Introduction to Numerical Linear Algebra
by Christoph Börgers

✅ Fit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems.

✅ is ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond lecturing,

✅ assumes that the reader has taken a course on linear algebra, but reviews background as needed, and

✅ covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, a detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration, a discussion of the use of the SVD for assigning grades, and multigrid methods.

✅ This textbook is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It can be used in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory