عنوان
پدید آورنده
موضوع
رده
TA330
TA330
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
3030242609
(Number (ISBN
3030242617
(Number (ISBN
3030242625
(Number (ISBN
3030242633
(Number (ISBN
9783030242602
(Number (ISBN
9783030242619
(Number (ISBN
9783030242626
(Number (ISBN
9783030242633
Erroneous ISBN
9783030242602
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Introduction to the foundations of applied mathematics /
General Material Designation
[Book]
First Statement of Responsibility
Mark H. Holmes.
EDITION STATEMENT
Edition Statement
Second edition.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cham, Switzerland :
Name of Publisher, Distributor, etc.
Springer,
Date of Publication, Distribution, etc.
2019.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (xvi, 528 pages) :
Other Physical Details
illustrations (some color)
SERIES
Series Title
Texts in applied mathematics,
Volume Designation
volume 56
ISSN of Series
0939-2475 ;
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
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
Text of Note
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
Text of Note
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
Text of Note
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
Text of Note
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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SUMMARY OR ABSTRACT
Text of Note
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.
ACQUISITION INFORMATION NOTE
Source for Acquisition/Subscription Address
Springer Nature
Stock Number
com.springer.onix.9783030242619
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
3030242609
TOPICAL NAME USED AS SUBJECT
Mechanics-- Mathematics.
Mechanics-- Mathematics.
(SUBJECT CATEGORY (Provisional
MAT003000
PBWH
PBWH
TBJ
DEWEY DECIMAL CLASSIFICATION
Number
531
.
01/51
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
TA330
PERSONAL NAME - PRIMARY RESPONSIBILITY
Holmes, Mark H.
ORIGINATING SOURCE
Date of Transaction
20200823093117.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
