SECTION 1: BASIC CONSTANTS, UNITS, AND CONVERSION FACTORS
CODATA
Recommended Values of the Fundamental Physical
Constants: 2010 ............................................... 1-1
Standard Atomic Weights (2013) ............................... 1-11
Atomic Masses and Abundances ................................. 1-13
Electron Configuration and Ionization Energy of Neutral
Atoms in the Ground State .................................... 1-17
International Temperature Scale of 1990 (ITS-90) ............. 1-19
Conversion of Temperatures from the 1948 and 1968 Scales
to ITS-90 .................................................... 1-20
International System of Units (SI) ........................... 1-22
Units for Magnetic Properties ................................ 1-26
Conversion Factors ........................................... 1-27
Conversion of Temperatures ................................... 1-37
Conversion Factors for Energy Units .......................... 1-38
Conversion Factors for Pressure Units ........................ 1-38
Conversion Factors for Thermal Conductivity Units ............ 1-39
Conversion Factors for Electrical Resistivity Units .......... 1-39
Conversion Formulas for Concentration of Solutions ........... 1-40
Descriptive Terms for Solubility ............................. 1-40
Conversion Factors for Chemical Kinetics ..................... 1-41
Conversion Factors for Ionizing Radiation .................... 1-42
Values of the Gas Constant in Different Unit Systems ......... 1-44
SECTION 2: SYMBOLS, TERMINOLOGY, AND NOMENCLATURE
Symbols and Terminology for Physical and Chemical
Quantities .................................................... 2-1
Expression of Uncertainty of Measurements .................... 2-13
Nomenclature for Chemical Compounds .......................... 2-15
Nomenclature for Inorganic Ions and Ligands .................. 2-16
Organic Substituent Groups and Ring Systems .................. 2-23
Representation of Chemical Structures with the IUPAC
International Chemical Identifier (InChI) .................... 2-27
Scientific Abbreviations, Acronyms, and Symbols .............. 2-29
Greek, Russian, and Hebrew Alphabets ......................... 2-43
Definitions of ScientiflcTerms ............................... 2-44
Thermodynamic Functions and Relations ........................ 2-69
Nobel Laureates in Chemistry and Physics ..................... 2-70
SECTION 3: PHYSICAL CONSTANTS OF ORGANIC COMPOUNDS
Physical Constants of Organic Compounds ....................... 3-1
Synonym Index of Organic Compounds .......................... 3-554
Diamagnetic Susceptibility of Selected Organic Compounds .... 3-576
SECTION 4: PROPERTIES OF THE ELEMENTS AND INORGANIC COMPOUNDS
The Elements .................................................. 4-1
Physical Constants of Inorganic Compounds .................... 4-43
Formula Index of Inorganic Compounds ........................ 4-102
Physical Properties of the Rare Earth Metals ................ 4-115
Melting, Boiling, Triple, and Critical Points of the
Elements .................................................... 4-121
Heat Capacity of the Elements at 25 °C ...................... 4-124
Vapor Pressure of the Metallic Elements - Equations ......... 4-125
Vapor Pressure of the Metallic Elements - Data .............. 4-127
Density of Molten Elements and Representative Salts ......... 4-128
Magnetic Susceptibility of the Elements and Inorganic
Compounds ................................................... 4-131
Index of Refraction of Inorganic Liquids .................... 4-137
Physical and Optical Properties of Minerals ................. 4-138
Crystallographic Data on Minerals ........................... 4-145
SECTION 5: THERMOCHEMISTRY, ELECTROCHEMISTRY, AND SOLUTION
CHEMISTRY
CODATA Key Values for Thermodynamics .......................... 5-1
Standard Thermodynamic Properties of Chemical Substances ...... 5-4
Thermodynamic Properties as a Function of Temperature ........ 5-43
Thermodynamic Properties of Aqueous Ions ..................... 5-66
Heat of Combustion ........................................... 5-68
Energy Content of Fuels ...................................... 5-69
Ionization Constant of Water ................................. 5-70
Ionization Constant of Normal and Heavy Water ................ 5-71
Electrical Conductivity of Water ............................. 5-71
Electrical Conductivity of Aqueous Solutions ................. 5-72
Standard KCl Solutions for Calibrating Conductivity
Cells ........................................................ 5-73
Molar Conductivity of Aqueous HF, HCl, HBr, and HI ........... 5-74
Equivalent Conductivity of Electrolytes In Aqueous
Solution ..................................................... 5-75
Ionic Conductivity and Diffusion at Infinite Dilution ........ 5-76
