Contains more than 570 exercises of varying difficulty Provides proofs of basic results on existence and regularity of solutions of ordinary differential equations Includes a full treatment of the inverse function theorem in several variables Emphasizes the importance of estimates and computation in analysis

Autorentext

Michael Field has held appointments in the UK (Warwick University and Imperial College London), Australia (Sydney University) and the US (the University of Houston and Rice University) and has taught a wide range of courses at undergraduate and graduate level, including real analysis, partial differential equations, dynamical systems, differential manifolds, Lie groups, complex manifolds and sheaf cohomology. His publications in the areas of equivariant dynamical systems and network dynamics include nine books and research monographs as well as many research articles. His computer graphic art work, based on symmetric dynamics, has been widely exhibited and is on display at a number of universities around the world.

Inhalt
1 Sets, functions and the real numbers.- 2 Basic properties of real numbers, sequences and continuous functions.- 3 Infinite series.- 4 Uniform convergence.- 5 Functions.- 6. Topics from classical analysis: The Gamma-function and the EulerMaclaurin formula.- 7 Metric spaces.- 8 Fractals and iterated function systems.- 9 Differential calculus on Rm.- Bibliography. Index.