Vector and Tensor Analysis

Teaching semester

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 equations in physics, electromagnetism, elasticity theory and theory of general relativity. The course continues the general vector analysis form the multivariable course MAT212 to tensors of higher rank. A coordinate-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.

Learning Outcomes

Learning outcomes

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

• Do computations with tensors, both in coordinates and in a coordinate-free form.
• Know the mathematical language needed to formulate the Maxwell equations for electromagnetism, linear elasticity equations and other field 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

Exercises

Forms of Assessment

Oral examination

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.