diff --git a/notes/notes.pdf b/notes/notes.pdf index 2d2a33a..f4c289b 100644 --- a/notes/notes.pdf +++ b/notes/notes.pdf @@ -5,7 +5,7 @@ << /Type /Pages /Count 1 - /Kids [99 0 R] + /Kids [103 0 R] >> endobj @@ -13,8 +13,8 @@ endobj << /Type /Outlines /First 3 0 R - /Last 4 0 R - /Count 2 + /Last 5 0 R + /Count 3 >> endobj @@ -23,20 +23,30 @@ endobj /Parent 2 0 R /Next 4 0 R /Title - /Dest 97 0 R + /Dest 100 0 R >> endobj 4 0 obj << /Parent 2 0 R + /Next 5 0 R /Prev 3 0 R /Title - /Dest 98 0 R + /Dest 101 0 R >> endobj 5 0 obj +<< + /Parent 2 0 R + /Prev 4 0 R + /Title + /Dest 102 0 R +>> +endobj + +6 0 obj << /Type /StructTreeRoot /RoleMap << @@ -46,311 +56,306 @@ endobj /Strong /Span /Em /Span >> - /K [7 0 R] + /K [8 0 R] /ParentTree << - /Nums [0 6 0 R] + /Nums [0 7 0 R] >> /ParentTreeNextKey 1 >> endobj -6 0 obj -[76 0 R 75 0 R 73 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 73 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 68 0 R 66 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 66 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 61 0 R 59 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 60 0 R 59 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 53 0 R 52 0 R 51 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 46 0 R 44 0 R 45 0 R 44 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 39 0 R 35 0 R 38 0 R 35 0 R 37 0 R 35 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 35 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 29 0 R 28 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 23 0 R 21 0 R 22 0 R 22 0 R 22 0 R 22 0 R 21 0 R 21 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 16 0 R 14 0 R 15 0 R 15 0 R 15 0 R 15 0 R 14 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R 13 0 R] -endobj - 7 0 obj -<< - /Type /StructElem - /S /Document - /P 5 0 R - /K [76 0 R 54 0 R 53 0 R 8 0 R] ->> +[79 0 R 78 0 R 76 0 R 77 0 R 77 0 R 77 0 R 77 0 R 77 0 R 76 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 71 0 R 69 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 69 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 64 0 R 62 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 62 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 61 0 R 56 0 R 55 0 R 54 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 49 0 R 47 0 R 48 0 R 47 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 42 0 R 38 0 R 41 0 R 38 0 R 40 0 R 38 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 38 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 32 0 R 31 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 26 0 R 24 0 R 25 0 R 25 0 R 25 0 R 25 0 R 24 0 R 24 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 19 0 R 17 0 R 18 0 R 18 0 R 18 0 R 18 0 R 17 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 10 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R 9 0 R] endobj 8 0 obj << /Type /StructElem - /S /L - /P 7 0 R - /A [<< - /O /List - /ListNumbering /Decimal - >>] - /K [47 0 R 30 0 R 24 0 R 9 0 R] + /S /Document + /P 6 0 R + /K [79 0 R 57 0 R 56 0 R 11 0 R 10 0 R 9 0 R] >> endobj 9 0 obj << /Type /StructElem - /S /L + /S /Formula /P 8 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Layout + /Placement /Block >>] - /K [17 0 R 10 0 R] + /K [267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310] + /Pg 103 0 R >> endobj 10 0 obj << /Type /StructElem - /S /LI - /P 9 0 R - /K [16 0 R 11 0 R] + /S /H3 + /P 