Update cookies preferences

Applied Mathematical Modelling of Engineering Problems 2003 ed. [Hardback]

,
  • Format: Hardback, 286 pages, height x width x depth: 234x156x19 mm, weight: 615 g, biography
  • Series: Applied Optimization v. 81
  • Pub. Date: 30-Jun-2003
  • Publisher: Kluwer Academic Publishers
  • ISBN-10: 1402074840
  • ISBN-13: 9781402074844
Other books in subject:
  • Hardback
  • Price: 189,46 €*
  • * the price is final i.e. no additional discount will apply
  • Regular price: 252,61 €
  • Save 25%
  • This book is not in stock. Book will arrive in about 3-4 weeks. Please allow another 2 weeks for shipping outside Estonia.
  • Quantity:
  • Add to basket
  • Delivery time 2-4 weeks
  • Add to Wishlist
Applied Mathematical Modelling of Engineering Problems 2003 ed.Larger Image
  • Format: Hardback, 286 pages, height x width x depth: 234x156x19 mm, weight: 615 g, biography
  • Series: Applied Optimization v. 81
  • Pub. Date: 30-Jun-2003
  • Publisher: Kluwer Academic Publishers
  • ISBN-10: 1402074840
  • ISBN-13: 9781402074844
Other books in subject:
Permanent link: https://www.kriso.ee/db/9781402074844.html
Keywords:
Hritonenko (mathematics, Prairie View A&M University) and Yatsenko (College of Business and Economics, Houston Baptist University) show how to construct mathematical models and adjust them to a new engineering environment, how to analyze models for the purpose of investigating real-life phenomena, and how the models can extend the understanding of specific engineering processes, covering applications including electrical and acoustic processes, bioengineering, and production systems. The book is suitable as a reference for mathematicians and engineers and as a text for advanced courses in mathematical modeling. Annotation (c) Book News, Inc., Portland, OR (booknews.com)

The subject of the book is the "know-how" of applied mathematical modelling: how to construct specific models and adjust them to a new engineering environment or more precise realistic assumptions; how to analyze models for the purpose of investigating real life phenomena; and how the models can extend our knowledge about a specific engineering process.Two major sources of the book are the stock of classic models and the authors' wide experience in the field. The book provides a theoretical background to guide the development of practical models and their investigation. It considers general modelling techniques, explains basic underlying physical laws and shows how to transform them into a set of mathematical equations. The emphasis is placed on common features of the modelling process in various applications as well as on complications and generalizations of models.The book covers a variety of applications: mechanical, acoustical, physical and electrical, water transportation and contamination processes; bioengineering and population control; production systems and technical equipment renovation. Mathematical tools include partial and ordinary differential equations, difference and integral equations, the calculus of variations, optimal control, bifurcation methods, and related subjects. Audience: The book may be used as a professional reference for mathematicians, engineers, applied or industrial scientists, and advanced students in mathematics, science or engineering. It provides excellent material for upper-level undergraduate and graduate courses in mathematical modelling.

