After completing this course succesfully, the student will know

• the basic definitions about manifolds, differentiable mappings, tangent space at a point and differentials of smooth mappings,
• what immersion, imbedding and submanifold means,
• what a vector field is and the meaning of integrability of vector fields,
• basic definitions and computational tools about tensor fields, differential forms, exterior differentiation and some computational techniques concerning these concepts,
• orientation of manifolds, volume form,
• the definition of integration on manifolds,
• the concept of manifolds with boundary,
• Stokes' Theorem on manifolds with boundary and the relation to other important theorems of Calculus.