Electrochemical Series ....................................... 5-79
Reduction and Oxidation Potentials for Certain Ion
Radicals ..................................................... 5-89
Dissociation Constants of Inorganic Acids and Bases .......... 5-91
Dissociation Constants of Organic Acids and Bases ............ 5-93
Activity Coefficients of Acids, Bases, and Salts ............ 5-103
Mean Activity Coefficients of Electrolytes as a
Function of Concentration ................................... 5-105
Enthalpy of Dilution of Acids ............................... 5-109
Enthalpy of Solution of Electrolytes ........................ 5-110
Enthalpy of Hydration of Gases .............................. 5-111
pH Scale for Aqueous Solutions .............................. 5-115
Buffer Solutions Giving Round Values of pH at 25°C .......... 5-119
Concentrative Properties of Aqueous Solutions:
Density, Refractive Index, Freezing Point Depression,
and Viscosity ............................................... 5-120
Solubility of Selected Gases in Water ....................... 5-146
Solubility of Carbon Dioxide in Water at Various
Temperatures and Pressures .................................. 5-150
Aqueous Solubility and Henry's Law Constants of Organic
Compounds ................................................... 5-151
Aqueous Solubility of Inorganic Compounds at Various
Temperatures ................................................ 5-187
Octanol-Water Partition Coefficients ........................ 5-193
Solubility Product Constants ................................ 5-198
Solubility of Common Salts at Ambient Temperatures .......... 5-201
Solubility of Hydrocarbons in Seawater ...................... 5-202
Solubility of Organic Compounds in Pressurized Hot
Water ....................................................... 5-204
Solubility Chart ............................................ 5-207
SECTION 6: FLUID PROPERTIES
Thermophysical Properties of Water and Steam .................. 6-1
Vapor Pressure and Other Saturation Properties of Water
Standard Density of Water ..................................... 6-5
Fixed-Point Properties of H20 and D20 ......................... 6-7
Properties of Saturated Liquid D2O ............................ 6-9
Properties of Ice and Supercooled Water ...................... 6-10
Vapor Pressure of Ice ........................................ 6-12
Melting Point of Ice as a Function of Pressure ............... 6-13
Permittivity (Dielectric Constant) of Water at Various
Frequencies .................................................. 6-14
Thermophysical Properties of Air ............................. 6-15
Thermophysical Properties of Fluids .......................... 6-21
Thermophysical Properties of Selected Fluids at
Saturation ................................................... 6-38
Virial Coefficients of Selected Gases ........................ 6-47
Mean Free Path and Related Properties of Gases ............... 6-56
Influence of Pressure on Freezing Points ..................... 6-57
Critical Constants of Organic Compounds ...................... 6-58
Critical Constants of Inorganic Compounds .................... 6-82
Sublimation Pressure of Solids ............................... 6-85
Vapor Pressure ............................................... 6-87
Vapor Pressure of Fluids at Temperatures below 300 К ........ 6-117
Vapor Pressure of Saturated Salt Solutions .................. 6-125
Recommended Data for Vapor-Pressure Calibration ............. 6-126
Enthalpy of Vaporization .................................... 6-127
Enthalpy of Fusion .......................................... 6-145
Compressibility and Expansion Coefficients of Liquids ....... 6-155
Temperature and Pressure Dependence of Liquid Density ....... 6-157
Volumetric Properties of Aqueous Sodium Chloride
Solutions ................................................... 6-162
Properties of Cryogenic Fluids .............................. 6-163
Properties of Liquid Helium ................................. 6-164
Properties of Refrigerants .................................. 6-165
Properties of Gas Clathrate Hydrates ........................ 6-168
Ionic Liquids ............................................... 6-173
Density and Specific Volume of Mercury ...................... 6-177
Thermal Properties of Mercury ............................... 6-178
Melting Curve of Mercury .................................... 6-179
Vapor Pressure of Mercury ................................... 6-180
Surface Tension of Common Liquids ........................... 6-181
Surface Tension of Aqueous Mixtures ......................... 6-185
Permittivity (Dielectric Constant) of Liquids ............... 6-186
Permittivity (Dielectric Constant) of Gases ................. 6-208
Azeotropic Data for Binary Mixtures ......................... 6-209
