Olver P.J., Shakiban C. Applied Mathematics

Prentice-Hall, 2004. — 1165 p.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.