1<html><head> 2 3 4 5 6<style> 7body{ 8 margin: 0; 9 padding: 30px 30px 30px 30px; 10} 11#text{ 12 margin: 10px 0; 13 padding: 10px 0px 0px 15px; 14 width:900px; 15} 16 17#link_bar ul{ 18 text-align: center; 19 font-weight: bolder; 20 font-size: 1.25em; 21} 22#link_bar a:link, 23#link_bar a:visited{ 24 color: #003b98; 25 margin-left: 14px; 26 margin-right: 16px; 27 text-decoration: none; 28 background-color: transparent; 29} 30#link_bar a:hover, 31#link_bar a:focus, 32#link_bar a:active{ 33 color: #000000; 34 text-decoration: none; 35 background-color: transparent; 36} 37 38#link_bar strong{ 39 color: #000000; 40 font: inherit; 41} 42#link_bar li{ 43 margin-left:0px; 44 margin-right:0px; 45 display: inline; 46} 47 48ul{ 49 margin: 0; 50} 51 52 53 54</style> 55 56 57 58 59 60 61</style> 62 63 64 65 66 67 68<base href="https://heather-math.github.io/307/"/> 69 70<title>Math 307 Video Lectures </title></head><body> 71 72 73 74<center> <h2> <font color = "#008000"> Math 307 - Introduction to Differential Equations - Video Lecture Materials </font> </h2> 75 76<h3> Heather Lee (heath<!--despam-->m<!-- -->l@<!-- 77-->uw.edu) </h3> 78 79<div id="link_bar"> <ul> <li><a href="#lectures">Lectures </a>|</li> 80<li><a href="#numerical">
80Numerical Resources </a></li> <li>          </li></ul> </div> 81 82</center> 83<br><br> 84 85 86 <hr> 87 88<h2><font color = "#008000"> Lectures <a name="lectures"> </a> 89</font> </h2> 90 The textbook referenced is Boyce and DiPrima's Elementary Differential Equations.<br><br> 91 92It is essential that you watch the videos, not just read the notes. Minor mistakes/typos in the videos are corrected in the notes, so make sure you check the notes that are posted here. <br><br> 93 94 95The videos on Youtube and Panopto are identical, and they are captioned (not by me). You can also watch all videos from the <a href="https://www.youtube.com/playlist?list=PLfg11VFLKL2u4NpBEN1L1W8db120PZULF" target="_blank">Youtube playlist</a> or the <a href="https://uw.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=2938086a-8885-47f7-b84e-ab8d011d3fc3" target="_blank"> Panopto playlist</a>. Panopto videos are restricted to those with an UW NetID. <font color="#FF0000">Edit:</font> starting Aug. 20, 2021, the videos will no longer be publicly available. <br><br> 96 97 98 <table border="1" cellpadding="2"> <tr style="font-weight: bold; background: 99 #ffe5b4"><td> No. </td><td>Video</td> <td>Topics and Comments</td> <td> Notes              </td></tr> 100 101 102 103<tr> 104<td>L1</td> 105 106<td> <a href="https://www.youtube.com/watch?v=4RYZ049_Pf8" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=d7d2681b-9ed6-4c15-8c3f-ab8d011ed79f" target="_blank">Panopto</a> 107</td> 108 109<td> 110 111<font color="#008000">Textbook reading:</font> 1.1<br> 112<font color="#008000">Keywords:</font> modeling, slope field, long term behavior<br> 113<font color="#008000">Modeling examples:</font> population growth and decay <br> 114 115<font color="#008000">Objectives:</font> <br> 116<ul>(1) Translate from words to equations, e.g. translating information about the amount of change in a quantity per unit time as a derivative. <br> 117(2) Draw a slope field from a differential equation. <br> 118(3) Understand the geometric meaning of a solution, i.e. solutions are integral curves to the slope field. <br> 119(4) Qualitatively describe the solution by looking at the slope field, e.g. predict the future by describing the long term behavior of the solution curve.