Viscosity of Gases .......................................... 6-228
Viscosity of Liquids ........................................ 6-230
Viscosity of Carbon Dioxide along the Saturation Line ....... 6-235
Viscosity and Density of Aqueous Hydroxide Solutions ........ 6-236
Viscosity of Liquid Metals .................................. 6-237
Thermal Conductivity of Gases ............................... 6-240
Thermal Conductivity of Liquids ............................. 6-242
Diffusion in Gases .......................................... 6-247
Diffusion of Gases in Water ................................. 6-249
Diffusion Coefficients in Liquids at Infinite Dilution ...... 6-250
SECTION 7: BIOCHEMISTRY
Properties of Amino Acids ..................................... 7-1
Structures of Common Amino Acids .............................. 7-3
Properties of Purine and Pyrimidine Bases ..................... 7-5
The Genetic Code .............................................. 7-6
Properties of Fatty Acids and Their Methyl Esters ............. 7-7
Properties of Fatty Acid Methyl and Ethyl Esters Related
to Biofuels ................................................... 7-9
Composition and Properties of Common Oils and Fats ........... 7-12
Carbohydrate Names and Symbols ............................... 7-17
Standard Transformed Gibbs Energies of Formation for
Biochemical Reactants ........................................ 7-19
Apparent Equilibrium Const&'ts for Enzyme-Catalyzed
Reactions .................................................... 7-22
Thermodynamic Quantities for the Ionization Reactions of
Buffers in Water ............................................. 7-26
Biological Buffers ........................................... 7-29
Typical pH Values of Biological Materials and Foods .......... 7-30
Structure and Functions of Some Common Drugs ................. 7-31
Chemical Constituents of Human Blood ......................... 7-50
Chemical Composition of the Human Body ....................... 7-53
Nutrient Values of Foods ..................................... 7-54
SECTION 8: ANALYTICAL CHEMISTRY
Abbreviations and Symbols Used in Analytical Chemistry ........ 8-1
Basic Instrumental Techniques of Analytical Chemistry ......... 8-6
Analytical Standardization and Calibration .................... 8-9
Figures of Merit ............................................. 8-15
Mass- and Volume-Based Concentration Units ................... 8-16
Detection of Outliers in Measurements ........................ 8-17
Properties of Carrier Gases for Gas Chromatography ........... 8-18
Common Symbols Used in Gas and Liquid Chromatographic
Schematic Diagrams ........................................... 8-19
Stationary Phases for Porous-Layer Open Tubular Columns ...... 8-20
Coolants for Cryotrapping .................................... 8-21
Properties of Common Cross-Linked Silicone Stationary
Phases ....................................................... 8-22
Detectors for Gas Chromatography ............................. 8-23
Varieties of Hyphenated Gas Chromatography with Mass
Spectrometry ................................................. 8-25
Solid-Phase Microextraction Sorbents ......................... 8-27
Gas Chromatographic Retention Indices ........................ 8-30
Eluotropic Values of Solvents on Octadecylsilane and
Octylsilane .................................................. 8-32
Instability of HPLC Solvents ................................. 8-33
Detectors for Liquid Chromatography .......................... 8-34
Solvents for Ultraviolet Spectrophotometry ................... 8-35
Correlation Table for Ultraviolet Active Functionalities ..... 8-36
Wavelength-Wavenumber Conversion Table ....................... 8-39
Middle-Range Infrared Absorption Correlation Charts .......... 8-42
Common Spurious Infrared Absorption Bands .................... 8-48
Nuclear Spins, Moments, and Other Data Related to NMR
Spectroscopy ................................................. 8-49
Properties of Important NMR Nuclei ........................... 8-52
Proton NMR Absorption of Major Chemical Families ............. 8-53
Proton NMR Correlation Chart for Major Organic
Functional Groups ............................................ 8-59
Proton NMR Shifts of Common Organic Solvents ................. 8-60
13C-NMR Absorptions of Major Functional Groups ............... 8-67
13C NMR Chemical Shifts of Common Organic Solvents ........... 8-68
15N-NMR Chemical Shifts of Major Chemical Families ........... 8-69
Natural Abundance of Important Isotopes ...................... 8-71
Common Mass Spectral Fragmentation Patterns of Organic
Compound Families ............................................ 8-72
Common Mass Spectral Fragments Lost .......................... 8-74
Major Reference Masses in the Spectrum of
Heptacosafluorotributylamine (Perfluorotributylamine) ........ 8-75
