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E-raamat: Inequalities: With Applications to Engineering

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 06-May-2014
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319053110
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Inequalities: With Applications to EngineeringSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 06-May-2014
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319053110
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This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra and calculus and proceeds with a presentation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed and inner product spaces. It also provides full coverage of the central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the CauchySchwarz inequality, Chebyshev's inequality, Jensen's inequality and the triangle inequality.

The second edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additional examples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate students, as well as researchers in engineering, mathematics, physics, chemistry or any other quantitative science.

Arvustused

This second edition of Inequalities with Applications to Engineering is aimed at readers having customary backgrounds in engineering mathematics. It is interesting to note that the authors included not only classical inequalities but also some discussion of extremum problems and an introduction to interval analysis. It should be of interest to both undergraduate and graduate students of mathematics, physics and engineering, as well as to practicing engineers. (Victor A. Eremeyev, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 95 (8), 2015)

It reads at an undergraduate mathematics level but gives soft introductions and reviews on all topics leaving it possible for those without a formal mathematical or applied mathematical background to follow. Any mathematician would enjoy this book and appreciate its clear, concise descriptions. It simply is a very nice applied mathematics book. (Anna Heffernan, Irish Mathematical Bulletin, Issue 75, 2015)

"...a remarkable addition to the literature on inequalities, and not only engineers or other applied scientists, but the students of mathematics and researchers will appreciate it." - József Sándor, zbMATH

1 Basic Review and Elementary Facts
1(32)
1.1 Why Study Inequalities?
1(8)
1.2 Quick Review of the Basics
9(3)
1.3 Triangle Inequality for Real Numbers
12(1)
1.4 Simple Inequalities for Real Functions of One Variable
13(4)
1.5 Complex Numbers and Some Complex Functions
17(3)
1.6 Vectors in Rn and Associated Inequalities
20(3)
1.7 Some Techniques for Establishing Inequalities
23(5)
1.8 Problems
28(5)
2 Methods from the Calculus
33(20)
2.1 Introduction
33(1)
2.2 Limits and Continuity
33(4)
2.3 Basic Results for Integrals
37(3)
2.4 Results from the Differential Calculus
40(7)
2.5 Problems
47(6)
3 Some Standard Inequalities
53(22)
3.1 Introduction
53(1)
3.2 Bernoulli's Inequality
53(1)
3.3 Young's Inequality
54(1)
3.4 Inequality of the Means
54(2)
3.5 Holder's Inequality
56(3)
3.6 Minkowski's Inequality
59(1)
3.7 Cauchy--Schwarz Inequality
60(3)
3.8 Chebyshev's Inequality
63(2)
3.9 Jensen's Inequality
65(2)
3.10 Friedrichs- and Poincare-Type Inequalities
67(2)
3.11 Problems
69(6)
4 Inequalities in Abstract Spaces
75(26)
4.1 Introduction
75(1)
4.2 Vectors and Norms
75(4)
4.3 Metric Spaces
79(6)
4.4 Linear Spaces
85(11)
4.5 Operators
96(3)
4.6 Problems
99(2)
5 Some Applications
101(62)
5.1 Introduction
101(1)
5.2 Estimation of Integrals
101(1)
5.3 The o and O Symbols
102(2)
5.4 Series Expansions
104(3)
5.5 Simpson's Rule
107(3)
5.6 Taylor's Method
110(3)
5.7 Special Functions of Mathematical Physics
113(6)
5.8 A Projectile Problem
119(2)
5.9 Geometric Shapes
121(3)
5.10 Electrostatic Fields and Capacitance
124(5)
5.11 Applications to Matrices
129(7)
5.12 Topics in Signal Analysis
136(3)
5.13 Dynamical System Stability and Control
139(7)
5.14 Some Inequalities of Probability
146(3)
5.15 Applications in Communication Systems
149(3)
5.16 Existence of Solutions
152(5)
5.17 A Duality Theorem and Cost Minimization
157(2)
5.18 Problems
159(4)
6 Inequalities for Differential Equations
163(16)
6.1 Chaplygin's Theorem
163(1)
6.2 Gronwall's Inequality
164(2)
6.3 On Poisson's Equation
166(1)
6.4 Membrane with Fixed Edge
167(2)
6.5 Theory of Linear Elasticity
169(4)
6.6 Theory of Elastic Plates
173(1)
6.7 On the Weak Setup of Linear Mechanics Problems
174(3)
6.8 Problems
177(2)
7 A Brief Introduction to Interval Analysis
179(16)
7.1 Introduction
179(1)
7.2 The Interval Number System
180(2)
7.3 Outward Rounding for Rigorous Containment of Solutions
182(1)
7.4 Interval Extensions of Real-Valued Functions
182(4)
7.5 A Few Techniques of Interval Analysis
186(6)
7.6 Further Reading
192(1)
7.7 Problems
193(2)
Appendix A Hints for Selected Problems 195(36)
References 231(4)
Index 235
Michael J. Cloud received a Ph.D. in Electrical Engineering from Michigan State University. He has been a faculty member in the Department of Electrical and Computer Engineering at Lawrence Technological University since 1987 and currently holds the rank of Associate Professor.

Byron C. Drachman is Emeritus Professor of Mathematics at Michigan State University. He received a Ph.D. in Mathematics from Brown University in 1966.

Leonid P. Lebedev completed a Ph.D. in Physics and Mathematics at Southern Federal University in Russia. He is a professor of mathematics at the National University of Colombia at Bogota and holds a faculty appointment at Southern Federal University.
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