8 0 R + /T + /K [266] + /Pg 103 0 R >> endobj 11 0 obj << /Type /StructElem - /S /LBody - /P 10 0 R - /K [14 0 R 12 0 R] + /S /L + /P 8 0 R + /A [<< + /O /List + /ListNumbering /Decimal + >>] + /K [50 0 R 33 0 R 27 0 R 12 0 R] >> endobj 12 0 obj << /Type /StructElem - /S /P + /S /L /P 11 0 R - /K [13 0 R] + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [20 0 R 13 0 R] >> endobj 13 0 obj << /Type /StructElem - /S /Formula + /S /LI /P 12 0 R - /K [235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265] - /Pg 99 0 R + /K [19 0 R 14 0 R] >> endobj 14 0 obj << /Type /StructElem - /S /P - /P 11 0 R - /K [229 15 0 R 234] - /Pg 99 0 R + /S /LBody + /P 13 0 R + /K [17 0 R 15 0 R] >> endobj 15 0 obj << /Type /StructElem - /S /Formula + /S /P /P 14 0 R - /K [230 231 232 233] - /Pg 99 0 R + /K [16 0 R] >> endobj 16 0 obj << /Type /StructElem - /S /Lbl - /P 10 0 R - /K [228] - /Pg 99 0 R + /S /Formula + /P 15 0 R + /K [235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265] + /Pg 103 0 R >> endobj 17 0 obj << /Type /StructElem - /S /LI - /P 9 0 R - /K [23 0 R 18 0 R] + /S /P + /P 14 0 R + /K [229 18 0 R 234] + /Pg 103 0 R >> endobj 18 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 17 0 R - /K [21 0 R 19 0 R] + /K [230 231 232 233] + /Pg 103 0 R >> endobj 19 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [20 0 R] + /S /Lbl + /P 13 0 R + /K [228] + /Pg 103 0 R >> endobj 20 0 obj << /Type /StructElem - /S /Formula - /P 19 0 R - /K [199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227] - /Pg 99 0 R + /S /LI + /P 12 0 R + /K [26 0 R 21 0 R] >> endobj 21 0 obj << /Type /StructElem - /S /P - /P 18 0 R - /K [192 22 0 R 197 198] - /Pg 99 0 R + /S /LBody + /P 20 0 R + /K [24 0 R 22 0 R] >> endobj 22 0 obj << /Type /StructElem - /S /Formula + /S /P /P 21 0 R - /K [193 194 195 196] - /Pg 99 0 R + /K [23 0 R] >> endobj 23 0 obj << /Type /StructElem - /S /Lbl - /P 17 0 R - /K [191] - /Pg 99 0 R + /S /Formula + /P 22 0 R + /K [199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227] + /Pg 103 0 R >> endobj 24 0 obj << /Type /StructElem - /S /LI - /P 8 0 R - /K [29 0 R 25 0 R] + /S /P + /P 21 0 R + /K [192 25 0 R 197 198] + /Pg 103 0 R >> endobj 25 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 24 0 R - /K [28 0 R 26 0 R] + /K [193 194 195 196] + /Pg 103 0 R >> endobj 26 0 obj << /Type /StructElem - /S /P - /P 25 0 R - /K [27 0 R] + /S /Lbl + /P 20 0 R + /K [191] + /Pg 103 0 R >> endobj 27 0 obj << /Type /StructElem - /S /Formula - /P 26 0 R - /K [150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190] - /Pg 99 0 R + /S /LI + /P 11 0 R + /K [32 0 R 28 0 R] >> endobj 28 0 obj << /Type /StructElem - /S /P - /P 25 0 R - /K [149] - /Pg 99 0 R + /S /LBody + /P 27 0 R + /K [31 0 R 29 0 R] >> endobj 29 0 obj << /Type /StructElem - /S /Lbl - /P 24 0 R - /K [148] - /Pg 99 0 R + /S /P + /P 28 0 R + /K [30 0 R] >> endobj 30 0 obj << /Type /StructElem - /S /L - /P 8 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [40 0 R 31 0 R] + /S /Formula + /P 29 0 R + /K [150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190] + /Pg 103 0 R >> endobj 31 0 obj << /Type /StructElem - /S /LI - /P 30 0 R - /K [39 0 R 32 0 R] + /S /P + /P 28 0 R + /K [149] + /Pg 103 0 R >> endobj 32 0 obj << /Type /StructElem - /S /LBody - /P 31 0 R - /K [35 0 R 33 0 R] + /S /Lbl + /P 27 0 R + /K [148] + /Pg 103 0 R >> endobj 33 0 obj << /Type /StructElem - /S /P - /P 32 0 R - /K [34 0 R] + /S /L + /P 11 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [43 0 R 34 0 R] >> endobj 34 0 obj << /Type /StructElem - /S /Formula + /S /LI /P 33 0 R - /K [132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147] - /Pg 99 0 R + /K [42 0 R 35 0 R] >> endobj 35 0 obj << /Type /StructElem - /S /P - /P 32 0 R - /K [119 38 0 R 121 37 0 R 123 36 0 R 131] - /Pg 99 0 R + /S /LBody + /P 34 0 R + /K [38 0 R 36 0 R] >> endobj 36 0 obj << /Type /StructElem - /S /Formula + /S /P /P 35 0 R - /K [124 125 126 127 128 129 130] - /Pg 99 0 R + /K [37 0 R] >> endobj @@ -358,448 +363,478 @@ endobj << /Type /StructElem /S /Formula - /P 35 0 R - /K [122] - /Pg 99 0 R + /P 36 0 R + /K [132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147] + /Pg 103 0 R >> endobj 38 0 obj << /Type /StructElem - /S /Formula + /S /P /P 35 0 R - /K [120] - /Pg 99 0 R + /K [119 41 0 R 121 40 0 R 123 39 0 R 131] + /Pg 103 0 R >> endobj 39 0 obj << /Type /StructElem - /S /Lbl - /P 31 0 R - /K [118] - /Pg 99 0 R + /S /Formula + /P 38 0 R + /K [124 125 126 127 128 129 130] + /Pg 103 0 R >> endobj 40 0 obj << /Type /StructElem - /S /LI - /P 30 0 R - /K [46 0 R 41 0 R] + /S /Formula + /P 38 0 R + /K [122] + /Pg 103 0 R >> endobj 41 0 obj << /Type /StructElem - /S /LBody - /P 40 0 R - /K [44 0 R 42 0 R] + /S /Formula + /P 38 0 R + /K [120] + /Pg 103 0 R >> endobj 42 0 obj << /Type /StructElem - /S /P - /P 41 0 R - /K [43 0 R] + /S /Lbl + /P 34 0 R + /K [118] + /Pg 103 0 R >> endobj 43 0 obj << /Type /StructElem - /S /Formula - /P 42 0 R - /K [105 106 107 108 109 110 111 112 113 114 115 116 117] - /Pg 99 0 R + /S /LI + /P 33 0 R + /K [49 0 R 44 0 R] >> endobj 44 0 obj << /Type /StructElem - /S /P - /P 41 0 R - /K [102 45 0 R 104] - /Pg 99 0 R + /S /LBody + /P 43 0 R + /K [47 0 R 45 0 R] >> endobj 45 0 obj << /Type /StructElem - /S /Formula + /S /P /P 44 0 R - /K [103] - /Pg 99 0 R + /K [46 0 R] >> endobj 46 0 obj << /Type /StructElem - /S /Lbl - /P 40 0 R - /K [101] - /Pg 99 0 R + /S /Formula + /P 45 0 R + /K [105 106 107 108 109 110 111 112 113 114 115 116 117] + /Pg 103 0 R >> endobj 47 0 obj << /Type /StructElem - /S /LI - /P 8 0 R - /K [52 0 R 48 0 R] + /S /P + /P 44 0 R + /K [102 48 0 R 104] + /Pg 103 0 R >> endobj 48 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 47 0 R - /K [51 0 R 49 0 R] + /K [103] + /Pg 103 0 R >> endobj 49 0 obj << /Type /StructElem - /S /P - /P 48 0 R - /K [50 0 R] + /S /Lbl + /P 43 0 R + /K [101] + /Pg 103 0 R >> endobj 50 0 obj << /Type /StructElem - /S /Formula - /P 49 0 R - /K [86 87 88 89 90 91 92 93 94 95 96 97 98 99 100] - /Pg 99 0 R + /S /LI + /P 11 0 R + /K [55 0 R 51 0 R] >> endobj 51 0 obj << /Type /StructElem - /S /P - /P 48 0 R - /K [85] - /Pg 99 0 R + /S /LBody + /P 50 0 R + /K [54 0 R 52 0 R] >> endobj 52 0 obj << /Type /StructElem - /S /Lbl - /P 47 0 R - /K [84] - /Pg 99 0 R + /S /P + /P 51 0 R + /K [53 0 R] >> endobj 53 0 obj << /Type /StructElem - /S /H3 - /P 7 0 R - /T - /K [83] - /Pg 99 0 R + /S /Formula + /P 52 0 R + /K [86 87 88 89 90 91 92 93 94 95 96 97 98 99 100] + /Pg 103 0 R >> endobj 54 0 obj << /Type /StructElem - /S /L - /P 7 0 R - /A [<< - /O /List - /ListNumbering /Decimal - >>] - /K [69 0 R 62 0 R 55 0 R] + /S /P + /P 51 0 R + /K [85] + /Pg 103 0 R >> endobj 55 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [61 0 R 56 0 R] + /S /Lbl + /P 50 0 R + /K [84] + /Pg 103 0 R >> endobj 56 0 obj << /Type /StructElem - /S /LBody - /P 55 0 R - /K [59 0 R 57 0 