Mass Spectral Peaks of Common Organic Solvents ............... 8-76
Common Spurious Signals Observed in Mass Spectrometers ....... 8-82
Chlorine-Bromine Combination Isotope Intensities ............. 8-83
Reduction of Weighings in Air to Vacuo ....................... 8-84
Standards for Laboratory Weights ............................. 8-85
Indicators for Acids and Bases ............................... 8-87
Preparation of Special Analytical Reagents ................... 8-88
Organic Analytical Reagents for the Determination of
Inorganic Ions ............................................... 8-93
Precipitation of Sulfides ................................... 8-106
pH Range for Precipitation of Metal Hydroxides and
Oxides ...................................................... 8-107
SECTION 9: MOLECULAR STRUCTURE AND SPECTROSCOPY
Bond Lengths in Crystalline Organic Compounds ................. 9-1
Bond Lengths in Organometallic Compounds ..................... 9-17
Structure of Free Molecules in the Gas Phase ................. 9-19
Characteristic Bond Lengths in Free Molecules ................ 9-48
Atomic Radii of the Elements ................................. 9-49
Dipole Moments ............................................... 9-51
Hindered Internal Rotation ................................... 9-60
Bond Dissociation Energies ................................... 9-65
Electronegativity ............................................ 9-97
Force Constants for Bond Stretching .......................... 9-98
Fundamental Vibrational Frequencies of Small Molecules ....... 9-99
Spectroscopic Constants of Diatomic Molecules ............... 9-102
SECTION 10: ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
Line Spectra of the Elements ................................. 10-1
Atomic Transition Probabilities ............................. 10-93
Electron Affinities ........................................ 10-147
Proton Affinities .......................................... 10-168
Atomic and Molecular Polarizabilities ...................... 10-187
Ionization Energies of Atoms and Atomic Ions ............... 10-197
Ionization Energies of Gas-Phase Molecules ................. 10-200
X-Ray Atomic Energy Levels ................................. 10-218
Electron Binding Energies of the Elements .................. 10-222
Natural Width of X-Ray Lines ............................... 10-228
Photon Attenuation Coefficients ............................ 10-229
Classification of Electromagnetic Radiation ................ 10-234
Sensitivity of the Human Eye to Light of Different
Wavelengths ................................................ 10-236
Blackbody Radiation ........................................ 10-237
Characteristics of Infrared Detectors ...................... 10-239
Index of Refraction of Inorganic Crystals .................. 10-240
Refractive Index and Transmittance of Representative
Glasses .................................................... 10-244
Index of Refraction of Water ............................... 10-245
Index of Refraction of Liquids for Calibration Purposes . 10-246
Index of Refraction of Air ................................. 10-247
Index of Refraction of Gases ............................... 10-248
Characteristics of Laser Sources ........................... 10-249
Infrared Laser Frequencies ................................. 10-255
Infrared and Far-Infrared Absorption Frequency
Standards .................................................. 10-262
SECTION 11: NUCLEAR AND PARTICLE PHYSICS
Summary Tables of Particle Properties ........................ 11-1
Table of the Isotopes ........................................ 11-2
Neutron Scattering and Absorption Properties ............... 11-173
Cosmic Radiation ........................................... 11-186
SECTION 12: PROPERTIES OF SOLIDS
Techniques for Materials Characterization .................... 12-1
Symmetry of Crystals ......................................... 12-5
Ionic Radii in Crystals ..................................... 12-11
Polarizabilities of Atoms and Ions in Solids ................ 12-13
Crystal Structures and Lattice Parameters of Allotropes
of the Elements ............................................. 12-15
Phase Transitions in the Solid Elements at Atmospheric
Pressure .................................................... 12-19
Lattice Energies ............................................ 12-21
The Madelung Constant and Crystal Lattice Energy ............ 12-34
Elastic Constants of Single Crystals ........................ 12-35
Electrical Resistivity of Pure Metals ....................... 12-41
Electrical Resistivity of Selected Alloys ................... 12-43
Electrical Resistivity of Graphite Materials ................ 12-46
Permittivity (Dielectric Constant) of Inorganic Solids ...... 12-47
Curie Temperature of Selected Ferroelectric Crystals ........ 12-56
