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BL
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| Record Number
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862595
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| Main Entry
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Holmes, Mark H.
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| Title & Author
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Introduction to the foundations of applied mathematics /\ Mark H. Holmes.
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| Edition Statement
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Second edition.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2019.
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| Series Statement
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Texts in applied mathematics,; volume 56
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| Page. NO
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1 online resource (xvi, 528 pages) :: illustrations (some color)
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| ISBN
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3030242609
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: 3030242617
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: 3030242625
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: 3030242633
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: 9783030242602
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: 9783030242619
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: 9783030242626
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: 9783030242633
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9783030242602
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface to the Second Edition; Preface to the First Edition; Contents; 1 Dimensional Analysis; 1.1 Introduction; 1.2 Examples of Dimensional Reduction; 1.2.1 Maximum Height of a Projectile; 1.2.2 Drag on a Sphere; Find the General Product Solution; Determine the General Solution; Representation of Solution; Determining F; Scale Models; Endnotes; 1.2.3 Toppling Dominoes; 1.2.4 Endnotes; 1.3 Theoretical Foundation; 1.3.1 Pattern Formation; 1.4 Similarity Variables; 1.4.1 Dimensional Reduction; 1.4.2 Similarity Solution; 1.5 Nondimensionalization and Scaling; 1.5.1 Projectile Problem
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1.5.1.1 Change Variables1.5.1.2 The Dimensionless Groups; 1.5.1.3 Use Dimensionless Groups to Determine Scaling; 1.5.1.4 Changing Your Mind; 1.5.2 Weakly Nonlinear Diffusion; 1.5.3 Endnotes; Exercises; Section 1.2; Section 1.4; Section 1.5; Additional Questions; 2 Perturbation Methods; 2.1 Regular Expansions; 2.2 How to Find a Regular Expansion; 2.2.1 Given a Specific Function; 2.2.2 Given an Algebraic or Transcendental Equation; 2.2.3 Given an Initial Value Problem; 2.3 Scales and Approximation; 2.4 Introduction to Singular Perturbations; 2.5 Introduction to Boundary Layers; 2.5.1 Endnotes
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2.6 Examples Involving Boundary Layers2.6.1 Example 1: Layer at Left End; 2.6.2 Example 2: Layer at Right End; 2.6.3 Example 3: Boundary Layer at Both Ends; 2.7 Multiple Scales; 2.7.1 Regular Expansion; 2.7.2 Multiple Scales Expansion; Exercises; Sections 2.1 and 2.2; Section 2.3; Sections 2.4-2.6; Section 2.7; Additional Questions; 3 Kinetics; 3.1 Introduction; 3.1.1 Radioactive Decay; 3.1.2 Predator-Prey; 3.1.3 Epidemic Model; 3.2 Kinetic Equations; 3.2.1 The Law of Mass Action; 3.2.2 Conservation Laws; 3.2.3 Steady States; 3.2.4 Examples; 3.2.5 End Notes
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3.3 Modeling Using the Law of Mass Action3.3.1 Michaelis-Menten Kinetics; 3.3.2 Disease Modeling; 3.3.3 Reverse Mass Action; 3.4 General Mathematical Formulation; 3.5 Steady States and Stability; 3.5.1 Reaction Analysis; 3.5.2 Geometric Analysis; 3.5.3 Perturbation Analysis; 3.6 Solving the Michaelis-Menten Problem; 3.6.1 Numerical Solution; 3.6.2 Quasi-Steady-State Approximation; 3.6.3 Perturbation Approach; 3.6.3.1 Nondimensionalization; 3.6.3.2 Outer Expansion; 3.6.3.3 Inner Expansion; 3.6.3.4 Matching and Composite Expansion; 3.6.3.5 Analysis of Solution; 3.6.3.6 Connection with QSSA
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3.7 Oscillators3.7.1 Stability; 3.8 Modeling with the QSSA; 3.9 Epilogue; Exercises; Section 3.2; Section 3.3; Section 3.4; Section 3.5; Sections 3.6 and 3.7; Sections 3.8; Additional Questions; 4 Diffusion; 4.1 Introduction; 4.2 Random Walks and Brownian Motion; 4.2.1 Calculating w(m, n); 4.2.2 Large n Approximation; 4.3 Continuous Limit; 4.3.1 What Does D Signify?; Diffusion in a Gas; Diffusion in a Fluid; Diffusion in a Solid; 4.4 Solutions of the Diffusion Equation; 4.4.1 Point Source Solution; 4.4.2 A Step Function Initial Condition; 4.5 Fourier Transform
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| Abstract
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This book deals with the construction, analysis and interpretation of mathematical models to help us understand the world. It develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering.
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| Subject
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Mechanics-- Mathematics.
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| Subject
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Mechanics-- Mathematics.
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| Dewey Classification
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531.01/51
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| LC Classification
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TA330
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