Maple 9 Learning Guide - Maplesoft

Contents • viiLast-Name Evaluation . . . . . . . . . . . . . . . . . . . . 203One-Level Evaluation . . . . . . . . . . . . . . . . . . . . 205Commands with Special Evaluation Rules . . . . . . . . . 206Quotation and Unevaluation . . . . . . . . . . . . . . . . . 207Using Quoted Variables as Function Arguments . . . . . . 210Concatenation of Names . . . . . . . . . . . . . . . . . . . 2116.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 2137 Solving Calculus Problems 215In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 2157.1 Introductory Calculus . . . . . . . . . . . . . . . . . . . . 215The Derivative . . . . . . . . . . . . . . . . . . . . . . . . 215A Taylor Approximation . . . . . . . . . . . . . . . . . . . 221The Integral . . . . . . . . . . . . . . . . . . . . . . . . . . 232Mixed Partial Derivatives . . . . . . . . . . . . . . . . . . 2367.2 Ordinary Differential Equations . . . . . . . . . . . . . . . 240The dsolve Command . . . . . . . . . . . . . . . . . . . . 241Example: Taylor Series . . . . . . . . . . . . . . . . . . . . 255When You Cannot Find a Closed Form Solution . . . . . 259Plotting Ordinary Differential Equations . . . . . . . . . . 260Discontinuous Forcing Functions . . . . . . . . . . . . . . 264Interactive ODE Analyzer . . . . . . . . . . . . . . . . . . 2697.3 Partial Differential Equations . . . . . . . . . . . . . . . . 270The pdsolve Command . . . . . . . . . . . . . . . . . . . 270Changing the Dependent Variable in a PDE . . . . . . . . 272Plotting Partial Differential Equations . . . . . . . . . . . 2737.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 2768 Input and Output 277In This Chapter . . . . . . . . . . . . . . . . . . . . . . . 2778.1 Reading Files . . . . . . . . . . . . . . . . . . . . . . . . . 277Reading Columns of Numbers from a File . . . . . . . . . 278Reading Commands from a File . . . . . . . . . . . . . . . 2808.2 Writing Data to a File . . . . . . . . . . . . . . . . . . . . 281Writing Columns of Numerical Data to a File . . . . . . . 281Saving Expressions in the Maple Internal Format . . . . . 283Converting to L A TEX Format . . . . . . . . . . . . . . . . . 2848.3 Exporting Worksheets . . . . . . . . . . . . . . . . . . . . 286HTML and HTML with MathML . . . . . . . . . . . . . . 286L A TEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289Maple Input . . . . . . . . . . . . . . . . . . . . . . . . . . 291