Differential Calclus A, Avez

Include appendix, bibliography and index.

1. The concept of a derivative -- 2. Mean-value theorems -- 3. The concept of diffeomorphism, and the solution of equations -- 4. Higher-order derivatives -- 5. The exponential function, and linear differential equation with constant coefficents -- 6. The integral product, and linear differential equations -- 7. Vector field and differential equations -- 8. Conjuigacy and local coordinates -- 9. Differentiable submanifolds -- 10. Calculus of variations.

Original, rigorous, and lively, this text offers a concise approach to in differential calculus, Basedon courses conduc ted by the author at the Universite Pierre et Marie Curie, it encourage reader to pursue the subject in greater depth. The calculus is presented in a Banach space setting, covvering Vector fields, One-parameter groups of diffeomorphisms, the Morse-Plais lemma, Differentiable submanifolds.