1 00:00:05,540 --> 00:00:12,750 the main thing to get a sense for today 2 00:00:10,280 --> 00:00:20,010 the first thing really is the goals of 3 00:00:12,750 --> 00:00:21,540 the course and there's really three of 4 00:00:20,010 --> 00:00:23,970 them and they align nicely with the 5 00:00:21,540 --> 00:00:25,680 questions people answered in the online 6 00:00:23,970 --> 00:00:26,160 quiz as to what they hope to get out of 7 00:00:25,680 --> 00:00:29,539 it 8 00:00:26,160 --> 00:00:35,059 what they saw challenging the first is 9 00:00:29,539 --> 00:00:44,989 what I would call put those finishing 10 00:00:35,059 --> 00:00:47,520 touches on your math you've had you know 11 00:00:44,989 --> 00:00:49,440 roughly six quarters of math through the 12 00:00:47,520 --> 00:00:51,059 math department depending what you 13 00:00:49,440 --> 00:00:52,050 placed out of what you placed into how 14 00:00:51,059 --> 00:00:53,870 many of you have taken previously 15 00:00:52,050 --> 00:00:57,239 whether you're doing stuff concurrently 16 00:00:53,870 --> 00:00:58,649 it's been siloed into fixed courses you 17 00:00:57,239 --> 00:01:01,260 haven't had to deal with it sort of all 18 00:00:58,649 --> 00:01:03,059 at once in an integrated fashion there 19 00:01:01,260 --> 00:01:07,200 may be things that you found easy things 20 00:01:03,059 --> 00:01:11,939 you found hard not all math topics you 21 00:01:07,200 --> 00:01:14,459 had are relevant to your physics so this 22 00:01:11,939 --> 00:01:16,939 is kind of to go through that and and 23 00:01:14,459 --> 00:01:22,639 what I would call clean that up and 24 00:01:16,939 --> 00:01:30,920 write in that is really to provide a 25 00:01:22,639 --> 00:01:34,859 framework for why the math you learned 26 00:01:30,920 --> 00:01:38,789 we're going to use in physics I try very 27 00:01:34,859 --> 00:01:42,209 hard so in this regard there will be a 28 00:01:38,789 --> 00:01:43,740 big difference most of the time a pretty 29 00:01:42,209 --> 00:01:46,380 big difference between what I am doing 30 00:01:43,740 --> 00:01:47,009 in lecture and what is in the bow as 31 00:01:46,380 --> 00:01:50,520 reading 32 00:01:47,009 --> 00:01:52,529 the bow as is about doing the math so 33 00:01:50,520 --> 00:01:54,270 the reading will be very specific give 34 00:01:52,529 --> 00:01:56,369 you the you know how you do it the 35 00:01:54,270 --> 00:01:58,340 details of that I will be doing how you 36 00:01:56,369 --> 00:02:00,509 do the math to to a large extent but 37 00:01:58,340 --> 00:02:02,130 everything I would do will be focused 38 00:02:00,509 --> 00:02:03,599 and aimed at why would we use this in 39 00:02:02,130 --> 00:02:05,669 physics where would we use this in 40 00:02:03,599 --> 00:02:07,649 physics why do physicists care about 41 00:02:05,669 --> 00:02:10,130 that that tends to be my focus and 42 00:02:07,649 --> 00:02:10,130 priority 43 00:02:13,340 --> 00:02:17,810 there we hopefully won't show that again 44 00:02:18,320 --> 00:02:26,520 and then the third one really is this 45 00:02:23,760 --> 00:02:29,070 Mathematica issue to give you the basic 46 00:02:26,520 --> 00:02:30,660 skills in Mathematica and it's very 47 00:02:29,070 --> 00:02:32,970 useful in a lot of our upper division 48 00:02:30,660 --> 00:02:35,960 courses it depends who you have you will 49 00:02:32,970 --> 00:02:38,070 use more or less Mathematica in your 50 00:02:35,960 --> 00:02:40,140 classical mechanics ENM quantum 51 00:02:38,070 --> 00:02:42,930 mechanics courses so I'm used a lot some 52 00:02:40,140 --> 00:02:46,110 use less you should always check but in 53 00:02:42,930 --> 00:02:48,120 fact most faculty if you get really good 54 00:02:46,110 --> 00:02:49,770 