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<p>Preface xiii</p> <p><b>1 Fundamentals </b><b>1</b></p> <p>1.1 Getting Started With wxMaxima 1</p> <p>1.1.1 Input Cells 2</p> <p>1.1.2 The Toolbar 3</p> <p>1.1.3 The Menus 3</p> <p>1.1.4 Command History 4</p> <p>1.1.5 Basic Arithmetic 5</p> <p>1.1.6 Mathematical Functions 7</p> <p>1.1.7 Assigning Variables 8</p> <p>1.1.8 Defining Functions 10</p> <p>1.1.9 Comments, Images, and Sectioning 12</p> <p>1.2 A Tour of the General Math Pane 12</p> <p>1.2.1 Basic Plotting 13</p> <p>1.2.1.1 Plotting Multiple Curves 14</p> <p>1.2.1.2 Parametric Plots 15</p> <p>1.2.1.3 Discrete Plots 15</p> <p>1.2.1.4 Three-Dimensional Plots 17</p> <p>1.2.2 Basic Algebra 18</p> <p>1.2.2.1 Equations 18</p> <p>1.2.2.2 Substitutions 18</p> <p>1.2.2.3 Simplification 20</p> <p>1.2.2.4 Solving Equations 21</p> <p>1.2.2.5 Simplifying Trigonometric and Exponential Functions 21</p> <p>1.2.3 Basic Calculus 22</p> <p>1.2.3.1 Limits 22</p> <p>1.2.3.2 Differentiation 23</p> <p>1.2.3.3 Series 24</p> <p>1.2.3.4 Integration 25</p> <p>1.2.4 Differential Equations 28</p> <p>1.3 Controlling Execution 28</p> <p>1.4 Using Packages 30</p> <p><b>2 Storing and Transforming Data </b><b>33</b></p> <p>2.1 Numbers 33</p> <p>2.1.1 Floating Point Numbers 33</p> <p>2.1.2 Integers and Rational Numbers 37</p> <p>2.1.3 Complex Numbers 38</p> <p>2.1.4 Constants 42</p> <p>2.1.5 Units and Physical Constants 43</p> <p>2.2 Boolean Expressions and Predicates 47</p> <p>2.2.1 Relational Operators 47</p> <p>2.2.2 Logical Operators 48</p> <p>2.2.3 Predicates 49</p> <p>2.3 Lists 51</p> <p>2.3.1 List Assignments 51</p> <p>2.3.2 Indexing List Items 52</p> <p>2.3.3 Arithmetic with Lists 52</p> <p>2.3.4 Building and Editing Lists 54</p> <p>2.3.4.1 Adding Items 54</p> <p>2.3.4.2 Deleting Items 55</p> <p>2.3.5 Nested Lists 55</p> <p>2.3.6 Sublists 56</p> <p>2.4 Matrices 57</p> <p>2.4.1 Row and Column Vectors 57</p> <p>2.4.2 Indexing Matrices 58</p> <p>2.4.3 Entering Matrices 59</p> <p>2.4.4 Assigning Matrices 60</p> <p>2.4.5 Editing Matrices 61</p> <p>2.4.6 Reading and Writing Matrices From Files 63</p> <p>2.4.7 Transforming Data in a Matrix 65</p> <p>2.5 Strings 66</p> <p>2.5.1 Using String Functions toWork with Files 67</p> <p><b>3 Plotting Data and Functions </b><b>71</b></p> <p>3.1 Plotting in Two Dimensions 71</p> <p>3.1.1 Changing Plot Size and Resolution 71</p> <p>3.1.2 Plotting Multiple Curves 73</p> <p>3.1.3 Changing Axis Ranges 74</p> <p>3.1.4 Plotting Complex Functions 74</p> <p>3.1.5 Plotting Data 74</p> <p>3.1.5.1 Plotting Data in Separate X, Y Lists 75</p> <p>3.1.5.2 Plotting Data as Lists of X, Y Points 75</p> <p>3.1.5.3 Plotting Data in Matrices 76</p> <p>3.1.5.4 Plotting Data with Units 76</p> <p>3.1.5.5 Plotting Functions and Data Together 77</p> <p>3.1.6 Adding Text Labels to Graphs 77</p> <p>3.1.7 Plotting Rapidly Rising Functions 78</p> <p>3.1.7.1 Solving Axis Scaling Problems 81</p> <p>3.1.7.2 Positioning the Legend 83</p> <p>3.1.8 Parametric Plots 84</p> <p>3.1.9 Implicit Plots 87</p> <p>3.1.10 Histograms 89</p> <p>3.2 Plotting inThree Dimensions 91</p> <p>3.2.1 Plotting Functions of x, y, andz 91</p> <p>3.2.2 Plotting Multiple Surfaces 93</p> <p>3.2.3 Plotting in Spherical Coordinates 94</p> <p>3.2.4 Plotting in Cylindrical Coordinates 