Applied functional analysis : main principles and their applications
This is the second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws (the Noether theorem), the quark model, and gauge theory in elementary particle physics. The presentation is self-contained
xvi, 404 pages : illustrations ; 25 cm.
9780387944227, 0387944222
31411778
Contents of AMS Volume 108
1. The Hahn-Banach Theorem Optimization Problems
2. Variational Principles and Weak Convergence
3. Principles of Linear Functional Analysis
4. The Implicit Function Theorem
5. Fredholm Operators