at typing solutions in Mathematica even 55 00:02:48,120 --> 00:02:52,350 if they're handed in paper ones if you 56 00:02:49,770 --> 00:02:54,300 format it nicely and print it that is 57 00:02:52,350 --> 00:02:56,310 much more fun to read than handwritten 58 00:02:54,300 --> 00:02:58,320 solutions and once you get good at 59 00:02:56,310 --> 00:03:00,600 Mathematica you'll find you can do those 60 00:02:58,320 --> 00:03:02,910 solutions quite quickly and and you know 61 00:03:00,600 --> 00:03:06,600 a happy grader is one who is likely to 62 00:03:02,910 --> 00:03:08,160 give you more points but one of the 63 00:03:06,600 --> 00:03:09,960 things about Mathematica and I want to 64 00:03:08,160 --> 00:03:16,230 go back to the Dropbox here briefly 65 00:03:09,960 --> 00:03:19,680 whoops is there are lots of ways to 66 00:03:16,230 --> 00:03:22,320 often do things and I really want to 67 00:03:19,680 --> 00:03:25,410 encourage you to use this shared student 68 00:03:22,320 --> 00:03:27,510 files I'll be showing you one way or how 69 00:03:25,410 --> 00:03:29,520 to do things I find the students 70 00:03:27,510 --> 00:03:32,010 particularly ones who are very computer 71 00:03:29,520 --> 00:03:33,570 inclined quickly find cooler formatting 72 00:03:32,010 --> 00:03:36,480 better ways to prepare the text 73 00:03:33,570 --> 00:03:38,610 shortcuts to things keyboard shortcuts 74 00:03:36,480 --> 00:03:41,100 you find anything interesting or cool 75 00:03:38,610 --> 00:03:43,410 post it for your fellow students keep in 76 00:03:41,100 --> 00:03:46,080 mind there's no curve in this class you 77 00:03:43,410 --> 00:03:47,790 can all get A's so it really is a class 78 00:03:46,080 --> 00:03:48,840 where you can share this information and 79 00:03:47,790 --> 00:03:50,640 knowledge with each other and with 80 00:03:48,840 --> 00:03:53,220 Mathematica that's particularly helpful 81 00:03:50,640 --> 00:03:55,350 so I do encourage people to use this 82 00:03:53,220 --> 00:03:58,500 shared student file to share with each 83 00:03:55,350 --> 00:04:01,050 other good ways or tricks if you find 84 00:03:58,500 --> 00:04:03,570 for doing stuff that in this class is 85 00:04:01,050 --> 00:04:06,000 not considered cheating so feel free to 86 00:04:03,570 --> 00:04:08,240 share any Mathematica ideas with each 87 00:04:06,000 --> 00:04:08,240 other 88 00:04:10,370 --> 00:04:19,250 now the other issue that I like to go 89 00:04:15,270 --> 00:04:24,420 over is given that these are the goals 90 00:04:19,250 --> 00:04:28,650 the real question is how to achieve 91 00:04:24,420 --> 00:04:31,170 these and when students first look at my 92 00:04:28,650 --> 00:04:32,460 courses typically at the websites and as 93 00:04:31,170 --> 00:04:34,050 some of you said this they're like oh my 94 00:04:32,460 --> 00:04:36,150 god there's so much stuff to keep track 95 00:04:34,050 --> 00:04:38,070 of that's the hard challenge how am I 96 00:04:36,150 --> 00:04:40,620 going to do all this I've done this 97 00:04:38,070 --> 00:04:45,350 hopefully long enough and well enough it 98 00:04:40,620 --> 00:04:53,790 actually is all designed with a purpose 99 00:04:45,350 --> 00:04:57,570 so the lecture the lecture and the 100 00:04:53,790 --> 00:04:59,610 readings that's really about giving you 101 00:04:57,570 --> 00:05:02,640 the key information that you need for 102 00:04:59,610 --> 00:05:04,830 the course the stuff you know the 103 00:05:02,640 --> 00:05:12,050 details of how to do things why we're 104 00:05:04,830 --> 00:05:12,050 doing it all of that the pre assignments 105 00:05:14,620 --> 00:05:18,780 that's critical for both of us 106 00:05:22,340 --> 00:05:25,030 where 107 00:05:26,380 --> 