Topology, Calculus and Approximation

• Main Author: Komornik, Vilmos (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2017.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Approximation theory.; Differential equations.; Numerical analysis.; Ordinary Differential Equations.; Numerical Analysis.; Approximations and Expansions.

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán.  The exposition style of Top...

Table of Contents:

• Part 1. Topology
• Chapter 1. Metric spaces
• Chapter 2. Topological spaces
• Chapter 3. Normed spaces
• Part 2. Differential calculus
• Chapter 4. The Derivative
• Chapter 5. Higher-order derivatives
• Chapter 6. Ordinary differential equations
• Chapter 7. Implicit functions and their applications
• Part 3. Approximation methods
• Chapter 8. Interpolation
• Chapter 9. Orthogonal polynomials
• Chapter 10. Numerical integration
• Chapter 11. Finding roots
• Chapter 12. Numerical solution of differential equations.