<br> 120</ul> 121</td> 122 123<td rowspan="3"> <a href="01-03Introduction.pdf" target="_blank">Notes</a> <br> 124 for L1-L3 125</td> 126</tr> 127 128<tr> 129<td>L2</td> 130 131<td> <a href="https://www.youtube.com/watch?v=v-d3_j1d0gM" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=f3aed3a5-be72-4e14-87d1-ab8d0122350f" target="_blank">Panopto</a> 132</td> 133 134<td> 135<font color="#008000">Textbook reading:</font> 2.7, 1.2<br> 136<font color="#008000">Keywords:</font> Euler's method, separable equations, doubling time<br> 137<font color="#008000">Modeling examples:</font> population growth and decay<br> 138<font color="#008000">Objectives:</font> <br> 139<ul>(1) Understand the idea of Euler's method (iterative tangent line approximations). Given a 1st order differential equation and an initial condition, be able to use Euler's method to compute the value of the solution at a future time. <br> 140(2) Solve simple separable equations like the example provided in this lecture. We'll learn more about separable equations in future lectures, so no worries if you don't feel like you know them really well in this intro lecture. <br> 141(3) Understand the relationship between the doubling time and the exponential growth rate. <br> 142</ul> 143<font color="#008000">Extra links:</font> Euler's method with Python, <a href="eulerExp.py"target="_blank">eulerExp.py</a> and <a href="euler_method.pdf"target="_blank">explanations</a>, written by William Casper. Also see the <a href="#numerical">numerical resources </a> section. 144 145</td> 146 147 148</tr> 149 150 151<tr> 152<td>L3</td> 153 154<td> <a href="https://www.youtube.com/watch?v=ZZGyZyPB780" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=8cdb7e6d-c5a2-40bb-bc51-ab8d01230b9b" target="_blank">Panopto</a> 155</td> 156 157<td> 158<font color="#FFA500">Note:</font>
158 turns out <a href="https://www.doh.wa.gov/Emergencies/COVID19" target-"_blank">WA DoH</a> went back and corrected some of their numbers later on (now 3/20=1751, 3/21=1979, 3/25=3227). One can now see all previous dates' data (when I was making the videos, I could only see the data from the day of, so I recorded the numbers on the above 3 dates at the end of each day). The corrected numbers make our model look a bit better, but it still has all those issues I mentioned especially for long term estimates. Note another way to estimate r when you have several days' numbers is to look at the doubling time. <br> 159<font color="#008000">Textbook reading:</font> 2.7, 1.1, 1.2 <br> 160<font color="#008000">Keywords:</font> Euler's method cont'd, separable equations<br> 161<font color="#008000">Modeling examples:</font> population growth and decay, population growth with harvesting<br> 162<font color="#008000">Objectives:</font> <ul>(1)The discussion about the errors of Euler's methods and other approximation methods are completely optional. <br> 163(2) All mathematical models are approximations to the real scenario and can have minor or major drawbacks, know what they are. <br> 164(3) The whole process: modeling by translating words into equations, draw slope fields and solution curves to qualitatively describe the behavior of the solutions, solve the equation numerically or analytically to obtain more quantative information. <br> 165</ul> 166</td> 167 168 169</tr> 170 171<tr> 172<td>L4</td> 173 174<td> <a href="https://www.youtube.com/watch?v=Qy69fASTIGQ" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=dc963ed3-980d-4ba4-84b8-ab930081346b" target="_blank">Panopto</a> 175</td> 176 177<td> 178<font color="#008000">Textbook reading:</font> 1.1, 1.2 <br> 179<font color="#008000">Keywords:</font> equation of motion, laws for forces<br> 180<font color="#008000">Modeling examples:</font> vertical motion experiencing gravity and drag <br> 181<font color="#008000">Objectives:</font> <ul> 182(1) Equation of motion: m dv/dt = force <br> 183(2) The magnitude of the force due to gravity near the surface of the earth = mg. <br> 184(3) The magnitude of the drag force depends on various factors (the two common cases are proportional to v and v^2, respectively). Students are not responsible to figuring out which case it is; the problems given to you by the instructors will indicate that information.