Introduction to Numerical Analysis Exploring Connections Between Computation and Theory

This textbook introduces numerical analysis from a modern, mathematical perspective. Organized to showcase the fundamental connections between computation and analysis, the text offers a cohesive view of topics in use today. Striking a balance between rigor and approachability, the author prepares readers to tackle a wide range of problems from a strong conceptual base. Beginning with the fundamental concepts of convergence and its rate, the book goes on to explore function approximation in detail. Chebyshev polynomials are encountered early and recur throughout the book. Having established the power of numerical methods, the text returns to the essentials of computer arithmetic, round-off errors, and numerical differentiation. Numerical integration brings together ideas from the first half of the book to construct and analyze quadratures. Numerical linear algebra precedes nonlinear equations, allowing the inclusion of nonlinear systems. Finally, ordinary and partial differential equations are illuminated through the interrelated concepts of consistency, stability, and convergence. Introduction to Numerical Analysis is suitable for a single semester or year-long sequence, using the instructor's preferred coding language. Exercise sets accompany each section and a capstone project brings together ideas from across the book. Prerequisites are vector calculus, linear algebra, and real analysis, along with basic coding skills. Some knowledge of differential equations and complex variables is desirable.