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Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature.
Henryk Żołądek is a Polish mathematician and a professor of mathematical sciences. He specializes in mathematical physics and differential equations.
Preface.- 1. Analytic Functions and Morse Theory.- 2. Normal Forms of Functions.- 3. Algebraic Topology of Manifolds.- 4. Topology and Monodromy of Functions.- 5. Integrals along Vanishing Cycles.- 6. Vector Fields and Abelian Integrals.- 7. Hodge Structures and Period Map.- 8. Linear Differential Systems.- 9. Holomorphic Foliations. Local Theory.- 10. Holomorphic Foliations. Global Aspects.- 11. The Galois Theory.- 12. Hypergeometric Functions.- Bibliography.- Index.