<br> 185(4) Students should be able to figure out the sign of the force based on chosen sign convention and the direction of the force. <br> 186</ul> 187<font color="#008000">Extra links:</font> drag of a <a href="https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html"target="_blank">sphere</a> or <a href="https://www.grc.nasa.gov/WWW/K-12/airplane/balldrag.html"target="_blank">baseball </a> baseball (briefly discussed in this lecture), and in case you want a job at the <a href="https://www.aa.washington.edu/AERL/KWT/employment"target="_blank">UW wind tunnel</a> 188 189</td> 190 <td rowspan="2"> <a href="04-05aIntroduction.pdf" target="_blank">Notes</a> <br> 191 for L4, L5(part a) <br><br><br><a href="05bSeparableEquations.pdf" target="_blank">Notes</a> <br> 192 for <br> L5(part b) 193</td> 194 195</tr> 196 197<tr> 198<td>L5</td> 199 200<td> <a href="https://www.youtube.com/watch?v=3UDreV4Hk9c" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=23516587-b457-4105-8c3c-ab9401790e7f" target="_blank">Panopto</a> 201</td> 202 203<td> 204<font color="#FFA500">Note:</font>there is a typo in example 2, y'=x+y, which is NOT separable (I said it correctly but wrote down the wrong thing). This is corrected in the notes. <br> 205<font color="#008000">Textbook reading:</font> 1.1, 1.2, 2.2 <br> 206<font color="#008000">Keywords:</font> equation of motion cont'd, separable equations<br> 207<font color="#008000">Objectives:</font> <ul> 208(1) Describe the solutions to the equations of motion. <br> 209(2) Identify separable equations, and find implicit, and sometimes explicit, solutions to them.<br> 210(3) You don't need to be able to draw the slope field and solution curves exactly by hand for separable equations, but you need to be able to identify some qualitative features about them, e.g. where the slope is vertical, where the initial point is, pick out the curve representing the solution to an initial value problem, etc. <ul> 211 212</ul> 213 214 215 216</tr> 217 218</tr> 219 220<tr> 221<td>L6</td> 222 223<td> <a href="https://www.youtube.com/watch?v=e-XW63oPoAs" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=37a77813-0a93-4af7-ab72-ab97009c1df0" target="_blank">Panopto</a> 224</td> 225 226<td> 227<font color="#008000">Textbook reading:</font> 2.1 <br> 228<font color="#008000">Keywords:</font> linear first order equations<br> 229<font color="#008000">Objectives:</font> <ul> 230(1) Identify linear equations<br> 231(2) Introducing the method of integrating factors. <br> 232(3) You don't need to be able to draw the slope field and solution curves exactly by hand for linear equations, but you need to be able to identify some qualitative features about them, e.g. where the slope is horizontal, where the slope is positive or negative, etc. 233 234</td> 235 <td> <a href="06Linear1stOrderEqnI.pdf" target="_blank">Notes</a> 236 237</td> 238 239</tr> 240 241<tr> 242<td>L7</td> 243 244<td> <a href="https://www.youtube.com/watch?v=NLDbvc67kAQ" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=72ff629a-9f7a-46a0-b8bb-ab9b005b4e73" target="_blank">Panopto</a> 245</td> 246 247<td> 248<font color="#008000">Textbook reading:</font> 2.1 (optional: example 3 of 2.4) <br> 249<font color="#008000">Keywords:</font> linear first order equations cont'd<br> 250<font color="#008000">Objectives:</font> <ul> 251(1) Solve any linear 1st order equations using the method of integrating factors. Note that students won't be asked to carry out derivations of general formulas (i.e. entirely symbolic formulas without numbers) as done at the beginning of this lecture, but you should watch it once to get the idea. To solve equations, you can either carry out the whole procedure every time, or simply use the general formula we derived to compute the integrating factor (the example in this lecture shows both ways). Either way, you should understand what makes this method work. <br> 252(2) The existence and uniqueness theorem for linear equations is optional (i.e. won't be asked on exams), so is the counterexample when the equation is nonlinear shown at the end of this lecture, but you should get a sense of what they s
