Vector and Tensor Analysis
- ECTS credits
- Teaching semesters
- Course code
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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.
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.