R] + /S /H3 + /P 8 0 R + /T + /K [83] + /Pg 103 0 R >> endobj 57 0 obj << /Type /StructElem - /S /P - /P 56 0 R - /K [58 0 R] + /S /L + /P 8 0 R + /A [<< + /O /List + /ListNumbering /Decimal + >>] + /K [72 0 R 65 0 R 58 0 R] >> endobj 58 0 obj << /Type /StructElem - /S /Formula + /S /LI /P 57 0 R - /K [61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82] - /Pg 99 0 R + /K [64 0 R 59 0 R] >> endobj 59 0 obj << /Type /StructElem - /S /P - /P 56 0 R - /K [50 60 0 R 60] - /Pg 99 0 R + /S /LBody + /P 58 0 R + /K [62 0 R 60 0 R] >> endobj 60 0 obj << /Type /StructElem - /S /Formula + /S /P /P 59 0 R - /K [51 52 53 54 55 56 57 58 59] - /Pg 99 0 R + /K [61 0 R] >> endobj 61 0 obj << /Type /StructElem - /S /Lbl - /P 55 0 R - /K [49] - /Pg 99 0 R + /S /Formula + /P 60 0 R + /K [61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82] + /Pg 103 0 R >> endobj 62 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [68 0 R 63 0 R] + /S /P + /P 59 0 R + /K [50 63 0 R 60] + /Pg 103 0 R >> endobj 63 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 62 0 R - /K [66 0 R 64 0 R] + /K [51 52 53 54 55 56 57 58 59] + /Pg 103 0 R >> endobj 64 0 obj << /Type /StructElem - /S /P - /P 63 0 R - /K [65 0 R] + /S /Lbl + /P 58 0 R + /K [49] + /Pg 103 0 R >> endobj 65 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [34 35 36 37 38 39 40 41 42 43 44 45 46 47 48] - /Pg 99 0 R + /S /LI + /P 57 0 R + /K [71 0 R 66 0 R] >> endobj 66 0 obj << /Type /StructElem - /S /P - /P 63 0 R - /K [27 67 0 R 33] - /Pg 99 0 R + /S /LBody + /P 65 0 R + /K [69 0 R 67 0 R] >> endobj 67 0 obj << /Type /StructElem - /S /Formula + /S /P /P 66 0 R - /K [28 29 30 31 32] - /Pg 99 0 R + /K [68 0 R] >> endobj 68 0 obj << /Type /StructElem - /S /Lbl - /P 62 0 R - /K [26] - /Pg 99 0 R + /S /Formula + /P 67 0 R + /K [34 35 36 37 38 39 40 41 42 43 44 45 46 47 48] + /Pg 103 0 R >> endobj 69 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [75 0 R 70 0 R] + /S /P + /P 66 0 R + /K [27 70 0 R 33] + /Pg 103 0 R >> endobj 70 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 69 0 R - /K [73 0 R 71 0 R] + /K [28 29 30 31 32] + /Pg 103 0 R >> endobj 71 0 obj << /Type /StructElem - /S /P - /P 70 0 R - /K [72 0 R] + /S /Lbl + /P 65 0 R + /K [26] + /Pg 103 0 R >> endobj 72 0 obj << /Type /StructElem - /S /Formula - /P 71 0 R - /K [9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] - /Pg 99 0 R + /S /LI + /P 57 0 R + /K [78 0 R 73 0 R] >> endobj 73 0 obj << /Type /StructElem - 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/Size 104 - /Root 103 0 R - /Info 101 0 R - /ID [(Y68uThMfPSDRFIpUikGslw==) (Y68uThMfPSDRFIpUikGslw==)] + /Size 108 + /Root 107 0 R + /Info 105 0 R + /ID [(l4eYHWSW88zZmyR8XXAn7Q==) (l4eYHWSW88zZmyR8XXAn7Q==)] >> startxref -35460 +39623 %%EOF \ No newline at end of file diff --git a/notes/notes.typ b/notes/notes.typ index cb9c2c0..cbf5754 100644 --- a/notes/notes.typ +++ b/notes/notes.typ @@ -18,3 +18,9 @@ - Если $alpha plus.minus beta i$ не являются корнями характеристического уравнения, то #align(center)[$y_"частное" eq e^(alpha x) dot (P_N (x) dot cos beta x + Q_N (x) dot sin beta x).$] - Если $alpha plus.minus beta i$ - корни характеристического уравнения, то #align(center)[$y_"частное" eq x dot e^(alpha x) dot (P_N (x) dot cos beta x + Q_N (x) dot sin beta x).$] + +=== Метод Лагранжа (Метод вариации постоянных) + +$ +cases(C'_1 (x) y_1 plus C'_2 (x) y_2 eq 0, C'_1 (x) y'_1 plus C'_2 (x) y'_2 eq f(x)) +$