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Mathematical analysis --- 517 --- Analysis --- Differentiable dynamical systems. --- Manifolds (Mathematics) --- Stokes' theorem. --- Manifolds (Mathematics). --- 517 Analysis --- Programmation (mathématiques) --- Equations differentielles sur une variete --- Equations aux derivees partielles sur une variete --- Calcul des variations --- Optimisation

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This book gives the reader a thorough knowledge of the basic topological ideas necessary for studying differential manifolds. These topics include immersions and imbeddings, approach techniques, and the Morse classification of surfaces and their cobordism. The author keeps the mathematical prerequisites to a minimum; this and the emphasis on the geometric and intuitive aspects of the subject make the book an excellent and useful introduction for the student. There are numerous excercises on many different levels ranging from practical applications of the theorems to significant further development of the theory and including some open research problems.

Differential topology --- Topologie différentielle --- Topologie différentielle --- Differential topology. --- 515.16 --- Geometry, Differential --- Topology --- 515.16 Topology of manifolds --- Topology of manifolds --- Equations differentielles sur une variete --- Topologie differentielle

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Operator theory --- Asymptotic expansions. --- Boundary value problems. --- Eigenvalues. --- Elliptic operators. --- Fiberings (Mathematics) --- Initial value problems. --- Spectral theory (Mathematics) --- Fiberings (Mathematics). --- Spectral theory (Mathematics). --- Valeurs propres. --- Développements asymptotiques --- Asymptotic expansions --- Développements asymptotiques --- Valeurs propres --- Problèmes aux limites --- Singularités (mathématiques) --- Equations aux derivees partielles sur une variete --- Theorie spectrale

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Differential geometry. Global analysis --- 517 --- 530.145 --- Analysis --- Quantum theory --- Gauge fields (Physics) --- Geometry, Differential --- Congresses. --- 530.145 Quantum theory --- 517 Analysis --- Champs de jauge (Physique) --- Géométrie différentielle --- Congresses --- Congrès --- Champs de jauge (physique) --- Géometrie différentielle globale --- Théorie quantique --- Géometrie différentielle globale --- Théorie quantique --- Equations aux derivees partielles sur une variete

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Partial differential equations --- 517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations, Hyperbolic --- Pseudodifferential operators. --- Singularities (Mathematics) --- Numerical solutions. --- Singularities (Mathematics). --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Opérateurs pseudo-différentiels. --- Singularités (mathématiques) --- Opérateurs pseudo-différentiels --- Singularités (mathématiques) --- Analyse sur une variété --- Equations aux derivees partielles sur une variete