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1 The Basics: Mathematical Functions, Rearranging Equations and Handling Units |
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3 | (32) |
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1.1 Reversible Reactions, Reversible Mathematics |
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3 | (2) |
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1.2 An Introduction to Mathematical Operations |
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5 | (10) |
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1.3 Treating Both Sides Fairly: The Nature of Equality |
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15 | (4) |
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19 | (6) |
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1.5 Interconvertirig Units |
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25 | (2) |
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27 | (8) |
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2 Probability and Statistics in Chemistry |
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35 | (28) |
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2.1 Probability In Chemical Kinetics |
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36 | (1) |
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2.2 Flipping Coins, Riling Reactions |
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37 | (12) |
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2.3 Standard Distributions and Standard Deviations |
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49 | (9) |
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58 | (5) |
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3 Experimental Uncertainty and Significant |
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63 | (40) |
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3.1 Figures: What Are the Bounds of Experimental Error? |
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63 | (3) |
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3.2 Managing Significant Figures |
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66 | (8) |
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74 | (3) |
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3.4 Combining Uncertainties |
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77 | (8) |
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3.5 Identifying Outliers in a Single Data Series |
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85 | (4) |
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3.6 Comparing Data Series-Student's t Test |
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89 | (5) |
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94 | (9) |
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4 Tables and Graphs -- Presenting and Analysing Experimental Data |
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103 | (28) |
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103 | (3) |
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4.2 Straight-line Graphs: `y = mx + c' |
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106 | (6) |
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4.3 Determining Gradients and Intercepts |
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112 | (3) |
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4.4 Uncertainties In Straight-line Graphs |
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115 | (3) |
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4.5 Plotting Experimental Data |
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118 | (3) |
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121 | (10) |
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5 Trigonometry and Coordinate Systems: Describing Molecular Positions |
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131 | (30) |
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5.1 Determination of Molecular Distances |
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131 | (11) |
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5.2 Molecular Geometry: Molecular Spectroscopy |
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142 | (4) |
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146 | (8) |
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154 | (7) |
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6 Vectors, Directions and Crystal Structures |
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161 | (24) |
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6.1 A Brief Introduction to the Vector |
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161 | (2) |
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6.2 Two (and Higher) Dimensional Vectors |
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163 | (2) |
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6.3 Vector Addition, Subtraction and Scaling |
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165 | (4) |
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6.4 Vector Multiplication: Work Done and Torque |
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169 | (10) |
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6.5 Vectors In Crystallography |
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179 | (2) |
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181 | (4) |
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7 Calculus 1, Differentiation: Mean Speeds and Equilibrium Separations |
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185 | (38) |
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185 | (10) |
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7.2 Differentiating Special Functions |
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195 | (3) |
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7.3 Finding the Maximum and the Minimum |
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198 | (5) |
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7.4 More Advanced Differentiation |
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203 | (7) |
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7.5 Partial Differentiation of Multiple Variables |
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210 | (3) |
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213 | (10) |
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8 Calculus 2, Integration: Reaction Kinetics and Rate Laws |
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223 | (38) |
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8.1 The Need for an Inverse Function |
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223 | (1) |
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8.2 Integration-Exploring the Harmonic Oscillator |
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224 | (6) |
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8.3 Chemical Kinetics-Determining the Rate Law |
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230 | (5) |
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8.4 Calculating Thermodynamic Work |
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235 | (10) |
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8.5 Integration In Context |
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245 | (9) |
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254 | (7) |
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9 Complex Numbers: Quantum Mechanics and Solving the Schrodinger Equation |
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261 | (27) |
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9.1 Complex Numbers in Chemistry |
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261 | (2) |
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9.2 Introduction to Complex Numbers |
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263 | (3) |
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9.3 Arithmetic With Complex Numbers |
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266 | (3) |
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9.4 Alternative Representations of Complex Numbers |
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269 | (5) |
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9.5 Complex Numbers and Wave Functions |
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274 | (3) |
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277 | (11) |
| Appendix: The Mathematical Toolkit |
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288 | (13) |
| Reading List |
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301 | (1) |
| Index |
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302 | |