UID:
almahu_9949728660402882
Umfang:
1 online resource (xi, 505 pages)
ISBN:
9781315370309
,
1315370301
,
9781498728010
,
1498728014
,
9781498728034
,
1498728030
,
9781498728027
,
1498728022
Inhalt:
Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes.
Anmerkung:
Cover -- Half Title -- Title -- Copyrights -- Contents -- Chapter 1. The Process Of Mathematical Modeling -- 1.1 What Os Model Building? -- 1.2 Modeling Framework -- 1.3 Gens And Biological Reproduction -- Chapter 2. Modeling With Ordinary Differential Equations -- 2.1 The Motion Of A Projectile -- 2.1.1 Approximations And Simplifications -- 2.1.2 Model -- 2.1.3 Model Compounding -- 2.2 Spring Mass Systems -- 2.2.1 Data Collection -- 2.2.2 Approximations And Simplifications -- 2.2.3 Mathematical Model -- 2.2.4 Remarks And Refinements -- 2.3 Electrical Circuits -- 2.3.1 Rlc Circuits -- 2.3.2 Approximations -- 2.4 Population Models -- 2.4.1 Logistic Model -- 2.4.2 Prototype Model -- 2.4.3 Data And Approximations -- 2.4.4 Solution Of The Logistic Equation -- 2.5 Motion In A Central Force Field -- 2.5.1 Radial Coordinate System In R2 -- 2.5.2 Linear Pendulum -- 2.5.3 Nonlinear Pendulum -- 2.5.4 A Short Introduction To Elliptic Functions -- 2.5.5 Motion Of A Projectile On A Rotating Earth -- 2.5.6 A Particle In A Central Force Field -- 2.5.7 Motion Of A Rocket -- 2.5.8 Multistage Rockets -- 2.5.9 Control Of A Satellite In Orbit -- 2.6 Greenhouse Effect -- 2.7 Current Energy Balance Of The Earth -- 2.7.1 Critique Of The Model -- 2.7.2 Humanity And Energy -- Chapter 3. Solutions Of Systems Of Odes -- 3.1 Review -- 3.1.1 Linear Differential Equations With Constant Coefficients -- 3.2 Review Of Linear Algebra -- 3.2.1 Eigenvalues And Eigenvectors -- 3.3 Reformulation Of Systems Odes -- 3.4 Linear Systems With Constant Coefficients -- 3.5 Numerical Solution Of Initial Value Problems -- 3.5.1 Euler Algorithm -- 3.6 Finite Difference Approximations -- 3.6.1 Extension To Higher Dimensions.
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3.7 Modified Euler And Runge Kutta Methods -- 3.7.1 Modified Euler Algorithm -- 3.7.2 Runge-kutta Methods -- 3.8 Boundary Value Problems -- Chapter 4. Stability Theory -- 4.1 General Introduction -- 4.2 Two Species Model -- 4.2.1 Steady States -- 4.2.2 Stability Analysis -- 4.3 Basic Concepts -- 4.4 Linearizable Dynamical Systems -- 4.5 Linearizable Systems In Two Dimensions -- 4.6 Liapounov Method -- 4.7 Periodic Solutions (limit Cycles -- Chapter 5. Bifurcations And Chaos -- 5.1 Introduction -- 5.2 Bifurcations Of Co Dimension One -- 5.2.1 Trans-critical Bifurcation -- 5.2.2 Saddle Point Bifurcation -- 5.2.3 Pitchfork Bifurcation -- 5.2.4 Subcritical Bifurcation (hysteresis -- 5.2.5 Hopf Bifurcation -- 5.3 Rossler Oscillator -- 5.4 Lorenz Equations -- 5.5 Nerve Models -- 5.6 Miscellaneous Topics -- 5.6.1 Dimension -- 5.6.2 Liapunov Exponents -- 5.7 Appendix A: Derivation Of Lorenz Equations -- Chapter 6. Perturbations -- 6.1 Introduction -- 6.2 Model Equations In Non Dimensional Form -- 6.3 Regular Perturbations -- 6.4 Singular Perturbations -- 6.5 Boundary Layers -- Chapter 7. Modeling With Partial Differential Equations -- 7.1 The Heat (or Diffusion) Equation -- 7.1.1 Burger's Equation -- 7.1.2 Similarity Solutions -- 7.1.3 Stephan Problem(s -- 7.2 Modeling Wave Phenomena -- 7.2.1 Nonlinear Wave Equations -- 7.2.2 Riemann Invariants -- 7.3 Shallow Water Waves -- 7.3.1 Tsunamis -- 7.4 Uniform Transmission Line -- 7.5 The Potential (or Laplace) Equation -- 7.5.1 Kirchoff Transformation -- 7.6 The Continuity Equation -- 7.7 Electromagnetism -- 7.7.1 Maxwell Equations -- 7.7.2 Electrostatic Fields -- 7.7.3 Multipole Expansion -- 7.7.4 Magnetostatic -- 7.7.5 Electromagnetic Waves.
