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| List of Titled Examples and Problems | |
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| Foreword to the First Edition | |
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| Foreword to the Second Edition | |
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| Acknowledgments | |
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| Preface to the First Edition | |
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| Preface to the Second Edition | |
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| Organization, Notation, and Conventions | |
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| Mathematical Preliminaries | |
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| Matrices and Determinants | |
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| Operations with Matrices | |
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| The Rank of a Matrix | |
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| Systems of Linear Equations | |
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| Homogeneous Case | |
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| Nonhomogeneous Case | |
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| List of Selected Publications Dealing with Linear Algebra and Matrices | |
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| Formats and Classification | |
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| Formats for Physical Relations | |
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| Numeric Format | |
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| Symbolic Format | |
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| Mixed Format | |
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| Classification of Physical Quantities | |
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| Variability | |
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| Dimensionality | |
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| Dimensional Systems | |
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| General Statements | |
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| Monodimensional System | |
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| Omnidimensional System | |
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| Multidimensional System | |
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| Classification | |
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| The SI | |
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| Preliminary Remarks | |
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| Structure | |
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| Fundamental Dimensions | |
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| Derived Dimensionless Units | |
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| Derived Dimensional Units with Specific Names | |
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| Derived Dimensional Units without Specific Names | |
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| Non-SI Units Permanently Permitted to be Used with SI | |
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| Non-SI Units Temporarily Permitted to be Used with SI | |
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| Prohibited Units | |
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| Prefixes | |
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| Rules of Etiquette in Writing Dimensions | |
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| Problems | |
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| Other Than SI Dimensional Systems | |
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| Metric, Mass-based Systems | |
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| CGS System | |
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| SI (for reference only) | |
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| Metric, Force-based System | |
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| American/British Force (Engineering) System | |
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| American/British Mass (Scientific) System | |
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| A Note on the Classification of Dimensional Systems | |
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| Transformation of Dimensions | |
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| Numerical Equivalences | |
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| Technique | |
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| Examples | |
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| Problems | |
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| Arithmetic of Dimensions | |
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| Dimensional Homogeneity | |
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| Equations | |
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| Graphs | |
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| Problems | |
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| Structure of Physical Relations | |
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| Monomial Power Form | |
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| The Dimensional Matrix | |
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| Generating Products of Variables of Desired Dimension | |
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| Number of Independent Sets of Products of Given Dimension (I) | |
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| Completeness of the Set of Products of Variables | |
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| Special Case: Matrix A is Singular | |
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| Number of Independent Sets of Products of Given Dimension (II); Buckingham's Theorem | |
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| Selectable and Nonselectable Dimensions in a Product of Variables | |
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| Minimum Number of Independent Products of Variables of Given Dimension | |
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| Constancy of the Sole Dimensionless Product | |
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| Number of Dimensions Equals or Exceeds the Number of Variables | |
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| Number of Dimensions Equals the Number of Variables | |
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| Number of Dimensions Exceeds the Number of Variables | |
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| Problems | |
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| Systematic Determination of Complete Set of Products of Variables | |
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| Dimensional Set; Derivation of Products of Variables of a Given Dimension | |
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| Checking the Results | |
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| The Fundamental Formula | |
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| Transformations | |
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| Theorems Related to Some Specific Transformations | |
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| Transformation Between Systems of Different D Matrices | |
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| Transformation Between Dimensional Sets | |
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| Independence of Dimensionless Products of the Dimensional System Used | |
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| Number of Sets of Dimensionless Products of Variables | |
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| Distinct and Equivalent Sets | |
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| Changes in a Dimensional Set Not Affecting the Dimensionless Variables | |
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| Prohibited Changes in a Dimensional Set | |
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| Duplications | |
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| Number of Distinct Sets | |
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| Exceptions | |
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| Dimensionally Irrelevant Variable | |
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| In Matrix C, One Row is a Multiple of Another Row | |
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| Problems | |
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| Relevancy of Variables | |
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| Dimensional Irrelevancy | |
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| Condition | |
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| Adding a Dimensionally Irrelevant Variable to a Set of Relevant Variables | |
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| The Cascading Effect | |
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| Physical Irrelevancy | |
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| Condition | |
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| Techniques to Identify a Physically Irrelevant Variable | |
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| Common Sense | |
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| Existence of Dimensional Irrelevancy | |
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| Heuristic Reasoning | |
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| Tests Combined with Deft Interpretation of Results | |
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| Problems | |
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| Economy of Graphical Presentation | |
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| Number of Curves and Charts | |
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| Problems | |
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| Forms of Dimensionless Relations | |
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| General Classification | |
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| Monomial is Mandatory | |
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| Monomial is Impossible-Proven | |
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| Monomial is Impossible-Not Proven | |
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| Reconstructions | |
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| Determination of Exponents of Monomials | |
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| The Measurement Method | |
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| The Analytic Method | |
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| The Heuristic Reasoning Method | |
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| Determination of Some Nonmonomials | |
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| Problems | |
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| Sequence of Variables in the Dimensional Set | |
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| Dimensionless Physical Variable is Present | |
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| Physical Variables of Identical Dimensions are Present | |
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| Independent and Dependent Variables | |
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| Problems | |
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| Alternate Dimensions | |
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| Methods of Reducing the Number of Dimensionless Variables | |
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| Reduction of the Number of Physical Variables | |
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| Fusion of Dimensionless Variables | |
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| Increasing the Number of Dimensions | |
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| Dimension Splitting | |
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| Importation of New Dimensions | |
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| Using Both Mass and Force Dimensions | |
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| Problems | |
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| Dimensional Modeling | |
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| Introductory Remarks | |
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| Homology | |
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| Specific Similarities | |
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| Geometric Similarity | |
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| Kinematic Similarity | |
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| Dynamic Similarity | |
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| Thermal or (Thermic) Similarity | |
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| Dimensional Similarity | |
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| Scale Factors | |
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| Model Law | |
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| Categories and Relations | |
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| Categories | |
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| Relations | |
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| Modeling Data Table | |
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| Scale Effects | |
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| Problems | |
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| Fifty-two Additional Applications | |
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| References | |
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| Numerical Order | |
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| Alphabetical Order of Authors' Surnames | |
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| Appendices | |
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| Recommended Names and Symbols for Some Physical Quantities | |
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| Some More-Important Physical Constants | |
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| Some More-Important Named Dimensionless Variables | |
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| Notes Attached to Figures | |
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| Acronyms | |
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| Solutions of Problems | |
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| Proofs of Selected Theorems and Equations | |
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| Blank Modeling Data Table | |
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| Indices | |
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| Subject Index | |
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| Surname Index | |