Olver P.J., Shakiban C. Applied Mathematics

Prentice-Hall, 2004. — 1165 p.The source of linear algebra is the solution of systems of linear algebraic equations. Linear algebra is the foundation upon which almost all applied mathematics rests. This is not to say that nonlinear equations are less important; rather, progress in the vastly more complicated nonlinear realm is impossible without a firm grasp of the fundamentals of linear systems.This text aims to teach basic methods and algorithms used in modern, real problems that are likely to be encountered by engineering and science students-and to foster understanding of why mathematical techniques work and how they can be derived from first principles. No text goes as far (and wide) in applications. The authors present applications hand in hand with theory, leading students through the reasoning that leads to the important results, and provide theorems and proofs where needed. Because no previous exposure to linear algebra is assumed, the text can be used for a motivated entry-level class as well as advanced undergraduate and beginning graduate engineering/applied math students.Linear Algebra
Vector Spaces
Inner Products and Norms
Minimization and Least Squares Approximation
Orthogonality
Equilibrium
Linear Functions
Linear Transformations
Eigenvalues
Linear Dynamical Systems
Iteration of Linear Systems
Boundary Value Problems in One Dimension
Fourier Series
Fourier Analysis
Vibration and Diffusion in One-Dimensional Media
The Laplace Equation
Complex Analysis
Dynamics of Planar Media
Partial Differential Equations in Space
Nonlinear Systems
Nonlinear Ordinary Differential Equations
The Calculus of Variations
Nonlinear Partial Differential Equations.