Properties of Antiferroelectric Crystals .................... 12-57
Dielectric Constants of Glasses ............................. 12-57
Properties of Superconductors ............................... 12-58
High-Temperature Superconductors ............................ 12-74
Organic Superconductors ..................................... 12-76
Properties of Semiconductors ................................ 12-78
Selected Properties of Semiconductor Solid Solutions ........ 12-92
Properties of Organic Semiconductors ........................ 12-94
Diffusion Data for Semiconductors ........................... 12-98
Properties of Magnetic Materials ........................... 12-106
Organic Magnets ............................................ 12-115
Electron Inelastic Mean Free Paths ......................... 12-118
Electron Stopping Powers ................................... 12-120
Electron Work Function of the Elements ..................... 12-122
Secondary Electron Emission ................................ 12-123
Optical Properties of Selected Elements .................... 12-124
Optical Properties of Selected Inorganic and Organic
Solids ..................................................... 12-149
Elasto-Optic, Electro-Optic, and Magneto-Optic
Constants .................................................. 12-168
Nonlinear Optical Constants ................................ 12-182
Phase Diagrams ............................................. 12-185
Properties of Selected Materials at Cryogenic
Temperatures ............................................... 12-203
Heat Capacity of Selected Solids ........................... 12-214
Thermal and Physical Properties of Pure Metals ............. 12-215
Thermophysical Properties of Stainless Steel 310 ........... 12-217
Thermal Conductivity of Metals and Semiconductors as
a Function of Temperature .................................. 12-218
Thermal Conductivity of Alloys as a Function of
Temperature ................................................ 12-220
Thermal Conductivity of Crystalline Dielectrics ............ 12-221
Thermal Conductivity of Ceramics and Other Insulating
Materials .................................................. 12-223
Thermal Conductivity of Glasses ............................ 12-225
Thermoelectric Properties of Metals and Semiconductors ..... 12-229
Fermi Energy and Related Properties of Metals .............. 12-231
Properties of Commercial Metals and Alloys ................. 12-233
Hardness of Minerals and Ceramics .......................... 12-234
SECTION 13: POLYMER PROPERTIES
Abbreviations Used in Polymer Science and Technology ......... 13-1
Physical Properties of Selected Polymers ..................... 13-3
Nomenclature for Organic Polymers ............................ 13-5
Solvents for Common Polymers ................................. 13-9
Glass Transition Temperature for Selected Polymers .......... 13-10
Dielectric Constant of Selected Polymers .................... 13-17
Second Virial Coefficients of Polymer Solutions ............. 13-18
Pressure-Volume-Temperature Relationships for Polymer
Melts ....................................................... 13-21
Upper Critical (UCST) and Lower Critical (LCST) Solution
Temperatures of Binary Polymer Solutions .................... 13-26
Vapor Pressures (Solvent Activities) for Binary Polymer
Solutions ................................................... 13-40
Specific Enthalpies of Solution of Polymers and
Copolymers .................................................. 13-45
Solubility Parameters of Selected Polymers .................. 13-69
SECTION 14: GEOPHYSICS, ASTRONOMY, AND ACOUSTICS
Astronomical Constants ....................................... 14-1
Properties of the Solar System
Satellites of the Planets .................................... 14-2
Interstellar Molecules ....................................... 14-4
Mass, Dimensions, and Other Parameters of the Earth .......... 14-7
Geological Time Scale ....................................... 14-11
Acceleration Due to Gravity ................................. 14-13
Density, Pressure, and Gravity as a Function of Depth
within the Earth ............................................ 14-14
Ocean Pressure as a Function of Depth and Latitude .......... 14-15
Properties of Seawater ...................................... 14-16
Abundance of Elements in the Earth's Crust and in the
Sea ......................................................... 14-18
Solar Irradiance at the Earth ............................... 14-19
U.S. Standard Atmosphere (1976) ............................. 14-20
Geographical and Seasonal Variations in Solar Radiation ..... 14-26
Major World Earthquakes ..................................... 14-27
Weather-Related Scales ...................................... 14-31