95</p> <p>3.2.5 Parametric Surface Plots 96</p> <p>3.2.6 Plotting DiscreteThree-Dimensional Data 98</p> <p>3.2.7 Contour Plotting 99</p> <p><b>4 Programming Maxima </b><b>103</b></p> <p>4.1 Nouns and Verbs 103</p> <p>4.2 Writing Multiline Functions 106</p> <p>4.3 Decision Making 108</p> <p>4.4 Recursive Functions 109</p> <p>4.5 Contexts 110</p> <p>4.6 Iteration 114</p> <p>4.6.1 Indexed Loops 114</p> <p>4.6.2 Conditional Loops 116</p> <p>4.6.3 Looping Over Lists 117</p> <p>4.6.4 Nested Loops 118</p> <p><b>5 Algebra </b><b>119</b></p> <p>5.1 Series 119</p> <p>5.1.1 Simplifying Sums 120</p> <p>5.1.2 Reindexing and Combining Sums 122</p> <p>5.1.3 Applying Functions to Sums and Products 123</p> <p>5.2 Products 124</p> <p>5.3 Equations 126</p> <p>5.3.1 Simplifying Equations 126</p> <p>5.3.2 Simplifying Trigonometric and Exponential Functions 127</p> <p>5.3.3 Extracting Expressions From an Equation 128</p> <p>5.3.4 Expanding Expressions 131</p> <p>5.3.5 Factoring Expressions 134</p> <p>5.3.6 Substitution 135</p> <p>5.3.7 Solving an Equation Symbolically 138</p> <p>5.3.7.1 Handling Multiple Solutions 139</p> <p>5.3.8 Solving an Equation Numerically 140</p> <p>5.4 Systems of Equations 141</p> <p>5.4.1 Eliminating Variables 141</p> <p>5.4.2 Solving Systems of EquationsWithout Elimination 143</p> <p>5.5 Interpolation 144</p> <p>5.5.1 Piecewise Linear Interpolation 146</p> <p>5.5.2 Spline Interpolation 147</p> <p><b>6 Differentiation, Integration, and Minimization </b><b>149</b></p> <p>6.1.1 Limits for Discontinuous Functions 151</p> <p>6.1.2 Limits for Indefinite Functions 152</p> <p>6.2 Differentials 153</p> <p>6.3 Derivatives 154</p> <p>6.3.1 Explicit Partial and Total Derivatives 156</p> <p>6.3.2 Derivatives Evaluated at a Specific Point 157</p> <p>6.3.3 Higher-Order Derivatives 158</p> <p>6.3.4 Mixed Derivatives 159</p> <p>6.3.5 Assigning Partial Derivatives 160</p> <p>6.3.5.1 Partial Derivatives from Total Differential Expansions 161</p> <p>6.3.5.2 Writing Total Differential Expansions in Terms of New Variables 161</p> <p>6.3.6 Implicit Differentiation 162</p> <p>6.4 Maxima, Minima, and Inflection Points 164</p> <p>6.4.1 Critical Points of Surfaces 167</p> <p>6.4.2 Numerical Minimization 169</p> <p>6.5 Integration 173</p> <p>6.5.1 Integration Constants 174</p> <p>6.5.2 Definite Integration 174</p> <p>6.5.3 When Symbolic Integration Fails 175</p> <p>6.5.4 Numerical Integration 178</p> <p>6.5.4.1 Numerical Integration over Infinite Intervals 179</p> <p>6.5.4.2 Numerical Integration with Strongly Oscillating Integrands 180</p> <p>6.5.4.3 Numerical Integration with Discontinuous Integrands 181</p> <p>6.5.5 Multiple Integration 182</p> <p>6.5.6 Discrete Integration 183</p> <p>6.6 Power Series 186</p> <p>6.6.1 Testing Power Series for Convergence 186</p> <p>6.7 Taylor Series 187</p> <p>6.7.1 Exploring Function Properties with Taylor Series 188</p> <p>6.7.2 The Remainder Term 190</p> <p>6.7.3 Taylor Series for Multivariate Functions 191</p> <p>6.7.4 Approximating Taylor Series 191</p> <p><b>7 Matrices and Vectors </b><b>193</b></p> <p>7.1 Vectors 193</p> <p>7.1.1 Vector Arithmetic 194</p> <p>7.1.2 The Dot Product 195</p> <p>7.1.3 Vector Lengths and Angles 196</p> <p>7.1.4 The Cross Product 197</p> <p>7.1.5 Angular Momentum 198</p> <p>7.1.6 Vector Algebra 