Front Cover -- Applied Dimensional Analysis and Modeling -- Copyright Page -- Contents -- List of Titled Examples and Problems -- Foreword to the First Edition -- Foreword to the Second Edition -- Acknowledgments -- Preface to the First Edition -- Preface to the Second Edition -- Organization, Notation, and Conventions -- Chapter 1. Mathematical Preliminaries -- 1.1. Matrices and Determinants -- 1.2. Operations with Matrices -- 1.3. The Rank of a Matrix -- 1.4. Systems of Linear Equations -- 1.5. List of Selected Publications Dealing with Linear Algebra and Matrices -- Chapter 2. Formats and Classification -- 2.1. Formats for Physical Relations -- 2.2. Classification of Physical Quantities -- Chapter 3. Dimensional Systems -- 3.1. General Statements -- 3.2. Classification -- 3.3. The SI -- 3.4. Other Than SI Dimensional Systems -- 3.5. A Note on the Classification of Dimensional Systems -- Chapter 4. Transformation of Dimensions -- 4.1. Numerical Equivalences -- 4.2. Technique -- 4.3. Examples -- 4.4. Problems -- Chapter 5. Arithmetic of Dimensions -- Chapter 6. Dimensional Homogeneity -- 6.1. Equations -- 6.2. Graphs -- 6.3. Problems -- Chapter 7. Structure of Physical Relations -- 7.1. Monomial Power Form -- 7.2. The Dimensional Matrix -- 7.3. Generating Products of Variables of Desired Dimension -- 7.4. Number of Independent Sets of Products of Given Dimension (I) -- 7.5. Completeness of the Set of Products of Variables -- 7.6. Special Case: Matrix A is Singular -- 7.7. Number of Independent Sets of Products of Given Dimension (II) -- Buckingham's Theorem -- 7.8. Selectable and Nonselectable Dimensions in a Product of Variables -- 7.9. Minimum Number of Independent Products of Variables of Given Dimension -- 7.10. Constancy of the Sole Dimensionless Product -- 7.11. Number of Dimensions Equals or Exceeds the Number of Variables.

7.12. Problems -- Chapter 8. Systematic Determination of Complete Set of Products of Variables -- 8.1. Dimensional Set -- Derivation of Products of Variables of a Given Dimension -- 8.2. Checking the Results -- 8.3. The Fundamental Formula -- Chapter 9. Transformations -- 9.1. Theorems Related to Some Specific Transformations -- 9.2. Transformation Between Systems of Different Matrics -- 9.3. Transformation Between Dimensional Sets -- 9.4. Independence of Dimensionless Products of the Dimensional System Used -- Chapter 10. Number of Sets of Dimensionless Products of Variables -- 10.1. Distinct and Equivalent Sets -- 10.2. Changes in a Dimensional Set Not Affecting the Dimensionless Variables -- 10.3. Prohibited Changes in a Dimensional Set -- 10.4. Number of Distinct Sets -- 10.5. Exceptions -- 10.6. Problems -- Chapter 11. Relevancy of Variables -- 11.1. Dimensional Irrelevancy -- 11.2. Physical Irrelevancy -- 11.3. Problems -- Chapter 12. Economy of Graphical Presentation -- 12.1. Number of Curves and Charts -- 12.2. Problems -- Chapter 13. Forms of Dimensionless Relations -- 13.1. General Classification -- 13.2. Monomial is Mandatory -- 13.3. Monomial is Impossible-Proven -- 13.4. Monomial is Impossible- Not Proven -- 13.5. Reconstructions -- 13.6. Problems -- Chapter 14. Sequence of Variables in the Dimensional Set -- 14.1. Dimensionless Physical Variable is Present -- 14.2. Physical Variables of Identical Dimensions are Present -- 14.3. Independent and Dependent Variables -- 14.4. Problems -- Chapter 15. Alternate Dimensions -- Chapter 16. Methods of Reducing the Number of Dimensionless Variables -- 16.1. Reduction of the Number of Physical Variables -- 16.2. Fusion of Dimensionless Variables -- 16.3. Increasing the Number of Dimensions -- 16.4. Problems -- Chapter 17. Dimensional Modeling -- 17.1. Introductory Remarks -- 17.2. Homology.

17.3. Specific Similarities -- 17.4. Dimensional Similarity -- 17.5. Scale Effects -- 17.6. Problems -- Chapter 18. Fifty-two Additional Applications -- References: -- Numerical Order -- Alphabetical Order of Authors' Surnames -- Appendices: -- Appendix 1: Recommended Names and Symbols for Some Physical Quantities -- Appendix 2: Some More-Important Physical Constants -- Appendix 3: Some More-Important Named Dimensionless Variables -- Appendix 4: Notes Attached to Figures -- Appendix 5: Acronyms -- Appendix 6: Solutions of Problems -- Appendix 7: Proofs of Selected Theorems and Equations -- Appendix 8: Blank Modeling Data Table -- Indixes -- Subject Index -- Surname Index.