Still brief - but with the chapters that you wanted - Steven Chapra’s new second edition is written for engineering and science students who need to learn numerical problem solving. This text focuses on problem-solving applications rather than theory, using MATLAB throughout. Theory is introduced to inform key concepts which are framed in applications and demonstrated using MATLAB. The new second edition feature new chapters on Numerical Differentiation, Optimization, and Boundary-Value Problems (ODEs).
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.