An important objective of this textbook is to provide “math-on-line” for undergraduate students of science and engineering. It is expected that students have had at least one semester of calculus. Chapters one and two contain introductory material on complex numbers, 2D and 3D vectors and their products. A connection is established between geometric and algebraic approaches to these topics. This is continued into chapters three, four and five, where higher order algebraic systems are solved via row operations, inverse matrices and LU decomposition. Linearly independent vectors and subspaces are used to solve underdetermined and overdetermined systems. Chapters six and seven describe first and second order linear equations and introduce eigenvalues and eigenvectors for solutions of linear systems of initial value problems. The last two chapters use transform methods to filter distorted images and signals. The discrete Fourier transform is introduced via continuous versions of the Laplace and Fourier transforms. The discrete Fourier transform properties are derived from the Fourier matrix representation and are used to do image filtering in the frequency domain.
Most sections have some applications, indicating that these topics are really useful. Seven basic applications are developed in various sections of the text, including circuits, trusses, mixing tanks, heat conduction, data modeling and the motion of a mass and image filters. The applications are developed from very simple models to more complex ones. Matlab is used here to do more complicated computations. The strategy of how to use computing tools is given as: firstly learn the math and by-hand calculations; secondly use computing tools to confirm by-hand calculations; thirdly use computing tools to do more complicated calculations and applications.