Ostaszewski A. Advanced Mathematical Methods

Cambridge: Cambridge University Press, 2009. — 560 p.Written in an appealing and informal style, this text is a self-contained second course on mathematical methods in linear algebra and multivariate calculus. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a "cookbook" approach, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interests are in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.Linear algebra
Vector spaces (revision)
Geometry in Rn
Matrices
Projections
Spectral theory
Reduction to upper triangular form
Reduction to tridiagonal form
Inverses
Convexity
The separating hyperplane theorem
Linear inequalities
Linear programming and game theory
The simplex method
Partial derivatives (revision)
Convex functions
Non-linear programming
Advanced calculus
The integration process
Manipulation of integrals
Multiple integrals
Differential and difference equations (revision)
Laplace transforms
Series solution of linear ordinary differential equations
Calculus of variations
Solutions to selected exercises
Miscellany