| Description |
1 online resource (500 pages) |
| Contents |
Preface; Contents; 1. Basic Calculus of Variations; 1.1 Introduction; A function in n variables; Functionals; Minimization of a simple functional using calculus; Notation for various types of derivatives; 2. Consider the composite function; Brief summary of important terms; 1.2 Euler's Equation for the Simplest Problem; 1.3 Properties of Extremals of the Simplest Functional; 1.4 Ritz'sMethod; 1.5 Natural Boundary Conditions; 1.6 Extensions to More General Functionals; The functional b a f(x, y, y) dx; The functional b f(x, y, y ..., y(n)) dx |
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1.7 Functionals Depending on Functions in Many Variables1.8 A Functional with Integrand Depending on Partial Derivatives of Higher Order; 1.9 The First Variation; A few technical details; Back to the first variation; Variational derivative; Brief review of important ideas; 1.10 Isoperimetric Problems; Two problems; Quick summary; 1.11 General Formof the First Variation; 1.12 Movable Ends of Extremals; Quick review; 1.13 Broken Extremals: Weierstrass-Erdmann Conditions and Related Problems; Quick review; 1.14 Sufficient Conditions forMinimum; Some field theory; 1.15 Exercises |
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2. Applications of the Calculus of Variations in Mechanics2.1 Elementary Problems for Elastic Structures; 2.2 Some Extremal Principles of Mechanics; Elasticity; Reissner-Mindlin plate theory; Kirchhoff plate theory; Interaction of a plate with elastic beams; 2.3 Conservation Laws; 2.4 Conservation Laws and Noether's Theorem; The simplest case; Functional depending on a vector function; 2.5 Functionals Depending on Higher Derivatives of y; Functional depending on y; 2.6 Noether's Theorem, General Case; Functional depending on a function in n variables and its first derivatives |
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Elements of calculus for vector and tensor fieldsFundamental solution of a linear system of ordinary differential equations; 3.8 General Terminal Control Problem; 3.9 Pontryagin'sMaximum Principle for the Terminal Optimal Problem; 3.10 Generalization of the Terminal Control Problem; 3.11 Small Variations of Control Function for Terminal Control Problem; 3.12 A Discrete Version of Small Variations of Control Function for Generalized Terminal Control Problem; 3.13 Optimal Time Control Problems; 3.14 Final Remarks on Control Problems; 3.15 Exercises; 4. Functional Analysis |
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Functional depending on vector function in several variables2.7 Generalizations; Divergence invariance; Other generalizations; 2.8 Exercises; 3. Elements of Optimal Control Theory; 3.1 A Variational Problem as an Optimal Control Problem; 3.2 General Problem of Optimal Control; 3.3 Simplest Problem of Optimal Control; 3.4 Fundamental Solution of a Linear Ordinary Differential Equation; 3.5 The Simplest Problem, Continued; 3.6 Pontryagin's Maximum Principle for the Simplest Problem; 3.7 Some Mathematical Preliminaries; Matrices as the component representations of tensors and vectors |
| Summary |
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 |
| Notes |
4.1 A Normed Space as a Metric Space |
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Print version record |
| Form |
Electronic book
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| Author |
Cloud, Michael J.
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Eremeyev, Victor A.
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| ISBN |
9789814390484 |
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9814390488 |
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