More info

Springer Book Archives
PREFACE xi
ACKNOWLEDGEMENTS xxi
CHAPTER
1. SOME BASIC MODELS OF PHYSICAL SYSTEMS		 1(28)
1. BASIC MODELS OF PARTICLE DYNAMICS
2(17)
1.1 Motion of a Particle in Gravitational Field
3(3)
1.1.1 Vertical Projectile Problem.
4(1)
1.1.2 Free Fall with Air Resistance
4(1)
1.1.3 Plane Projectile Problem
5(1)
1.1.4 More General Ballistic Problems
6(1)
1.2 One-Dimensional Mechanical Vibrations
6(13)
1.2.1 Linear Oscillator
7(2)
1.2.2 Forced Linear Vibrations and Resonance.
9(2)
1.2.3 Nonlinear Oscillators
11(3)
1.2.4 Nonlinear Vibrations and Resonance.
14(2)
1.2.5 Nonlinear Electrical-Mechanical Systems
16(3)
2. INVERSE PROBLEMS AND INTEGRAL MODELS
19(10)
2.1 Sliding Particle and Abel's Equation
20(2)
2.2 Sliding Chain
22(2)
2.3 Models of Computerized Tomography
24(6)
2.3.1 Radon Transform
25(3)
2.3.2 Inverse Scattering Problems
28(1)
CHAPTER
2. MODELS OF CONTINUUM MECHANICAL SYSTEMS		 29(56)
1. CONSERVATION LAWS IN ONE-DIMENSIONAL MEDIUM
30(9)
1.1 Eulerian and Lagrangian Coordinates
31(1)
1.2 Mass Conservation
32(1)
1.3 Momentum Conservation
33(3)
1.4 Energy Conservation and Thermodynamics
36(3)
2. MODELS OF ONE-DIMENSIONAL CONTINUUM DYNAMICS
39(17)
2.1 Nonlinear Model of Solid Bar Dynamics
40(1)
2.2 Linearized Model of Solid Bar Dynamics
41(3)
2.3 Discontinuities in Linear Models
44(6)
2.3.1 Analysis of Discontinuity Propagation
45(2)
2.3.2 Analysis of Size of Discontinuity
47(2)
2.3.3 Discontinuities Fixed in Space
49(1)
2.4 Discontinuities in Nonlinear Models
50(4)
2.4.1 Nonlinear Conservation Laws.
51(2)
2.4.2 Impact of Diffusion and Dispersion.
53(1)
2.5 Models of Viscoelasticity
54(2)
3. THREE-DIMENSIONAL CONSERVATION LAWS AND MODELS
56(14)
3.1 Mass Conservation and Continuity Equations
57(1)
3.2 Momentum Conservation and Cauchy Equations
58(7)
3.2.1 Conservation of Angular Momentum
59(1)
3.2.2 Newtonian Viscous Fluids
60(1)
3.2.3 Inviscid Fluids
61(1)
3.2.4 Propagation of Sound in Space
62(1)
3.2.5 Elastic Waves in Solids
63(2)
3.3 Energy Balance and Thermodynamics
65(1)
3.4 Heat Balance and Diffusion Processes
66(4)
3.4.1 Diffusion Equation
68(1)
3.4.2 Advection-Diffusion Equation
69(1)
4. APPLIED MODELLING OF WATER TRANSPORT AND CONTAMINATION
70(15)
4.1 Description of Physical Processes
71(1)
4.2 Classification of Models
72(2)
4.3 Three-Dimensional Model
74(5)
4.3.1 Equation of Transport of the Ingredient in Solute
75(1)
4.3.2 Equation of Transport of Suspended Particles
76(1)
4.3.3 Equation of ingredient Transport on Suspended Particles
77(1)
4.3.4 Equations of Surface Water Dynamics
77(1)
4.3.5 Equations of Adsorption and Sedimentation
78(1)
4.4 Two-Dimensional Horizontal Model and Stationary Flows
79(6)
4.4.1 Equation of Ingredient Transport in Dissolved Phase
80(1)
4.4.2 Equation of Suspended Particles Transport
80(1)
4.4.3 Equation of Ingredient Transport on Suspended Particles
81(1)
4.4.4 Equations of Water Dynamics
81(1)
4.4.5 Equation of Ground Deposit Contamination
82(1)
4.4.6 Analysis of Stationary Flow Problem
82(2)
4.4.7 About Simulation Techniques
84(1)
CHAPTER
3. VARIATIONAL MODELS AND STRUCTURAL STABILITY		 85(20)
1. VARIATIONAL PRINCIPLES AND MODELS
85(11)
1.1 Basic Models of Continuum Mechanics
87(3)
1.1.1 Vibrations of String
87(1)
1.1.2 Transverse Vibrations of Bar
88(1)
1.1.3 Vibrations of Membrane
88(1)
1.1.4 Vibrations of Plate
89(1)
1.2 Variational Models for Spectral Problems
90(6)
1.2.1 Eigenvalues and Eigenfunctions: Simplest Case
90(1)
1.2.2 Raleigh Quotient and Raleigh Method
91(1)
1.2.3 Eigenvalues of Bar with Variable Shape
92(2)
1.2.4 Extremal Eigenvalues of Bar with Sought-For Shape
94(2)
2. VARIATIONAL MODELS OF STRUCTURAL STABILITY
96(9)
2.1 Model of Buckling Rod.
97(1)
2.2 Model of Anti-Plane Shear Collapse in Plasticity
98(3)
2.3 Model of Capillarity Stability.
101(4)
CHAPTER
4. INTEGRAL MODELS OF PHYSICAL SYSTEMS		 105(34)
1. CONSTRUCTION OF INTEGRAL MODELS
106(19)
1.1 Converting Differential Models to Integral Models
106(14)
1.1.1 Initial Value Problems
107(5)
1.1.2 Boundary Value Problems for Ordinary Differential Equations: Green's Function
112(2)