00:05:33,430 to figure out where we are in the class 108 00:05:28,810 --> 00:05:36,070 okay I need to know what it is you know 109 00:05:33,430 --> 00:05:37,630 and don't know so I already know for 110 00:05:36,070 --> 00:05:40,300 instance by asking you to find the 111 00:05:37,630 --> 00:05:42,580 magnitude of 3 plus 4i that pretty much 112 00:05:40,300 --> 00:05:43,840 all of you can do that we don't have to 113 00:05:42,580 --> 00:05:46,120 spend a lot of time in that particular 114 00:05:43,840 --> 00:05:48,520 problem that hasn't been true every year 115 00:05:46,120 --> 00:05:50,620 I taught the course a lot depends on you 116 00:05:48,520 --> 00:05:54,580 know where the math class is put in 117 00:05:50,620 --> 00:05:56,350 there complex analysis and if you know I 118 00:05:54,580 --> 00:05:58,480 decide oh most of the class got 119 00:05:56,350 --> 00:06:01,390 something right and we're not going to 120 00:05:58,480 --> 00:06:03,100 do much on it and you got it wrong you 121 00:06:01,390 --> 00:06:04,600 need to know okay did I just make a 122 00:06:03,100 --> 00:06:06,130 careless error there but I really know 123 00:06:04,600 --> 00:06:08,080 how to do that or is that something I 124 00:06:06,130 --> 00:06:09,550 actually don't know how to do professor 125 00:06:08,080 --> 00:06:10,990 Denton's assuming I know how to do it so 126 00:06:09,550 --> 00:06:13,030 I better meet with him his office hours 127 00:06:10,990 --> 00:06:14,860 I better find the TA I better figure out 128 00:06:13,030 --> 00:06:16,600 how to know that stuff talk to somebody 129 00:06:14,860 --> 00:06:19,030 else in the class so in these pre 130 00:06:16,600 --> 00:06:21,520 assignments keep in mind that most of 131 00:06:19,030 --> 00:06:23,860 them my assumption is you all know how 132 00:06:21,520 --> 00:06:25,270 to do everything in the pre assignments 133 00:06:23,860 --> 00:06:27,430 whether it's the homework problems or a 134 00:06:25,270 --> 00:06:30,580 quiz I happen to post except of course 135 00:06:27,430 --> 00:06:32,080 the Mathematica stuff that the reason 136 00:06:30,580 --> 00:06:33,550 it's a pre assignment is I think it's 137 00:06:32,080 --> 00:06:36,310 easy enough to learn on your own by 138 00:06:33,550 --> 00:06:39,300 going through the tutorial so that's 139 00:06:36,310 --> 00:06:44,640 both a check for you and a check for me 140 00:06:39,300 --> 00:06:44,640 the problem solving sessions are key 141 00:06:48,190 --> 00:06:56,360 because this is the one place you get 142 00:06:50,900 --> 00:06:57,740 and I get real-time feedback that's 143 00:06:56,360 --> 00:06:59,600 where we're doing the challenging 144 00:06:57,740 --> 00:07:01,460 problems in the course trying to push a 145 00:06:59,600 --> 00:07:03,320 little bit farther than we might 146 00:07:01,460 --> 00:07:04,880 otherwise but doing it an environment 147 00:07:03,320 --> 00:07:06,680 where I can see immediately what 148 00:07:04,880 --> 00:07:08,270 mistakes you're making you can see 149 00:07:06,680 --> 00:07:10,040 immediately what mistakes you're making 150 00:07:08,270 --> 00:07:11,570 and there could be that real-time 151 00:07:10,040 --> 00:07:13,310 feedback and that's critical and that 152 00:07:11,570 --> 00:07:14,960 really prepares you for the harder 153 00:07:13,310 --> 00:07:17,270 problems on the homework and for the 154 00:07:14,960 --> 00:07:19,310 exam problems obviously the exams are 155 00:07:17,270 --> 00:07:21,680 key I find the only things I really 156 00:07:19,310 --> 00:07:23,150 remember are the things I got wrong on 157 00:07:21,680 --> 00:07:25,280 exams and there's a reason I give you 158 00:07:23,150 --> 00:07:27,080 four exams before the final the four 159 