I have written the following books:
- Partial Differential Equations: Analytical and Numerical Methods (SIAM 2010). This text introduces the classic method of Fourier series and the modern finite element method on an equal footing. Another innovation is the explicit use of the concepts of linear algebra.
- Understanding and Implementing the Finite Element Method (SIAM, 2006). This is also an introductory text; it covers the Galerkin finite element method for stationary problems in two dimensions, and comes with a package of Matlab codes implementing the algorithms.
- Finite-Dimensional Linear Algebra (CRC Press, 2010). This is an advanced introduction to linear algebra and some of its most interesting applications. It develops the theory thoroughly and also presents a variety of applications.
- Linear Inverse Problems and Tikhonov Regularization (MAA Press, 2016). This is an expository study of the most popular general purpose regularization method for linear inverse problems. Inverse problems are characterized by instability, meaning that a small amount of noise in the data can be magnified into a large error in the computed solution, unless some method of regularization is used.
Each of the cover images below is a link; click to go to the publisher’s website.