Introduction to Tensor Calculus
Fundamentals of Tensor Calculus with a Primer on Manifolds
Tentative schedule (constantly updated)
Attention: bugs in homework 5  now corrected!
Week (cal.) 
Week (sem.) 
Lecture Thursday 14:0015:30 KKB1069 
Homework topics 
15 
1 
Introduction: geometry and space, vectors as geom. objects, diff. manifolds: first contact 
Euclidean geometry 
16 
2 
vector space, lin. independence and basis, Ricci notation, change of basis, dual space 
Riccinotation, algebraic operation with vectors and dual vectors 
17 
3 
inner product spaces, reciprocal basis 
metric coefficients, inner product and orthogonal mappings 
18 
4 
May Day 

19 
5 
Affine and euclidean space 
observer transformations 
20 
6 
2^{nd} order tensors as linear mappings 
transpose of a 2^{nd} order tensor, unity tensor, metric tensor 
21 
7 
tensors of arbitrary order 
orthogonal tensors, antisymmetric tensors 
22 
8 
Ascension Day 

23 
9 
Multivectors, multicovectors and exterior algebra 
Working with multiindices, exterior algebra 
24 
10 
exterior algebra 
exterior algebra 
25 
11 
tensor analysis in euclidean spaces 
Frechetderivative, Gateauxdifferential 
26 
12 
tensor analysis in euclidean spaces 
tangent plane to surfaces in R^{3} 
27 
13 
analysis on differentiable manifolds: tangent space and push forward 
example: same physical problem on a sphere with and without embedding in E^{3} 
28 
14 
cotangent space, differential forms 

29 
15 
Covariant derivative, Integration on manifolds 

Potential audience:
==================
CMS students 3rd semester
students of Mechanical Engineering specializing in computation and
simulation
researchers from engineering and physics
Lecture 2 SWS on Vector and Tensor Calculus