252ay. <br> 253(3) You don't need to be able to draw the slope field and solution curves exactly by hand for linear equations, but you need to be able to identify some qualitative features about them, e.g. where the slope is horizontal, where the slope is positive or negative, behaviors of the solutions when t approches a singularity and how the different initial conditions affect the behavior, etc. 254 255</ul> 256 257</td> 258 <td> <a href="07Linear1stOrderEqnII.pdf" target="_blank">Notes</a> 259 260</td> 261 262</tr> 263 264<tr> 265<td>L8</td> 266 267<td> <a href="https://www.youtube.com/watch?v=CSK0auT2Hrk" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=30e21e0c-0979-48fc-9eb5-ab9b0154fdf8" target="_blank">Panopto</a> 268</td> 269 270<td> 271<font color="#008000">Textbook reading:</font> 2.3 <br> 272<font color="#008000">Keywords:</font> modeling, unit conversions <br> 273<font color="#008000">Modeling example:</font> mixing problems <ul> 274 275</ul> 276 277</td> 278 <td> <a href="08MixingProblems.pdf" target="_blank">Notes</a> 279 280</td> 281 282</tr> 283 284<tr> 285<td>L9</td> 286 287<td> <a href="https://www.youtube.com/watch?v=zpCdpUXrtd0" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=7b41d71d-6b4d-46d1-ac93-aba00098af78" target="_blank">Panopto</a> 288</td> 289 290<td> 291<font color="#008000">Textbook reading:</font> 2.5 <br> 292<font color="#008000">Keywords:</font> autonomous equations <br> 293<font color="#008000">Modeling example:</font> logistic growth and variants of it <br> 294<font color="#008000">Objectives:</font> <ul> 295(1) You should be able to graph the slope field and solution curves by hand for autonomous equations, and classify stability.<br> 296(2) Modeling with autonomous equations. 297</ul> 298 299</td> 300 <td> <a href="09AutonomousEqn.pdf" target="_blank">Notes</a> 301 302</td> 303</tr> 304 305<tr> 306<td>L10</td> 307 308<td> <a href="https://www.youtube.com/watch?v=LRIg1KcurEI" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2b258b3a-7b3a-4a7b-aeb0-aba300944977" target="_blank">Panopto</a> 309</td> 310 311<td> 312<font color="#008000">Textbook reading:</font> 3.1 (optional: 3.2)<br> 313<font color="#008000">Keywords:</font> homogeneous 2nd order linear equations with constant coefficents <br> 314<font color="#008000">Modeling example:</font> harmonic oscillators<br> 315<font color="#008000">Objectives:</font> <ul> 316(1) Model for the spring-mass system (meaning of the equation and the initial conditions)<br> 317(2) Form of the set of solutions of a linear homogeneous equation. <br> 318(3) Solutions to a homogeneous 2nd order linear equation with constant coefficients whose characteristic polynomial has <u><i>two distinct real roots</i></u>. Once you understand the process, you can write down the solution directly after finding the roots, no need to show more work. 319</ul> 320 321</td> 322 <td rowspan="3"> <a href="10-12Linear2ndOrderWithConstantCoeff.pdf" target="_blank">Notes</a> <br> for L10-12 323 324</td> 325</tr> 326 327<tr> 328<td>L11</td> 329 330<td> <a href="https://www.youtube.com/watch?v=5STh_DuvzGE&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=cb374f39-d424-484d-83b4-aba300bcacab" target="_blank">Panopto</a> 331</td> 332 333<td> 334<font color="#008000">Textbook reading:</font> 3.3 <br> 335<font color="#008000">Keywords:</font> homogeneous 2nd order linear equations with constant coefficents <br> 336<font color="#008000">Objectives:</font> <ul> 337(1) Solutions to a homogeneous 2nd order linear equation with constant coefficients whose characteristic polynomial has <u><i>a pair of complex roots </i></u>. <br> 338(2) Write the