This textbook gives a unified treatment of the solution of various linear equations that arise in science and engineering with examples. It is based on a course taught by the first author for over thirty years. Some unique features include:

• Use of symbolic software for illustrating and enhancing the impact of physical parameter changes on solutions.
• Multi-scale analysis of engineering problems with physical interpretation of time and length scales in terms of eigenvalues and eigenvectors/eigenfunctions.
• Discussion of compartment models for various finite dimensional problems.
• Evaluation and illustration of functions of matrices (and use of symbolic manipulation) to solve multi-component diffusion-convection-reaction problems.
• Illustration of the techniques and interpretation of solutions to several classical engineering problems.
• Emphasis on the connection between discrete (matrix algebra) and continuum.
• Physical interpretation of adjoint operator and adjoint systems.
• Use of complex analysis and algebra in the solution of practical engineering problems.