diff --git a/notes/notes.pdf b/notes/notes.pdf index 08c9362..2d2a33a 100644 --- a/notes/notes.pdf +++ b/notes/notes.pdf @@ -5,7 +5,7 @@ << /Type /Pages /Count 1 - /Kids [100 0 R] + /Kids [99 0 R] >> endobj @@ -23,7 +23,7 @@ endobj /Parent 2 0 R /Next 4 0 R /Title - /Dest 98 0 R + /Dest 97 0 R >> endobj @@ -32,7 +32,7 @@ endobj /Parent 2 0 R /Prev 3 0 R /Title - /Dest 99 0 R + /Dest 98 0 R >> endobj @@ -55,7 +55,7 @@ endobj endobj 6 0 obj -[77 0 R 76 0 R 74 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 74 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 69 0 R 67 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 67 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 62 0 R 60 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 60 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 54 0 R 53 0 R 52 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 51 0 R 47 0 R 45 0 R 46 0 R 45 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 42 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] +[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 @@ -63,7 +63,7 @@ endobj /Type /StructElem /S /Document /P 5 0 R - /K [77 0 R 55 0 R 54 0 R 8 0 R] + /K [76 0 R 54 0 R 53 0 R 8 0 R] >> endobj @@ -76,7 +76,7 @@ endobj /O /List /ListNumbering /Decimal >>] - /K [48 0 R 30 0 R 24 0 R 9 0 R] + /K [47 0 R 30 0 R 24 0 R 9 0 R] >> endobj @@ -125,8 +125,8 @@ endobj /Type /StructElem /S /Formula /P 12 0 R - /K [241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271] - /Pg 100 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 >> endobj @@ -135,8 +135,8 @@ endobj /Type /StructElem /S /P /P 11 0 R - /K [235 15 0 R 240] - /Pg 100 0 R + /K [229 15 0 R 234] + /Pg 99 0 R >> endobj @@ -145,8 +145,8 @@ endobj /Type /StructElem /S /Formula /P 14 0 R - /K [236 237 238 239] - /Pg 100 0 R + /K [230 231 232 233] + /Pg 99 0 R >> endobj @@ -155,8 +155,8 @@ endobj /Type /StructElem /S /Lbl /P 10 0 R - /K [234] - /Pg 100 0 R + /K [228] + /Pg 99 0 R >> endobj @@ -192,8 +192,8 @@ endobj /Type /StructElem /S /Formula /P 19 0 R - /K [205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233] - /Pg 100 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 >> endobj @@ -202,8 +202,8 @@ endobj /Type /StructElem /S /P /P 18 0 R - /K [198 22 0 R 203 204] - /Pg 100 0 R + /K [192 22 0 R 197 198] + /Pg 99 0 R >> endobj @@ -212,8 +212,8 @@ endobj /Type /StructElem /S /Formula /P 21 0 R - /K [199 200 201 202] - /Pg 100 0 R + /K [193 194 195 196] + /Pg 99 0 R >> endobj @@ -222,8 +222,8 @@ endobj /Type /StructElem /S /Lbl /P 17 0 R - /K [197] - /Pg 100 0 R + /K [191] + /Pg 99 0 R >> endobj @@ -259,8 +259,8 @@ endobj /Type /StructElem /S /Formula /P 26 0 R - /K [156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196] - /Pg 100 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 >> endobj @@ -269,8 +269,8 @@ endobj /Type /StructElem /S /P /P 25 0 R - /K [155] - /Pg 100 0 R + /K [149] + /Pg 99 0 R >> endobj @@ -279,8 +279,8 @@ endobj /Type /StructElem /S /Lbl /P 24 0 R - /K [154] - /Pg 100 0 R + /K [148] + /Pg 99 0 R >> endobj @@ -329,8 +329,8 @@ endobj /Type /StructElem /S /Formula /P 33 0 R - /K [138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153] - /Pg 100 0 R + /K [132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147] + /Pg 99 0 R >> endobj @@ -339,8 +339,8 @@ endobj /Type /StructElem /S /P /P 32 0 R - /K [125 38 0 R 127 37 0 R 129 36 0 R 137] - /Pg 100 0 R + /K [119 38 0 R 121 37 0 R 123 36 0 R 131] + /Pg 99 0 R >> endobj @@ -349,8 +349,8 @@ endobj /Type /StructElem /S /Formula /P 35 0 R - /K [130 131 132 133 134 135 136] - /Pg 100 0 R + /K [124 125 126 127 128 129 130] + /Pg 99 0 R >> endobj @@ -359,8 +359,8 @@ endobj /Type /StructElem /S /Formula /P 35 0 R - /K [128] - /Pg 100 0 R + /K [122] + /Pg 99 0 R >> endobj @@ -369,8 +369,8 @@ endobj /Type /StructElem /S /Formula /P 35 0 R - /K [126] - /Pg 100 0 R + /K [120] + /Pg 99 0 R >> endobj @@ -379,8 +379,8 @@ endobj /Type /StructElem /S /Lbl /P 31 0 R - /K [124] - /Pg 100 0 R + /K [118] + /Pg 99 0 R >> endobj @@ -389,7 +389,7 @@ endobj /Type /StructElem /S /LI /P 30 0 R - /K [47 0 R 41 0 R] + /K [46 0 R 41 0 R] >> endobj @@ -398,7 +398,7 @@ endobj /Type /StructElem /S /LBody /P 40 0 R - /K [45 0 R 42 0 R] + /K [44 0 R 42 0 R] >> endobj @@ -407,8 +407,7 @@ endobj /Type /StructElem /S /P /P 41 0 R - /K [44 0 R 117 43 0 R] - /Pg 100 0 R + /K [43 0 R] >> endobj @@ -417,120 +416,110 @@ endobj /Type /StructElem /S /Formula /P 42 0 R - /K [118 119 120 121 122 123] - /Pg 100 0 R + /K [105 106 107 108 109 110 111 112 113 114 115 116 117] + /Pg 99 0 R >> endobj 44 0 obj << /Type /StructElem - /S /Formula - /P 42 0 R - /K [105 106 107 108 109 110 111 112 113 114 115 116] - /Pg 100 0 R + /S /P + /P 41 0 R + /K [102 45 0 R 104] + /Pg 99 0 R >> endobj 45 0 obj << /Type /StructElem - /S /P - /P 41 0 R - /K [102 46 0 R 104] - /Pg 100 0 R + /S /Formula + /P 44 0 R + /K [103] + /Pg 99 0 R >> endobj 46 0 obj << /Type /StructElem - /S /Formula - /P 45 0 R - /K [103] - /Pg 100 0 R + /S /Lbl + /P 40 0 R + /K [101] + /Pg 99 0 R >> endobj 47 0 obj << /Type /StructElem - /S /Lbl - /P 40 0 R - /K [101] - /Pg 100 0 R + /S /LI + /P 8 0 R + /K [52 0 R 48 0 R] >> endobj 48 0 obj << /Type /StructElem - /S /LI - /P 8 0 R - /K [53 0 R 49 0 R] + /S /LBody + /P 47 0 R + /K [51 0 R 49 0 R] >> endobj 49 0 obj << /Type /StructElem - /S /LBody + /S /P /P 48 0 R - /K [52 0 R 50 0 R] + /K [50 0 R] >> endobj 50 0 obj << /Type /StructElem - /S /P + /S /Formula /P 49 0 R - /K [51 0 R] + /K [86 87 88 89 90 91 92 93 94 95 96 97 98 99 100] + /Pg 99 0 R >> endobj 51 0 obj << /Type /StructElem - /S /Formula - /P 50 0 R - /K [86 87 88 89 90 91 92 93 94 95 96 97 98 99 100] - /Pg 100 0 R + /S /P + /P 48 0 R + /K [85] + /Pg 99 0 R >> endobj 52 0 obj << /Type /StructElem - /S /P - /P 49 0 R - /K [85] - /Pg 100 0 R + /S /Lbl + /P 47 0 R + /K [84] + /Pg 99 0 R >> endobj 53 0 obj -<< - /Type /StructElem - /S /Lbl - /P 48 0 R - /K [84] - /Pg 100 0 R ->> -endobj - -54 0 obj << /Type /StructElem /S /H3 /P 7 0 R /T /K [83] - /Pg 100 0 R + /Pg 99 0 R >> endobj -55 0 obj +54 0 obj << /Type /StructElem /S /L @@ -539,234 +528,234 @@ endobj /O /List /ListNumbering /Decimal >>] - /K [70 0 R 63 0 R 56 0 R] + /K [69 0 R 62 0 R 55 0 R] +>> +endobj + +55 0 obj +<< + /Type /StructElem + /S /LI + /P 54 0 R + /K [61 0 R 56 0 R] >> endobj 56 0 obj << /Type /StructElem - /S /LI + /S /LBody /P 55 0 R - /K [62 0 R 57 0 R] + /K [59 0 R 57 0 R] >> endobj 57 0 obj << /Type /StructElem - /S /LBody + /S /P /P 56 0 R - /K [60 0 R 58 0 R] + /K [58 0 R] >> endobj 58 0 obj << /Type /StructElem - /S /P + /S /Formula /P 57 0 R - /K [59 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 >> endobj 59 0 obj << /Type /StructElem - /S /Formula - /P 58 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 100 0 R + /S /P + /P 56 0 R + /K [50 60 0 R 60] + /Pg 99 0 R >> endobj 60 0 obj << /Type /StructElem - /S /P - /P 57 0 R - /K [50 61 0 R 60] - /Pg 100 0 R + /S /Formula + /P 59 0 R + /K [51 52 53 54 55 56 57 58 59] + /Pg 99 0 R >> endobj 61 0 obj << /Type /StructElem - /S /Formula - /P 60 0 R - /K [51 52 53 54 55 56 57 58 59] - /Pg 100 0 R + /S /Lbl + /P 55 0 R + /K [49] + /Pg 99 0 R >> endobj 62 0 obj << /Type /StructElem - /S /Lbl - /P 56 0 R - /K [49] - /Pg 100 0 R + /S /LI + /P 54 0 R + /K [68 0 R 63 0 R] >> endobj 63 0 obj << /Type /StructElem - /S /LI - /P 55 0 R - /K [69 0 R 64 0 R] + /S /LBody + /P 62 0 R + /K [66 0 R 64 0 R] >> endobj 64 0 obj << /Type /StructElem - /S /LBody + /S /P /P 63 0 R - /K [67 0 R 65 0 R] + /K [65 0 R] >> endobj 65 0 obj << /Type /StructElem - /S /P + /S /Formula /P 64 0 R - /K [66 0 R] + /K [34 35 36 37 38 39 40 41 42 43 44 45 46 47 48] + /Pg 99 0 R >> endobj 66 0 obj << /Type /StructElem - /S /Formula - /P 65 0 R - /K [34 35 36 37 38 39 40 41 42 43 44 45 46 47 48] - /Pg 100 0 R + /S /P + /P 63 0 R + /K [27 67 0 R 33] + /Pg 99 0 R >> endobj 67 0 obj << /Type /StructElem - /S /P - /P 64 0 R - /K [27 68 0 R 33] - /Pg 100 0 R + /S /Formula + /P 66 0 R + /K [28 29 30 31 32] + /Pg 99 0 R >> endobj 68 0 obj << /Type /StructElem - /S /Formula - /P 67 0 R - /K [28 29 30 31 32] - /Pg 100 0 R + /S /Lbl + /P 