1.1.3 Boundary Value Problems for Partial Differential Equations: Boundary Integral Equation Method
114(6)
1.2 Integral Models Occurring in Physical Problems
120(9)
1.2.1 Integral Model of Membrane Vibrations.
120(2)
1.2.2 Integral Models of Nuclear Reactors Dynamics.
122(3)
2. MODELLING OF TRAFFIC NOISE PROPAGATION
125(4)
3. MODELLING OF MINE ROPE DYNAMICS
129(10)
3.1 Description of Physical Process.
130(1)
3.2 Differential Model
131(3)
3.3 Integral Model
134(3)
3.4 Some Generalizations.
137(2)
CHAPTER
5. MODELING IN BIOENGINEERING		 139(44)
1. MODELS OF POPULATION DYNAMICS AND CONTROL
141(25)
1.1 Classic Models for One Species Population
142(6)
1.1.1 Malthus Model
142(2)
1.1.2 Verhulst-Pearl Model
144(2)
1.1.3 Population Control and Harvesting
146(2)
1.2 Age-Dependent Models for One Species Population
148(4)
1.2.1 Linear Integral Model (Lotka Model)
149(1)
1.2.2 Linear Differential Model (Lotka-Von Foerster Model)
150(1)
1.2.3 Equivalence of Integral and Differential Models
151(1)
1.3 Nonlinear Age-Dependent Models with Intra-Species Competition
152(2)
1.4 Models with Delay
154(1)
1.5 Difference Models
155(4)
1.6 Spatial Diffusion Models of Population Dynamics
159(7)
1.6.1 Random Walk Models
159(4)
1.6.2 Diffusion Models
163(3)
2. BIFURCATION ANALYSIS FOR NONLINEAR INTEGRAL MODELS
166(17)
2.1 Stationary Solutions
167(1)
2.2 Stability Analysis
168(9)
2.2 Connection with Difference Models
177(3)
2.3.1 Single Seasonal Reproduction
177(1)
2.3.2 Double Seasonal Reproduction.
178(2)
2.3 Open Problems
180(3)
CHAPTER
6. MODELS OF TECHNOLOGICAL RENOVATION IN PRODUCTION SYSTEMS		 183(58)
1. TRADITIONAL MODELS OF TECHNOLOGICAL RENOVATION
184(5)
1.1 Aggregated Models of Optimal Investments
185(1)
1.2 Age-Specific Models of Equipment Replacement
186(2)
1.3 Statistical Models of Equipment Renewal
188(1)
2. MODELS OF EQUIPMENT REPLACEMENT UNDER TECHNOLOGICAL CHANGE
189(17)
2.1 Self-Organizing Market Model of Enterprise Under Technological Change
190(4)
2.2 Aggregated Model with Endogenous Useful Life of Equipment
194(5)
2.2.1 Integral Macroeconomic Models of Technological Renovation
195(2)
2.2.2 Statement of Optimization Problem
197(2)
2.3 Disaggregated Integral Model of Equipment Replacement
199(7)
2.3.1 Description of Production System
199(1)
2.3.2 Construction of Model
200(2)
2.3.3 About Prediction Problems
202(2)
2.3.4 Statement of Optimization Problem
204(2)
3. QUALITATIVE ANALYSIS OF OPTIMAL EQUIPMENT REPLACEMENT
206(26)
3.1 About Optimal Control Problems in Integral Models
206(9)
3.1.1 General Statement of Optimal Control Problem
207(1)
3.1.2 Necessary Conditions of Extremum
208(3)
3.1.3 Lagrange Multipliers Method
211(3)
3.1.4 Novelty and Common Features
214(1)
3.2 Optimal Equipment Replacement in Aggregate Model
215(10)
3.2.1 Structure of Aggregated Optimization Problem
216(2)
3.2.2 Equation for Turnpike Regimes of Equipment Replacement
218(2)
3.2.3 Infinite-Horizon Discounted Optimization
220(1)
3.2.4 Finite-Horizon Optimization
221(2)
3.2.5 Discussion of Results
223(2)
3.3 Optimal Equipment Replacement in Disaggregated Models
225(5)
3.3.1 Model with Different Lifetimes of Equipment
229(1)
3.4 Open Problems
230(2)
4. MATHEMATICAL DETAILS AND PROOFS
232(9)
CHAPTER
7. APPENDIX		 241(20)
1. MISCELLANEOUS FACTS OF ANALYSIS
241(4)
1.1 Vector and Integral Calculus
241(2)
1.1.1 Gradient, Divergence and Rotation
241(1)
1.1.2 Gauss Divergence Theorem.
242(1)
1.1.3 Dubois-Reymond's Lemma.
243(1)
1.1.4 Leibniz's Formula for Derivatives
243(1)
1.2 Functional Spaces
243(1)
1.3 Calculus of Variations and Euter Equations
244(1)
2. MATHEMATICAL MODELS AND EQUATIONS
245(16)
2.1 Classification of Mathematical Models
245(9)
2.1.1 Deterministic and Stochastic Models
245(1)
2.1.2 Continuous and Discrete Models
246(1)
2.1.3 Linear and Nonlinear Models
247(1)
2.1.4 Difference, Differential and Integral Models
248(6)
2.2 Integral Dynamical Models and Volterra Integral Equations
254(7)
2.2.1 Solvability of Volterra Integral Equations
254(2)
2.2.2 Correctness and Stability of Volterra Integral Equations
256(2)
2.2.3 Stability of Volterra Integral Equations
258(1)
2.2.4 Integral Inequalities
258(3)
REFERENCES 261(16)
INDEX 277