Classical Mechanics and Special Relativity

Postgraduate course

Course description

Objectives and Content

The course aims to give an understanding of the Lagrangian and Hamiltonian formulations of classical mechanics as well as their application to both-non-relativitistic and relativistic systems. The course provides a rigorous introduction to special relativity. Topics include the central-force problem, rigid body motion, relativistic electrodynamics, as well as non-linear dynamics and chaos. The importance of symmetries for finding conserved quantities is emphasized. The lecture provides fundamental knowledge relevant for a variety of topics such as statistical physics, quantum mechanics, field theory, and general relativity.

Learning Outcomes

On completion of the course

the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

  • can explain and compare the Lagrangian and Hamiltonian formulations of classical mechanics
  • can derive Kepler's laws
  • can explain the fundamental concepts of special relativity and how to perform Lorentz transformations
  • is framiliar with the relativistic notation for 4-vectors and tensors
  • can explain the emergence of chaos in dynamical systems

Skills

The student

  • is able to determine the Lagrangian and Hamiltonian functons for a physical systems
  • is able to derive the equations of motion from these functions
  • is able to solve the equations of motion for simple systems
  • can determine the moments of inertia of a rigid body
  • is able to identify symmetries and to derive the corresponding conservation laws
  • is able to perform calculations using relativistic kinematics and conservation laws

General competence

The student

  • knows how to model physical systems in terms of abstract quantities
  • can hypothesize the solution of a problem qualitatively without performing a detailed calculation
  • is comfortable presenting calculations to peers

Semester of Instruction

Spring
Required Previous Knowledge
None
Recommended Previous Knowledge
Credit Reduction due to Course Overlap
MAT251 5 ECTS
Access to the Course
Access to the course equires admission to a programme of study at The Faculty of Mathematics and Natural Sciences.
Teaching and learning methods

The teaching methods are lectures and tutorials.

Lectures / 4 hours per week

Tutorials / 2 hours per week

Compulsory Assignments and Attendance
Two assignments. Valid for 6 subsequent semester.
Forms of Assessment
The forms of assessment are: Written exam.
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Assessment Semester
Examination both spring semester and autumn semester. In semester without teaching the examination will be arranged at the beginning of the semester.
Reading List
The reading list will be available within July 1st for the autumn semester and December 1st for the spring semester.
Course Evaluation
The course will be evaluated by the stdents in accordance with the quality assurance system at UiB and the department.
Examination Support Material
Examination support materials: Non- programmable calculator, according to model listed in faculty regulations. In addition the student can bring 5 A4 pages with own written notes and mathematic table of formulae.
Programme Committee
The Programme Committee is responsible for the content, structure and quality of the study programme and courses.
Course Administrator
The Faculty of Mathematics and Natural Sciences and Department of Physics and Technology are administratively responsible for the course.