Explorations in Numerical Analysis

USA, University of Southern Mississippi, 2015, 393 p. This book evolved from lecture notes written by James Lambers and used in undergraduate numerical analysis courses at the University of California at Irvine, Stanford University and the University of Southern Mississippi. It is written for a year-long sequence of numerical analysis courses for either advanced undergraduate or beginning graduate students. Part II is suitable for a semester-long first course on numerical linear algebra.The goal of this book is to introduce students to numerical analysis from both a theoretical and practical perspective, in such a way that these two perspectives reinforce each other. It is not assumed that the reader has prior programming experience. As mathematical concepts are introduced, code is used to illustrate them. As algorithms are developed from these concepts, the reader is invited to traverse the path from pseudocode to code. Coding examples throughout the book are written in Matlab. Preliminaries 1 Numerical Linear Algebra 41 Solution of Nonlinear Equations 151 Data Fitting and Function Approximation 197 Differential Equations 297 A Review of Calculus 335 B Review of Linear Algebra 349