00:07:25,280 --> 00:07:29,720 exams in class are really a chance to 160 00:07:27,080 --> 00:07:31,220 make sure and double-check do I really 161 00:07:29,720 --> 00:07:32,810 know all this stuff because until you do 162 00:07:31,220 --> 00:07:34,010 it under time conditions on your own 163 00:07:32,810 --> 00:07:38,420 you're just not going to know if you 164 00:07:34,010 --> 00:07:39,860 really know it yet or not well and the 165 00:07:38,420 --> 00:07:42,170 final exam is also a great place to 166 00:07:39,860 --> 00:07:44,480 learn stuff but hopefully by then you've 167 00:07:42,170 --> 00:07:46,700 learned it all in the four exams so 168 00:07:44,480 --> 00:07:52,370 there's four in-class exams plus a final 169 00:07:46,700 --> 00:07:54,170 so it's four plus one what it means is 170 00:07:52,370 --> 00:07:56,660 you'll have had an exam on every topic 171 00:07:54,170 --> 00:07:58,400 that's going to show up on the final so 172 00:07:56,660 --> 00:08:02,870 that's a useful thing going into the 173 00:07:58,400 --> 00:08:04,940 final and then a lot of students often 174 00:08:02,870 --> 00:08:09,380 complain about stuff that they declare 175 00:08:04,940 --> 00:08:11,390 to be busy work but it's just it's math 176 00:08:09,380 --> 00:08:13,669 you just have to practice a lot of stuff 177 00:08:11,390 --> 00:08:16,190 you just have to drill in practice and 178 00:08:13,669 --> 00:08:17,780 so there are a lot of things that you 179 00:08:16,190 --> 00:08:19,430 know if you're doing it and you've got 180 00:08:17,780 --> 00:08:21,470 it mastered you're doing more of it may 181 00:08:19,430 --> 00:08:23,210 not help you and so those are things you 182 00:08:21,470 --> 00:08:24,830 can probably spend less time on and 183 00:08:23,210 --> 00:08:28,520 ignore but until you actually have it 184 00:08:24,830 --> 00:08:34,039 mastered you really need to do it so 185 00:08:28,520 --> 00:08:36,700 that's the design of the course but any 186 00:08:34,039 --> 00:08:39,400 questions on that 187 00:08:36,700 --> 00:08:41,470 I just like to be upfront with why I put 188 00:08:39,400 --> 00:08:44,950 each piece in the course where I put it 189 00:08:41,470 --> 00:08:47,470 in how we're doing it the other thing 190 00:08:44,950 --> 00:08:49,420 just to give you an overview the topics 191 00:08:47,470 --> 00:08:56,080 we'll be doing we're going to start with 192 00:08:49,420 --> 00:08:59,620 series and complex numbers we're then 193 00:08:56,080 --> 00:09:01,000 going to go into matrices and the first 194 00:08:59,620 --> 00:09:04,050 thing we'll do is just review the 195 00:09:01,000 --> 00:09:06,460 mechanics you know how to use matrices 196 00:09:04,050 --> 00:09:08,170 determinates multiply add subtract all 197 00:09:06,460 --> 00:09:11,080 those good things with complex numbers 198 00:09:08,170 --> 00:09:12,940 we're going to focus and series why we 199 00:09:11,080 --> 00:09:15,250 um in physics because there's a lot of 200 00:09:12,940 --> 00:09:17,380 math machinery that you learned that 201 00:09:15,250 --> 00:09:20,860 doesn't necessarily get used a lot in 202 00:09:17,380 --> 00:09:22,510 the physics class right after doing 203 00:09:20,860 --> 00:09:27,220 matrices we're going to go into linear 204 00:09:22,510 --> 00:09:29,470 vector spaces this will be an 205 00:09:27,220 --> 00:09:31,600 interesting place because I know the 206 00:09:29,470 --> 00:09:34,840 math curriculum has reorganized in the 207 00:09:31,600 --> 00:09:36,220 past half the students typically had not 208 00:09:34,840 --> 00:09:38,530 really done a lot with linear vector 209 00:09:36,220 --> 00:09:40,150 spaces so this is where the pre-quiz 210 00:09:38,530 --> 00:09:41,980 will become