This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra. Key Features: o Giving the reader a more hands-on experience with the material than existing textbooks through Python exercises spliced throughout the presentation o Augment the text with visualization and experimentation in order to involve the reader in the derivation and analysis of each algorithm, as well as its implementation. Students can use the book in combination with programming languages such as Python in order to experiment with the concepts and techniques presented o Aid the reader in achieving this level of understanding through a combination of exposition about the evolution of problem-solving techniques and the theoretical results that support them, and coding exercises and demonstrations to illustrate this evolution

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