Principles of mathematical modeling.

Format:

Book

Author/Creator:

Dym, Clive L.

Language:

English

Subjects (All):

Mathematical models.

Physical Description:

1 online resource (323 p.)

Edition:

2nd ed. / Clive L. Dym.

Place of Publication:

Amsterdam ; Boston : Elsevier Academic Press, c2004.

Language Note:

English

Summary:

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and ""own"" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then intro

Contents:

Contents; Preface; Acknowledgments; Part A: Foundations; 1 What is Mathematical Modeling?; 1.1 Why do we do mathematical modeling?; 1.2 Principles of mathematical modeling; 1.3 Some methods of methematical modeling; 1.4 Summary; 1.5 References; 2 Dimensional Analysis; 2.1 Dimensions and units; 2.2 Dimensional homogeneity; 2.3 Why do we do dimensional analysis?; 2.4 How do we do dimensional analysis?; 2.5 Systems of units; 2.6 Summary; 2.7 References; 2.8 Problems; 3 Scale; 3.1 Abstraction and scale; 3.2 Size and shape: geometric scaling; 3.3 Size and function-I: Birds and flight

3.4 Size and function-II: Hearing and speech3.5 Size and limits: scale in equations; 3.6 Consequences of choosing a scale; 3.7 Summary; 3.8 References; 3.9 Problems; 4 Approximating and Validating MOdels; 4.1 Taylor's formula; 4.2 Algebraic approximations; 4.3 Numerical approximations: significant figures; 4.4 Validating the model-I: How do we know the model is OK?; 4.5 Validating the model-II: How large are the errors?; 4.6 Fitting curves to data; 4.7 Elementary statistics; 4.8 Summary; 4.9 Appendix: Elementary transcendental functions; 4.10 References; 4.11 Problems; Part B: Applications

5 Exponential Growth and Decay5.1 How do things get so out of hand?; 5.2 Exponential functions and their differential equations; 5.3 Radioactive decay; 5.4 Charging and discharging a capacitor; 5.5 Exponential models in money matters; 5.6 A nonlinear model of population growth; 5.7 A coupled model of fighting armies; 5.8 Summary; 5.9 References; 5.10 Problems; 6 Traffic Flow Models; 6.1 Can we really make sense of freeway traffic?; 6.2 Macroscopic traffic flow models; 6.3 Microscopic traffic models; 6.4 Summary; 6.5 References; 6.6 Problems; 7 Modeling Free Vibration

7.1 The freely-vibrating pendulum-I: Formulating a model7.2 The freely-vibrating pendulum-II: The linear model; 7.3 The spring-mass oscillator-I: Physical interpretations; 7.4 Stability of a two-mass pendulum; 7.5 The freely vibrating pendulum-III: The nonlinear model; 7.6 Modeling the popular growth of coupled species; 7.7 Summary; 7.8 References; 7.9 Problems; 8 Applying Vibration Models; 8.1 The spring-mass oscillator-II: Extensions and analogies; 8.2 The fundamental period of a tall, slender building; 8.3 The cyclotron frequency; 8.4 The fundamental frequency of an acoustic resonator

8.5 Forcing vibration: modeling an automobile suspension8.6 The differential equation md2x/dt2+kx=F(t_; 8.7 Resonance and impedance in forced vibration; 8.8 Summary; 8.9 References; 8.10 Problems; 9 Optimization: What Is the Best...?; 9.1 Continuous optimization modelling; 9.2 Optimization with linear programming; 9.3 The transportation problem; 9.4 Choosing the best alternative; 9.5 A miscellany of optimization problems; 9.6 Summary; 9.7 References; 9.8 Problems; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786610961320

9781280961328

1280961325

9780080470283

0080470289

OCLC:

162572033