199</p> <p>7.2 Matrices 200</p> <p>7.2.1 Matrix Arithmetic 201</p> <p>7.2.2 The Transpose 201</p> <p>7.2.3 The Matrix Product 202</p> <p>7.2.4 Determinants 203</p> <p>7.2.5 The Inverse of a Matrix 206</p> <p>7.2.6 Matrix Algebra 207</p> <p>7.2.7 Eigenvalues and Eigenvectors 211</p> <p>7.2.7.1 Application: Energies and Molecular Orbitals of Ethylene 212</p> <p>7.2.7.2 Eigenvalues and Eigenvectors for Symmetric Matrices 214</p> <p>7.2.7.3 Matrix Diagonalization 216</p> <p>7.3 Vector Calculus 217</p> <p>7.3.1 Derivative of a Vector with Respect to a Scalar 217</p> <p>7.3.2 The Jacobian 218</p> <p>7.3.3 The Gradient 220</p> <p>7.3.4 The Laplacian 222</p> <p>7.3.5 The Divergence 224</p> <p>7.3.6 The Curl 225</p> <p><b>8 Error Analysis </b><b>227</b></p> <p>8.1 Classifying Experimental Errors 227</p> <p>8.1.1 Systematic Error 229</p> <p>8.1.2 Random Error 230</p> <p>8.2 Probability Density 230</p> <p>8.2.1 Discrete Probability Distributions 230</p> <p>8.2.2 The Poisson Distribution 232</p> <p>8.2.3 Continuous Probability Distributions 235</p> <p>8.2.4 The Normal Distribution 236</p> <p>8.3 Estimating Precision 238</p> <p>8.3.1 Standard Error of the Mean 240</p> <p>8.3.2 Confidence Interval of the Mean 240</p> <p>8.4 Hypothesis Testing 241</p> <p>8.4.1 Comparing a Mean with a True Value 243</p> <p>8.4.2 Comparing Variances 244</p> <p>8.4.3 Comparing Two Sample Means 246</p> <p>8.5 Propagation of Error 249</p> <p>8.5.1 Propagation of Independent Systematic Errors 249</p> <p>8.5.2 Propagation of Independent Random Errors 251</p> <p>8.5.3 Covariance and Correlation 253</p> <p><b>9 Fitting Data to a Straight Line </b><b>257</b></p> <p>9.1 The Ordinary Least-Squares Method 259</p> <p>9.1.1 Using Built-In Functions 260</p> <p>9.1.2 Error Estimates for the Slope and the Intercept 263</p> <p>9.1.3 The Determination Coefficient 266</p> <p>9.1.4 Residual Analysis 268</p> <p>9.1.5 Testing the Fit Parameters 271</p> <p>9.1.6 Testing for Lack-of-Fit 272</p> <p>9.2 Multiple Linear Regression 274</p> <p>9.2.1 Matrix Form of Multiple Linear Regression 275</p> <p>9.2.2 Estimating the Errors in the Fit Parameters in MLR 277</p> <p>9.2.3 Example: Microwave Rotational Spectrum of HCl 278</p> <p>9.2.4 Detecting and Dealing with Outliers 281</p> <p>9.3 WLS 285</p> <p>9.3.1 The Fit Parameters inWLS 286</p> <p>9.3.2 Error Estimates for theWLS Fit Parameters 286</p> <p>9.3.3 Finding theWeights 287</p> <p>9.3.4 Residual Analysis inWLS 288</p> <p>9.3.5 Evaluating Goodness-of-Fit 288</p> <p>9.4 Fitting Data to a Line with Errors in Both X and Y 289</p> <p>9.4.1 Finding Fit Parameters in TLS 290</p> <p>9.4.2 Error Estimates for the TLS Fit Parameters 292</p> <p>9.4.3 Assessing Goodness-of-Fit in TLS 293</p> <p>9.4.4 Multiple Linear Regression with TLS 293</p> <p>9.5 Calibration and Standard Additions 294</p> <p>9.5.1 Error Estimates for Calibrated Values 294</p> <p>9.5.2 Standard Additions 295</p> <p><b>10 Fitting Data to a Curve </b><b>299</b></p> <p>10.1 Transforming Data to a Linear Form 299</p> <p>10.2 Polynomial Least-Squares Fitting 302</p> <p>10.2.1 How Many Fit Parameters Are Needed? 