Steven Chapra’s Applied Numerical Methods with MATLAB , third edition, is written for engineering and science students who need to learn numerical problem solving. Theory is introduced to inform key concepts which are framed in applications and demonstrated using MATLAB. The book is designed for a one-semester or one-quarter course in numerical methods typically taken by undergraduates. The third edition features new chapters on Eigenvalues and Fourier Analysis and is accompanied by an extensive set of m-files and instructor materials.
Definitely a good book for engineers and early graduate Math majors. The book delivers a very good overview of the general numerical techniques in various categories. However, one will have to do more research in specific topics to be able to thoroughly apply those techniques in her research.