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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.
Includes 100 illustrative problems in the text.
Additional 150 practice problems along with solutions.
Use of symbolic manipulators (such as Mathematica) and generation of graphics.
Various web based extensions.
Matrices and linear algebraic equations
Determinants
Vectors and vector expansions
Solution of linear equations by eigenvector expansions
Solution of linear equations containing a square matrix
Generalized eigenvectors and canonical forms
Quadratic forms, positive definite matrices and other applications
Vector space over a field
Linear transformations
Normed and inner product vector spaces
Applications of finite-dimensional linear algebra
The linear initial value problem
Linear systems with periodic coefficients
Analytic solutions, adjoints and integrating factors
Introduction to the theory of functions of a complex variable
Series solutions and special functions
Laplace transforms
Two-point boundary value problems
The nonhomogeneous BVP and Green’s function
Eigenvalue problems for differential operators
Sturm–Liouville theory and eigenfunction expansions
Introduction to the solution of linear integral equations
Finite Fourier transforms
Fourier transforms on infinite intervals
Fourier transforms in cylindrical and spherical geometries
The classical Graetz–Nusselt problem
Friction factors for steady-state laminar flow in ducts
Multicomponent diffusion and reaction
Packed-bed chromatography
Stability of transport and reaction processes