62 0 R + /K [26] + /Pg 99 0 R >> endobj 69 0 obj << /Type /StructElem - /S /Lbl - /P 63 0 R - /K [26] - /Pg 100 0 R + /S /LI + /P 54 0 R + /K [75 0 R 70 0 R] >> endobj 70 0 obj << /Type /StructElem - /S /LI - /P 55 0 R - /K [76 0 R 71 0 R] + /S /LBody + /P 69 0 R + /K [73 0 R 71 0 R] >> endobj 71 0 obj << /Type /StructElem - /S /LBody + /S /P /P 70 0 R - /K [74 0 R 72 0 R] + /K [72 0 R] >> endobj 72 0 obj << /Type /StructElem - /S /P + /S /Formula /P 71 0 R - /K [73 0 R] + /K [9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] + /Pg 99 0 R >> endobj 73 0 obj << /Type /StructElem - /S /Formula - /P 72 0 R - /K [9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] - /Pg 100 0 R + /S /P + /P 70 0 R + /K [2 74 0 R 8] + /Pg 99 0 R >> endobj 74 0 obj << /Type /StructElem - /S /P - /P 71 0 R - /K [2 75 0 R 8] - /Pg 100 0 R + /S /Formula + /P 73 0 R + /K [3 4 5 6 7] + /Pg 99 0 R >> endobj 75 0 obj << /Type /StructElem - /S /Formula - /P 74 0 R - /K [3 4 5 6 7] - /Pg 100 0 R + /S /Lbl + /P 69 0 R + /K [1] + /Pg 99 0 R >> endobj 76 0 obj << /Type /StructElem - /S /Lbl - /P 70 0 R - /K [1] - /Pg 100 0 R + /S /H3 + /P 7 0 R + /T + /K [0] + /Pg 99 0 R >> endobj 77 0 obj -<< - /Type /StructElem - /S /H3 - /P 7 0 R - /T - /K [0] - /Pg 100 0 R ->> -endobj - -78 0 obj << /Type /Font /Subtype /Type0 /BaseFont /HDKMVQ+LibertinusSerif-Bold-Identity-H /Encoding /Identity-H - /DescendantFonts [79 0 R] - /ToUnicode 82 0 R + /DescendantFonts [78 0 R] + /ToUnicode 81 0 R >> endobj -79 0 obj +78 0 obj << /Type /Font /Subtype /CIDFontType0 @@ -776,13 +765,13 @@ endobj /Ordering (Identity) /Supplement 0 >> - /FontDescriptor 81 0 R + /FontDescriptor 80 0 R /DW 0 /W [0 0 500 1 1 730 2 2 538 3 3 633 4 4 551 5 5 581 6 6 844 7 7 489 8 8 817] >> endobj -80 0 obj +79 0 obj << /Length 10 /Filter /FlateDecode @@ -792,7 +781,7 @@ x endstream endobj -81 0 obj +80 0 obj << /Type /FontDescriptor /FontName /HDKMVQ+LibertinusSerif-Bold @@ -803,12 +792,12 @@ endobj /Descent -246 /CapHeight 645 /StemV 168.6 - 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Специальный вид правой части: #align(center)[$f(x) eq P_n (x) dot e^(alpha x).$] - - Если $alpha$ не является корнем характеристического уравнения, то #align(center)[$y_"частное" eq e^(alpha x) dot Q_n (x)$, где $Q_n (x).$] + - Если $alpha$ не является корнем характеристического уравнения, то #align(center)[$y_"частное" eq e^(alpha x) dot Q_n (x).$] - Если $alpha$ - корень характеристического уравнения кратности $S$ ($S in {1, 2}$), то #align(center)[$y_"частное" eq x^S dot e^(alpha x) dot Q_n (x).$] 2. Специальный вид правой части: #align(center)[$f(x) eq e^(alpha x) dot (P_n (x) dot cos beta x + Q_m (x) dot sin beta x), space.quad N eq max(n, m).$]