solution to (1) in terms of real valued functions. Once you understand the process, you can write down the solution in terms of real valued functions directly after finding the roots, no need to show more work. 339</ul> 340 341</td> 342 343</tr> 344 345<tr> 346<td>L12 <br><font color="#FFA500">25min</font> </td> 347 348<td> <a href="https://www.youtube.com/watch?v=PfbPSWbEkrA&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=c5b934e4-6d28-4b49-8f0d-aba400892e3d" target="_blank">Panopto</a> 349</td> 350 351<td> 352<font color="#008000">Textbook reading:</font> 3.4-3.5 <br> 353<font color="#008000">Keywords:</font> solving 2nd order equations iteratively 354 <br> 355<font color="#008000">Objectives:</font> <ul> 356(1) Solutions to a homogeneous 2nd order linear equation with constant coefficients whose characteristic polynomial
356<u><i>two repeated real roots (i.e. a single root).</i></u> Once you understand the process, you can write down the solution directly after finding the roots, no need to show more work.<br> 357(2) The iterative method for solving differential equations is entirely optional, but it's helpful to know if you are curious about how to find the solutions to these equations in a systematic way rather than "staring" at it for long enough to intuitively come up with a good guess. 358</ul> 359</td> 360 361 362</tr> 363 364 365<tr> 366<td>L13</td> 367 368<td> <a href="https://www.youtube.com/watch?v=xe6FyuJn9d4&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=84532390-697f-4802-9f6f-abad009ae759" target="_blank">Panopto</a> 369</td> 370 371<td> 372<font color="#008000">Textbook reading:</font> 3.5<br> 373<font color="#008000">Keywords:</font> nonhomogeneous linear equations, method of undetermined coefficents <br> 374<font color="#008000">Objectives:</font> <ul> 375(1) Solutions of a nonhomogeneous 2nd order linear equation and how they are related to the solutions of the corresponding homogeneous equation. <br> 376(2) Introducing the method of undetermined coefficients 377</ul> 378 379</td> 380 <td rowspan="4"> <a href="13-14aNonhomogLinearEqn.pdf" target="_blank">Notes</a> <br> for L13, L14(part a) <br><br><br> <a href="14b-15-16aHarmonicOscillator.pdf" target="_blank">Notes</a> <br> for <br> L14(part b), <br>L15 <br>L16(part a)<br><br><br> <a href="16bDampedHarmonicOscillator.pdf" target="_blank">Notes</a> <br> for <br> L16(part b) 381 382</td> 383</tr> 384 385<tr> 386<td>L14</td> 387 388<td> <a href="https://www.youtube.com/watch?v=2tacaFQS9eQ&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=d0935e88-b8f7-4279-9e5c-abad0164f50f" target="_blank">Panopto</a> 389</td> 390 391<td> 392<font color="#008000">Textbook reading:</font> 3.5, 3.7<br> 393<font color="#008000">Keywards:</font> Method of undetermined coefficients, harmonic oscillators<br> 394<font color="#008000">Objectives:</font> <ul> 395(1) Use the method of undetermined coefficients to solve 2nd order linear equations with constant coefficients whose nonhomogeneous parts are of the form (polynomial)*(sin/cos)*(exp), or a superposition of these.<br> 396(2) Two experiments for for finding the spring constant of a spring. Note that experiment 2 is more commonly used (it's easier, also it's more accurate than experiment 1 since it doesn't have as much simplifying assumptions, like being frictionless.) 397 398</ul> 399</td> 400 401</tr> 402 403<tr> 404<td>L15</td> 405 406<td> <a href="https://www.youtube.com/watch?v=YXAQGwR3EsE&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=b2ffcef0-b19d-4999-9a78-abb100ab4555" target="_blank">Panopto</a> 407</td> 408 409<td> 410<font color="#FFA500">Note: </font>After the lecture, I added a little comment at the bottom of p7 of the notes. <br> 411<font color="#008000">Textbook reading:</font> 3.7<br> 412<font color="#008000">Keywords:</font> harmonic oscillators<br> 413<font color="#008000">Objectives:</font> <ul> 414(1) For a point in ℝ<sup>2</sup>, write in terms of the Cartesian coordinate (c<sub>1</sub>, c<sub>2</sub>) and the polar coordinate (A, δ). <br> 415(2) Graph the solution to the harmonic oscillator equation with initial condition, indicating the period, initial conditions, amplitude, and phase shift. Note that the period depends on the intrinsic properties of the system (i.e. spring constant and mass); amplitude and phase shift depend on the initial condition. 