced Variational and Diffusion Monte Carlo methods will also be discussed.

Other methods which are presented are eigenvalue problems, from the
simple Jacobi method to iterative Krylov methods. Popular methods from linear algebra such as the LU-decomposition method and spline interpolation are also discussed. A large fraction of the course is also devoted to solving ordinary differential equations with or without boundary conditions and finally methods for solving partial differential equations. Both finite difference and finite element methods will be discussed.

The student will thus develop a familiarity with some of the most used algorithms in Science. Several examples of problems in physics
and chemistry will be used in order to demonstrate various numerical methods. The examples span over several fields, from materials science to solid state physics, atomic physics, astrophysics, nuclear physics and eigenvalue problems in quantum chemistry. The course is project based and through the various projects, normally five, the participants will be exposed to fundamental research problems in these fields, where the aim of the last project is to reproduce state of the art scientific
results. The students will learn to develop and structure codes for studying these systems, develop a critical understanding of the capabilities and limits of the various numerical methods, get acquainted with supercomputing facilities and parallel computing and learn to handle scientific projects. The students will have to choose between C++, Python or Fortran2008 as computing languages. They will also learn how to interface python programs with C++ or Fortran programs.

A good scientific and ethical conduct is emphasized throughout the course.

Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Prerequisites

Formal prerequisite knowledge

No prerequisites.

Recommended previous knowledge

Knowledge corresponding to the following courses at the University of Oslo: INF1000 - Introduction to object-oriented programming (continued), FYS-MEK1110 - Mechanics, MOD100, MAT1100 - Calculus, MAT1110 - Calculus and linear algebra and MAT1120 - Linear algebra.

Overlapping courses

10 credits overlap against FYS3150 - Computational physics.

Teaching

The course is offered for one semester and comprises 4 hours of lectures per week, in addition to laboratory exercises aided by the use of a computer. The course will also include five projects that students will receive feedback on.

Examination

Five projects, including three that will each count 1/3 of the grade. The final project will be somewhat more difficult than the previous 2. There will be no written or oral examination, only a portfolio assessment.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Facts about this course

Credits

10

Level

Master

Teaching

Every autumn

Examination

Every autumn

Teaching language

Norwegian (English on request)