Advanced engineering analysis: the calculus of variations and functional analysis with applications in mechanics

The calculus of variations and functional analysis with applications in mechanics.

Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics.

The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study.

Readership: Academic and industry: engineers, students; advanced undergraduate in the field of mechanical engineering.

Preface

A little over half a century ago, it was said that even an ingenious person could not be an engineer unless he had nearly perfect skills with the
logarithmic slide rule. The advent of the computer changed this situation crucially; at present, many young engineers have never heard of the
slide rule.

The computer has profoundly changed the mathematical side of the engineering profession. Symbolic manipulation programs can calculate integrals and solve ordinary differential equations better and faster than professional mathematicians can.

Computers also provide solutions to differential equations in numerical form. The easy availability of modern graphics packages means that many engineers prefer such approximate solutions even when exact analytical solutions are available.

Because engineering courses must provide an understanding of the fundamentals, they continue to focus on simple equations and formulas that
are easy to explain and understand. Moreover, it is still true that students must develop some analytical abilities.

But the practicing engineer, armed with a powerful computer and sophisticated canned programs, employs models of processes and objects that are mathematically well beyond the traditional engineering background.

The mathematical methods used by engineers have become quite sophisticated. With insufficient base knowledge to understand these methods, engineers may come to believe that the computer is capable of solving any problem.

Worse yet, they may decide to accept nearly any formal result provided by a computer as long as it was generated by a program of a known trademark.

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