Infrared Absorption by the Earth's Atmosphere ............... 14-33
Atmospheric Concentration of Carbon Dioxide, 1958-2014 ...... 14-34
Global Temperature Trend, 1880-2014 ......................... 14-36
Global Warming Potential of Greenhouse Gases ................ 14-37
Atmospheric Electricity ..................................... 14-39
Speed of Sound in Various Media ............................. 14-46
Attenuation and Speed of Sound in Air as a Function of
Humidity and Frequency ...................................... 14-48
Speed of Sound in Dry Air ................................... 14-49
Musical Scales .............................................. 14-50
Characteristics of Human Hearing ............................ 14-51
SECTION 15: PRACTICAL LABORATORY DATA
Standard ITS-90 Thermocouple Tables .......................... 15-1
Reference Points on the ITS-90 Temperature Scale ............ 15-10
Relative Sensitivity of Bayard-Alpert Ionization Gauges
to Various Gases ............................................ 15-12
Laboratory Solvents and Other Liquid Reagents ............... 15-13
Miscibility of Organic Solvents ............................. 15-23
Density of Solvents as a Function of Temperature ............ 15-25
Dependence of Boiling Point on Pressure ..................... 15-26
EbuIIioscopic Constants for Calculation of Boiling Point
Elevation ................................................... 15-27
Cryoscopic Constants for Calculation of Freezing Point
Depression .................................................. 15-28
Freezing Point Lowering by Electrolytes in Aqueous
Solution .................................................... 15-28
Correction of Barometer Readings to 0 "C Temperature ........ 15-29
Determination of Relative Humidity from Dew Point ........... 15-30
Determination of Relative Humidity from Wet and Dry Bulb
Temperatures ................................................ 15-31
Constant Humidity Solutions ................................. 15-32
Standard Salt Solutions for Humidity Calibration ............ 15-33
Low-Temperature Baths for Maintaining Constant
Temperature ................................................. 15-33
Metals and Alloys with Low Melting Temperature .............. 15-34
Wire Tables ................................................. 15-35
Standard Fittings for Compressed Gas Cylinders .............. 15-36
Plug and Outlet Configurations for Common Laboratory
Devices ..................................................... 15-38
Characteristics of Particles and Particle Dispersoids ....... 15-39
Density of Various Solids ................................... 15-40
Density of Sulfuric Acid .................................... 15-41
Density of Ethanol-Water Mixtures ........................... 15-43
Dielectric Strength of Insulating Materials ................. 15-44
Coefficient of Friction ..................................... 15-49
Flame Temperatures .......................................... 15-51
Allocation of Frequencies in the Radio Spectrum ............. 15-52
SECTION 16: HEALTH AND SAFETY INFORMATION
Abbreviations Used in the Assessment and Presentation of
Laboratory Hazards ........................................... 16-1
Incompatible Chemicals ....................................... 16-2
Explosion (Shock) Hazards .................................... 16-4
Water-Reactive Chemicals ..................................... 16-5
Testing Requirements for Peroxidizable Compounds ............. 16-5
Tests for the Presence of Peroxides .......................... 16-6
Pyrophoric Compounds - Compounds That Are Reactive with
Air .......................................................... 16-6
Flammability Hazards of Common Solvents ...................... 16-7
Selection of Laboratory Gloves ............................... 16-9
Selection of Protective Laboratory Garments .................. 16-9
Selection of Respirator Cartridges and Filters .............. 16-10
Materials Compatible with and Resistant to 72 Percent
Perchloric Acid ............................................. 16-11
Protective Clothing Levels .................................. 16-12
Chemical Fume Hoods and Biological Safety Cabinets .......... 16-13
Cylinder Safety and Stamped Markings ........................ 16-15
Flammability of Chemical Substances ......................... 16-16
Threshold Limits for Airborne Contaminants .................. 16-32
Laser Hazards in the Laboratory ............................. 16-45
General Characteristics of Ionizing Radiation for the
Purpose of Practical Application of Radiation Protection .... 16-47
Radiation Safety Units ...................................... 16-48
Relative Dose Ranges from Ionizing Radiation ................ 16-50
Annual Limits on Intakes of Radionuclides ................... 16-51
Chemical Carcinogens ........................................ 16-55