key I'm going to have to get 211 00:09:40,150 --> 00:09:44,080 a sense where this class is they've 212 00:09:41,980 --> 00:09:46,210 reorganized this um and you may know 213 00:09:44,080 --> 00:09:48,730 more than past classes have and will 214 00:09:46,210 --> 00:09:50,920 adjust for that but this is a central 215 00:09:48,730 --> 00:09:58,090 for so much of physics and it really 216 00:09:50,920 --> 00:10:00,130 uses the matrices a lot then we're going 217 00:09:58,090 --> 00:10:01,870 to go into Fourier techniques just out 218 00:10:00,130 --> 00:10:04,810 of curiosity how many have already done 219 00:10:01,870 --> 00:10:07,710 Fourier series if you've done for a 220 00:10:04,810 --> 00:10:07,710 series raise your hand 221 00:10:09,160 --> 00:10:16,600 okay this is a great example of linear 222 00:10:14,890 --> 00:10:18,700 vector spaces so we're going to do it 223 00:10:16,600 --> 00:10:20,050 from the physics point of view of this 224 00:10:18,700 --> 00:10:22,660 being a linear vector space 225 00:10:20,050 --> 00:10:25,750 not necessarily the math class point of 226 00:10:22,660 --> 00:10:30,040 view which I think really will help and 227 00:10:25,750 --> 00:10:31,570 are something that you'll use a lot we 228 00:10:30,040 --> 00:10:34,420 spend a little bit of time reviewing 229 00:10:31,570 --> 00:10:36,640 differential equations and partial 230 00:10:34,420 --> 00:10:39,100 differential equations the reason there 231 00:10:36,640 --> 00:10:40,780 is you've all had or are taking 232 00:10:39,100 --> 00:10:45,670 concurrently the math differential 233 00:10:40,780 --> 00:10:47,400 equation course right yes say yes no but 234 00:10:45,670 --> 00:10:49,840 you did the differential equation yeah 235 00:10:47,400 --> 00:10:52,060 and so we just highlight a few things 236 00:10:49,840 --> 00:10:53,860 from that class that you use a lot in 237 00:10:52,060 --> 00:10:56,770 physics and there's just one or two 238 00:10:53,860 --> 00:10:59,050 things that you will use a lot going 239 00:10:56,770 --> 00:11:01,330 forward some of these topics like the 240 00:10:59,050 --> 00:11:03,010 partial differential equation a lot of 241 00:11:01,330 --> 00:11:04,930 topics you don't really learn until the 242 00:11:03,010 --> 00:11:06,310 second or third time you saw them so 243 00:11:04,930 --> 00:11:08,530 some things in this class like 244 00:11:06,310 --> 00:11:10,480 differential equations or a review I 245 00:11:08,530 --> 00:11:12,280 expect you to have seen it we're going 246 00:11:10,480 --> 00:11:13,870 to review it and so on or you might be 247 00:11:12,280 --> 00:11:15,130 taking it concurrently partial 248 00:11:13,870 --> 00:11:16,930 differential equations this will be 249 00:11:15,130 --> 00:11:18,670 first time you see it I don't 250 00:11:16,930 --> 00:11:20,640 necessarily expect you to master it in 251 00:11:18,670 --> 00:11:24,160 this class but when you see it again 252 00:11:20,640 --> 00:11:26,650 next year in your E&M class you'll be 253 00:11:24,160 --> 00:11:28,480 prepared to then understand it the 254 00:11:26,650 --> 00:11:30,220 second time you see it so there are 255 00:11:28,480 --> 00:11:33,130 things that I actually don't expect you 256 00:11:30,220 --> 00:11:38,040 to understand the first time and then we 257 00:11:33,130 --> 00:11:38,040 close by reviewing vector calculus and 258 00:11:38,190 --> 00:11:46,120 integration just because of how much 259 00:11:42,700 --> 00:11:50,200 they're used and really the unifying 260 00:11:46,120 --> 00:11:52,330 theme for the whole thing is how to 261 00:11:50,200 --> 00:11:55,740 physicists use all these topics so these 262 00:11:52,330 --> 00:11:55,740 are the topics we're going through