Explorations in Numerical Analysis

James V Lambers is a Professor in the School of Mathematics and Natural Sciences at The University of Southern Mississippi, and an ACUE Distinguished Teaching Scholar. His research interests span numerical methods for partial differential equations and numerical linear algebra. Amber C Sumner is an Assistant Professor of Mathematics at William Carey University. She was a PhD student of Lambers at USM. Her research interests include deep learning and numerical linear algebra. Vivian A Montiforte is a PhD student of Lambers at USM. Her research pertains to spectral methods and meshless methods for partial differential equations.

Preface; Preliminaries:What is Numerical Analysis?; Understanding Error; Numerical Linear Algebra:Direct Methods for Linear Systems; Least Squares Problems; Iterative Methods for Linear Systems; Eigenvalue Problems; Data Fitting and Function Approximation:Polynomial Interpolation; Approximation of Functions; Differentiation and Integration; Nonlinear Equations and Optimization:Zeros of Nonlinear Functions; Optimization; Differential Equations:Initial Value Problems; Two-Point Boundary Value Problems; Partial Differential Equations; Appendices:Review of Calculus; Review of Linear Algebra; Bibliography; Index;