APPENDIX A: MATHEMATICAL TABLES
1 Constants .................................................. A-2
1.1 Decimal Equivalents of Fractions (inches to mm) ....... A-2
1.2 Exponential and Hyperbolic Functions and their
Common Logarithms ..................................... A-3
1.3 Trigonometric Functions to Four Decimal Places ........ A-4
2 Algebra .................................................... A-5
2.1 Quadratic Formula ..................................... A-5
2.2 Vector Algebra ........................................ A-5
2.2.1 Definitions .................................... A-5
2.2.2 Vectors in Space ............................... A-5
2.2.3 The Scalar, Dot, or Inner Product of Two
Vectors ........................................ A-6
2.2.4 The Vector or Cross Product of Two Vectors ..... A-6
2.2.5 Scalar Triple Product .......................... A-6
2.2.6 Vector Triple Product .......................... A-7
3 Geometry ................................................... A-7
3.1 Geometry of the Plane, Straight Line, and Sphere ...... A-7
3.2 Geometry of Curves in Space ........................... A-9
4 Trigonometry .............................................. A-10
4.1 Trigonometric Functions in Terms of One Another ...... A-10
4.2 Hyperbolic Functions in Terms of One Another ......... A-10
5 Calculus .................................................. A-11
5.1 Differentiation ...................................... A-11
5.1.1 Differentiation Formulas ...................... A-ll
5.1.2 Derivatives of Common Functions ............... A-12
5.1.3 Vector Operations ............................. A-12
5.2 Orthogonal Coordinate Systems ........................ A-14
5.3 Integration .......................................... A-16
5.3.1 Integration Examples .......................... A-16
5.3.2 Transformation of Integrals ................... A-18
5.3.3 Table of Integrals ............................ A-19
5.4 Differential Equations ............................... A-45
5.4.1 Linear Differential Equations ................. A-45
5.4.2 Second Order Linear Constant Coefficient
Equation ...................................... A-45
5.4.1 Homogeneous Solutions of Higher Order
Constant Coefficient Equations ................ A-46
5.4.4 Particular Solutions .......................... A-46
5.4.5 Differential Equation Solution Techniques .......... A-48
6 Series .................................................... A-49
6.1 Fourier Series ....................................... A-49
6.2 Binomial Series ...................................... A-52
6.3 Reversion of Series .................................. A-52
6.4 Taylor Series ........................................ A-52
6.5 Exponential Series ................................... A-53
6.6 Logarithmic Series ................................... A-53
6.7 Trigonometric Series ................................. A-54
7 Transforms ................................................ A-54
7.1 Fourier Transforms ................................... A-54
7.2 Table of Fourier Cosine Transforms ................... A-55
7.3 Table of Finite Cosine Transforms .................... A-56
7.4 Table of Fourier Sine Transforms ..................... A-56
7.5 Table of Finite Sine Transforms ...................... A-57
7.6 Table of Fourier Transforms .......................... A-57
7.7 Table of Functional Relations for Fourier Transforms . A-58
7.8 Table of Multidimensional Fourier Transforms ......... A-59
7.9 Table of Laplace Transforms .......................... A-59
7.10 Table of Functional Relations for Laplace Transforms . A-62
8 Special Functions ......................................... A-62
8.1 Orthogonal Polynomials ............................... A-62
8.2 Tables of Orthogonal Polynomials ..................... A-65
8.3 Bessel Functions ..................................... A-66
8.4 Factorial Function ................................... A-68
8.5 Gamma Function ....................................... A-68
8.6 Beta Function ........................................ A-69
8.7 Error Function ....................................... A-69
9 Probability ............................................... A-70
9.1 Normal Probability Function .......................... A-70
9.2 Confidence Intervals ................................. A-71
9.3 Percentage Pointe, Student's t-Distribution .......... A-72
9.4 Percentage Points, Chi-Square Distribution ........... A-73
9.5 Percentage Points, F-Distribution .................... A-74
10 Physics Related .......................................... A-76
10.1 Clebsch-Gordan Coefficients .......................... A-76
10.2 Moment of Inertial for Different Shapes .............. A-78
APPENDIX B: SOURCES OF PHYSICAL AND CHEMICAL DATA ............. B-l
INDEX ......................................................... I-l
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