Engineering Computation with MATLAB

Concepts of Combinatorial Optimization, is divided into three parts:
– On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity;
– Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming;
– Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.

The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.

A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec­ trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of “starter” designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding “starter” designs.

The main features also include:

• A brief introduction of the material in each chapter, followed by an explanation of the concepts presented.
• Examples and applications in each chapter that will help you cement your knowledge on the topics, encouraging you to participate in the problem-solving process.
• Highlighted key points and important results, helping you remember what you study – especially during the revision process.

The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski’s theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.