Springer Theoretical Numerical Analysis Textbook - Math Series 39

Prepare for advanced research in computational mathematics with this comprehensive textbook from Springer. Part of the Texts in Applied Mathematics series, this volume provides graduate students with a rigorous mathematical framework centered on functional analysis. By grounding numerical analysis in functional analysis principles, the text helps students transition quickly into active research programs. This textbook covers essential topics required for modern mathematical study. Readers will explore basic results of functional analysis, approximation theory, and Fourier analysis alongside wavelets. The content also addresses iteration methods for nonlinear equations, finite difference methods, and Sobolev spaces. For those studying boundary value problems, the text provides detailed coverage of weak formulations, finite element methods, and elliptic variational inequalities. This structured approach makes it an essential resource for anyone pursuing a deep understanding of numerical analysis and its practical applications in mathematical research.