Linear algebra in action - Dym, H. (Harry), 1938- (Providence, Rhode Island : American Mathematical Society, 2013)
14.2. Taylor's formula with remainder -- 14.3. Application of Taylor's formula with remainder -- 14.4. Mean value theorem for functions of several variables -- 14.5. Mean value theorems for vector-valued functions of several variables -- 14.6. A contractive fixed point theorem -- 14.7. Newton's method -- 14.8. A refined contractive fixed point theorem -- 14.9. Spectral radius -- 14.10. The Brouwer fixed point theorem -- 14.11. Bibliographical notes -- 15.1. Preliminary discussion -- 15.2. The implicit function theorem -- 15.3. A generalization of the implicit function theorem -- 15.4. Continuous dependence of solutions -- 15.5. The inverse function theorem -- 15.6. Roots of polynomials -- 15.7. An instructive example -- 15.8. A more sophisticated approach -- 15.9. Dynamical systems -- 15.10. Lyapunov functions -- 15.11. Bibliographical notes -- 16.1. Classical extremal problems -- 16.2. Convex functions -- 16.3. Extremal problems with constraints -- 16.4. Examples -- 16.5. Krylov subspaces.
Includes bibliographical references (pages 575-578) and indexes.
Keywords: Algebras, Linear