Vector and Tensor Analysis
Every second autumn - even-numbered years.
Objectives and Content
Objectives and content
Tensor analysis contains tools and definitions used within modeling of continuous media, field wquations in physics, electromagnetism, elasticity theory and theory of general relativity. The course cotinues the general vector analysis form the multivariable course MAT212 to tensors of higher rank. A coorinate-free approach is also given for certain differential operators such as the exterior derivative, the Lie derivative and the covariant derivative. Furthermore, integration theory and Stokes theorem is treated in a general form. Finally, the Riemann curvature tensor and the torsion tensor is also treated.
After completed course, the students are expected to be able to:
- do computations with tensorsm both in coordinates and in a coordinate-free form.
- Know the mathematical language needed to formulate the Maxwell equations
- Be able to define curved spaces and be able to compute the curvature tensor for simple geometries.
Recommended Previous Knowledge
MAT212 Functions of Several Variables
Credit Reduction due to Course Overlap
M216: 9 ECTS
Compulsory Assignments and Attendance
Forms of Assessment
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.