416 417 418</ul> 419</td> 420</tr> 421<tr> 422 423<td>L16</td> 424 425<td> <a href="https://www.youtube.com/watch?v=N4yB54C3A0Y&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=b0b219d6-462a-4c7b-a1df-abb200d123a8" target="_blank">Panopto</a> 426</td> 427 428<td> 429<font color="#FFA500">Note: </font>Since someone asked, I added a comment on the last page of the notes giving a bit more explanation about cosh and sinh.<br> 430<font color="#008000">Textbook reading:</font> 3.7<br> 431<font color="#008000">Keywords:</font> linearization, damping <br> 432<font color="#008000">Modeling example:</font> pendulum, damped harmonic oscillators<br> 433<font color="#008000">Objectives:</font> <ul> 434(1) Solve damped harmonic oscillator equation. No need to memorize the formula since these are just homogeneous 2nd order equations with constant coefficients. <br> 435(2) Graph the solutions. Note that the graphs for the critically damped and overdamped cases are similar. In these two cases you don't need to be able to graph by hand precisely. But you should be able to illustrate the key features such as the initial condition, the peak/trough if there is any (i.e. when the derivative=0), the long term behavior (i.e. decay to 0), etc. 436</ul> 437 438</td> 439 440</tr> 441<tr> 442<td>L17</td> 443 444<td> <a href="https://www.youtube.com/watch?v=MxyJsn73s1k&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=1773ef03-7d9a-47a5-b8d4-abb301683321" target="_blank">Panopto</a> 445 446</td> 447 448<td> 449<font color="#008000">Textbook reading:</font> 3.8<br> 450<font color="#008000">Keywords:</font> forced vibrations<br> 451<font color="#008000">Objectives for §3.8 (i.e. L17, L18, and the first 8min of L19):</font> <ul> 452(1) Solving the equation for forced vibrations. Don't memorize the formulas! Understand how these are simply solved using the method of undetermined coefficients. <br> 453(2) Graphing the solutions. After you finish watching all the lectures on §3.8, I strongly recommend that you read the "gallery of graphs" (linked in L19's extra resources), which provides a summary of what was discussed in the lectures and what you are expected to know. 454 455</ul> 456 457</td> 458 <td rowspan="3"> <a href="17-18-19aForcedVibration.pdf" target="_blank">Notes</a> <br> for <br>L17,<br> L18,<br> L19(part a) <br><br><br><br><br><br><br><br> <a href="19bLaplaceTransform.pdf" target="_blank">Notes</a> <br> for <br> L19(part b) 459 460</td> 461</tr> 462 463<tr> 464<td>L18</td> 465 466<td> <a href="https://www.youtube.com/watch?v=PY0FZiEdTms&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=d7db895f-1568-4f8d-a3fd-abb801351f6e" target="_blank">Panopto</a> <br><br> 467 468<font color="#FF0000">2min correction video: </font><br> 469<a href="https://www.youtube.com/watch?v=v0xVGZLj9nA&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ee250333-b117-4fb3-bd71-abb900b3b3e2" target="_blank">Panopto</a> 470</td> 471 472<td> 473<font color="#FF0000">Note!! The beats graphs on Pages 4 and 6 were wrong, sorry! It has been corrected in the notes, and see the 2min correction video explaining this! Hope this will make you pay extra attention to this issue.