This book supplies a broad-based introduction to variational methods for formulating and solving problems in mathematics and the applied sciences. It refines and extends the author's earlier text on variational calculus and a supplement on optimal control.

It is the only current introductory text that uses elementary partial convexity of differentiable functions to characterize directly the solutions of some minimization problems before exploring necessary conditions for optimality or field theory methods of sufficiency. Through effective notation, it combines rudiments of analysis in (normed) linear spaces with simpler aspects of convexity to offer a multilevel strategy for handling such problems. It also employs convexity considerations to broaden the discussion of Hamilton's principle in mechanics and to introduce Pontjragin's principle in optimal control. It is mathematically self-contained but it uses applications from many disciplines to provide a wealth of examples and exercises.

The book is accessible to upper-level undergraduates and should help its user understand theories of increasing importance in a society that values optimal performance.