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7.7.6 Electromagnetic Energy And Momentum -- 7.7.7 Electromagnetic Potential -- Chapter 8. Solutions Of Partial Differential Equations -- 8.1 Method Of Separation Of Variables -- 8.1.1 Method Of Separation Of Variables By Example -- 8.1.2 Non Cartesian Coordinate Systems -- 8.1.3 Boundary Value Problems With General Initial Conditions -- 8.1.4 Boundary Value Problems With Inhomogeneous Equations -- 8.2 Green's Functions -- 8.3 Laplace Transform -- 8.3.1 Basic Properties Of The Laplace Transform -- 8.3.2 Applications To The Heat Equation -- 8.4 Numerical Solutions Of Pdes -- 8.4.1 Finite Difference Schemes -- 8.4.2 Numerical Solutions For The Poisson Equation -- 8.4.2.1 Other Boundary Conditions -- 8.4.3 Irregular Regions -- 8.4.4 Numerical Solutions For The Heat And Wave Equations -- Chapter 9. Variational Principles -- 9.1 Extrema Of Functions -- 9.2 Constraints And Lagrange Multipliers -- 9.3 Calculus Of Variations -- 9.3.1 Natural Boundary Conditions -- 9.3.2 Variational Notation -- 9.4 Extensions -- 9.5 Applications -- 9.6 Variation With Constraints -- 9.7 Airplane Control -- Minimum Flight Time -- 9.8 Applications In Elasticity -- 9.9 Rayleigh Ritz Method -- 9.10 The Finite Element Method In 2-d -- 9.10.1 Geometrical Triangulations -- 9.10.2 Linear Interpolation In 2-d -- 9.10.3 Galerkin Formulation Of Fem -- 9.11 Appendix -- Chapter 10. Modeling Fluid Flow -- 10.1 Strain And Stress -- 10.2 Equations Of Motion For Ideal Fluid -- 10.2.1 Continuity Equation -- 10.2.2 Euler's Equations -- 10.3 Navier Stokes Equations -- 10.4 Similarity And Reynolds' Number -- 10.5 Different Formulations Of Navier Stokes Equations -- 10.6 Convection And Boussinesq Approximation.
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10.7 Complex Variables In 2-d Hydrodynamics -- 10.8 Blasius Boundary Layer Equation -- 10.9 Introduction To Turbulence Modeling -- 10.9.1 Incompressible Turbulent Flow -- 10.9.2 Modeling Eddy Viscosity -- 10.9.3 K -- O Model -- 10.9.4 The Turbulent Energy Spectrum -- 10.10 Stability Of Fluid Flow -- 10.11 Astrophysical Applications -- 10.11.1 Derivation Of The Model Equations -- 10.11.2 Steady State Model Equations -- 10.11.3 Physical Meaning Of The Functions H(.), S -- 10.11.4 Radial Solutions For The Steady State Model -- 10.12 Appendix A Gauss Theorem And Its Variants -- 10.13 Appendix B Poincare Inequality And Burger's Equation -- 10.14 Appendix C Gronwell Inequality -- 10.15 Appendix D The Spectrum -- Chapter 11. Modeling Geophysical Phenomena -- 11.1 Atmospheric Structure -- 11.2 Thermodynamics And Compressibility -- 11.2.1 Thermodynamic Modeling -- 11.2.2 Compressibility -- 11.3 General Circulation -- 11.4 Climate -- Chapter 12. Stochastic Modeling -- 12.1 Introduction -- 12.2 Pure Birth Process -- 12.3 Kermack And Mckendrick Model -- 12.4 Queuing Models -- 12.5 Markov Chains -- Chapter 13. Answers To Problems.
Weitere Ausg.:
Print version: Humi, Mayer. Introduction to mathematical modeling. Boca Raton, FL : CRC Press, Taylor & Francis Group, [2017] ISBN 9781498728003
Sprache:
Englisch
URL:
https://www.taylorfrancis.com/books/9781315370309
URL:
https://www.taylorfrancis.com/books/9781315370309
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