factored normal form

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Unformatted text preview: . Factored Normal Form . . . . . . . . . . . . . . Simplifying Expressions . . . . . . . . . . . . . Simplification with Assumptions . . . . . . . . Simplification with Side Relations . . . . . . . . Sorting Algebraic Expressions . . . . . . . . . . Converting Between Equivalent Forms . . . . . 6.2 Assumptions . . . . . . . . . . . . . . . . . . . The assume Facility . . . . . . . . . . . . . . . The assuming Command . . . . . . . . . . . . 6.3 Structural Manipulations . . . . . . . . . . . . Mapping a Function onto a List or Set . . . . . Choosing Elements from a List or Set . . . . . Merging Two Lists . . . . . . . . . . . . . . . . Sorting Lists . . . . . . . . . . . . . . . . . . . The Parts of an Expression . . . . . . . . . . . Substitution . . . . . . . . . . . . . . . . . . . . Changing the Type of an Expression . . . . . . 6.4 Evaluation Rules . . . . . . . . . . . . . . . . . Levels of Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 132 133 134 136 137 143 144 144 149 152 153 155 155 155 156 156 158 161 163 164 165 168 169 169 171 172 174 174 178 180 180 182 184 185 188 196 200 202 202 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents • vii 6.5 Last-Name Evaluation . . . . . . . . . . . . . . One-Level Evaluation . . . . . . . . . . . . . . Commands with Special Evaluation Rules . . . Quotation and Unevaluation . . . . . . . . . . . Using Quoted Variables as Function Arguments Concatenation of Names . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 205 206 207 210 211 213 215 215 215 215 221 232 236 240 241 255 259 260 264 269 270 270 272 273 276 277 277 277 278 280 281 281 283 284 286 286 289 291 7 Solving Calculus Problems In This Chapter . . . . . . . . . . . . . . . . . . 7.1 Introductory Calculus . . . . . . . . . . . . . . . The Derivative . . . . . . . . . . . . . . . . . . . A Taylor Approximation . . . . . . . . . . . . . . The Integral . . . . . . . . . . . . . . . . . . . . . Mixed Partial Derivatives . . . . . . . . . . . . . 7.2 Ordinary Differential Equations . . . . . . . . . . The dsolve Command . . . . . . . . . . . . . . . Example: Taylor Series . . . . . . . . . . . . . . . When You Cannot Find a Closed Form Solution Plotting Ordinary Differential Equations . . . . . Discontinuous Forcing Functions . . . . . . . . . Interactive ODE Analyzer . . . . . . . . . . . . . 7.3 Partial Differential Equations . . . . . . . . . . . The pdsolve Command . . . . . . . . . . . . . . Changing the Dependent Variable in a PDE . . . Plotting Partial Differential...
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This note was uploaded on 08/27/2012 for the course MATH 1100 taught by Professor Nil during the Spring '12 term at National University of Singapore.

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