• Multilinear algebra: tensors and exterior forms. Differential forms on Rⁿ: exterior differentiation, the pull-back operation and the Poincaré lemma. Applications to physics: Maxwell's equations from the differential form perspective. Integration of forms on open sets of Rⁿ. The change of variables formula revisited. The degree of a differentiable mapping. Differential forms on manifolds and De Rham theory. Integration of forms on manifolds and Stokes'theorem. The push-forward operation for forms. Thom forms and intersection theory. Applications to differential topology.

• Textbook Information

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