304</p> <p>10.3 Nonlinear Least-Squares Models 306</p> <p>10.4 Estimating Error in Nonlinear Fit Parameters 310</p> <p>10.4.1 Estimating Parameter Errors with the Jackknife Method 311</p> <p>10.4.2 Estimating Parameter Errors with the Bootstrap Method 313</p> <p><b>11 Differential Equations </b><b>317</b></p> <p>11.1 Symbolic Solutions of ODEs 318</p> <p>11.1.1 Initial Value Problems 320</p> <p>11.1.2 Boundary Value Problems 322</p> <p>11.2 Power Series Solution of ODEs 325</p> <p>11.3 Direction Fields 329</p> <p>11.3.1 Direction Fields with Adjustable Parameters 331</p> <p>11.3.2 Direction Fields and Autonomous Equations 332</p> <p>11.4 Solving Systems of Linear Differential Equations 335</p> <p>11.5 Numerical Solution of ODEs 338</p> <p>11.6 Solving Partial Differential Equations 340</p> <p><b>12 Operators and Integral Transforms </b><b>343</b></p> <p>12.1 Defining Operators 344</p> <p>12.2 Fourier Series 347</p> <p>12.3 Fourier Transforms 351</p> <p>12.3.1 The Fast Fourier Transform 355</p> <p>12.4 The Laplace Transform 357</p> <p>Glossary 359</p> <p>References 367</p> <p>Index 371</p>

<p> <p><b>Professor Fred Senese</b> is a computational chemist at Frostburg State University with a particular focus on chemical education. His research interests include applications of artificial intelligence in chemical education, development of web-based narratives and construction kits for chemical education, remote control and access of instrumentation, and environmental chemical analysis applied to problems in ethnobotany.

<p><b>An essential guide to using Maxima, a popular open source symbolic mathematics engine to solve problems, build models, analyze data and explore fundamental concepts</b> <p><i>Symbolic Mathematics for Chemists</i> offers students of chemistry a guide to Maxima, a popular open source symbolic mathematics engine that can be used to solve problems, build models, analyze data, and explore fundamental chemistry concepts. The author — a noted expert in the field — focuses on the analysis of experimental data obtained in a laboratory setting and the fitting of data and modeling experiments. The text contains a wide variety of illustrative examples and applications in physical chemistry, quantitative analysis and instrumental techniques. <p>Designed as a practical resource, the book is organized around a series of worksheets that are provided in a companion website. Each worksheet has clearly defined goals and learning objectives and a detailed abstract that provides motivation and context for the material. This important resource: <ul> <li>Offers an text that shows how to use popular symbolic mathematics engines to solve problems</li> <li>Includes a series of worksheet that are prepared in Maxima</li> <li>Contains step-by-step instructions written in clear terms and includes illustrative examples to enhance critical thinking, creative problem solving and the ability to connect concepts in chemistry</li> <li>Offers hints and case studies that help to master the basics while proficient users are offered more advanced avenues for exploration</li> </ul> <p>Written for advanced undergraduate and graduate students in chemistry and instructors looking to enhance their lecture or lab course with symbolic mathematics materials,<i>Symbolic Mathematics for Chemists: A Guide for Maxima Users</i> is an essential resource for solving and exploring quantitative problems in chemistry.

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