</font><br> 474<font color="#008000">Textbook reading:</font> 3.8<br> 475<font color="#008000">Keywords:</font> forced vibrations<br> 476 477 478 479 480</td> 481 482</tr> 483 484<tr> 485<td>L19 </td> 486 487 488 489<td> <a href="https://www.youtube.com/watch?v=R8soDTQeNzU&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=7e764f1e-aaa2-4ae2-a608-abba011753d0" target="_blank">Panopto</a> 490</td> 491 492<td> 493<font color="#008000">Textbook reading:</font> 3.8, 6.1<br> 494<font color="#FFA500">Note: </font> only the first 8 min of this video is on §3.8, and the rest is on section §6.1. <br> 495<font color="#008000">Keywords:</font> forced vibrations, Laplace transform <br> 496<font color="#008000">Extra Resources:</font> 497<ul> 498<li> <a href="vibrationSum.pdf" target="_blank">Summary of mechanical vibrations</a> 499</li> 500<li> <a href="Gallery.pdf" target="_blank">Gallery of graphs</a> 501</li> 502<li> My solution to a couple of past exam problems by Prof. John Sylvester: 503<a href="SylvesterT2.pdf" target="_blank">Q1</a>,  <a href="SylvesterT2soln.pdf" target="_blank">Q1soln</a>,  <a href="SylvesterT2p.pdf" target="_blank">
503Q2</a>,   <a href="SylvesterT2psoln.pdf" target="_blank">Q2soln</a> 504</li> 505<li> <a href="https://www.geogebra.org/"target="_blank">Geogebra</a> is a neat graphing tool. I used it to make some of the graphs in today's notes. 506</li> 507 508</ul> 509<font color="#008000">Objectives for §6.1:</font> <ul> 510(1) Understand the definition of Laplace transform and use the definition to compute Laplace transforms <br> 511(2) It is important to understand that the Laplace transform is only defined on the interval of convergence, though you'll not be required to figure out what that interval is in this class. 512 513</ul> 514 515 516</td> 517 518</tr> 519 520<tr> 521<td colspan="4"><a href="LaplaceTableComment.pdf" target="_blank">Table of Laplace Transforms</a><br> 522 523<a href="LaplaceTable.pdf" target="_blank">Table of Laplace Transforms (without sinh and cosh)</a> 524</td> 525</tr> 526 527 528 529<tr> 530<td rowspan="2"> L20 531 532</td> 533 534<td> <a href="https://www.youtube.com/watch?v=XYGuV8l9DZ4&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=25b072ce-fadd-4768-bb84-abbb0168ada4" target="_blank">Panopto</a> 535 536</td> 537 538<td> 539<font color="#008000">Textbook reading:</font> 6.2<br> 540<font color="#008000">Keywords:</font> solving differential equations using Laplace transforms<br> 541<font color="#008000">Objectives:</font> <ul> 542(1) Properties 1,2,3 <br> 543(2) Solving initial value problems using Laplace transforms for equations whose solutions are continuous. 544 545</ul> 546 547</td> 548 <td> <a href="20SolvingDiffeqLaplace.pdf" target="_blank">Notes</a> 549 550</td> 551</tr> 552 553 554<tr> 555 556 557<td colspan="3"> Extra brief (9min) review of partial fraction decompositions:<br> video (<a href="https://www.youtube.com/watch?v=r-j79IlGLOY&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a>,   <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=c911a7cf-bfde-42ad-aa1d-abbb0156b893" target="_blank">Panopto</a>),   <a href="partialFraction.pdf" target="_blank">notes</a> 558 559</td> 560 561 562</tr> 563 564 565 <tr> 566<td> L21 567 568</td> 569 570<td> <a href="https://www.youtube.com/watch?v=F9_Cbwpk_8A&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a917ccae-9fae-4c89-8010-abbb015b1bf8" target="_blank">Panopto</a> 571 572</td> 573 574<td> 575<font color="#008000">Textbook reading:</font> 6.3<br> 576<font color="#008000">Keywords:</font> step functions<br> 577<font color="#008000">Objectives:</font> <ul> 578(1) Writing a piecewise continuous function in terms of step functions. <br> 579(2) Properties 4,5 <br> 580(3) Laplace transforms of step functions and piecewise continuous functions. 581 582</ul> 583 584</td> 585 <td> <a href="21StepFunction.pdf" target="_blank">Notes</a> 586 587</td> 588</tr> 589 590<tr> 591<td> L22 592 593</td> 594 595<td> <a href="https://www.youtube.com/watch?v=dbDEYJaZQLo&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=810d8ed4-8279-43ba-b632-abc000d82c31" target="_blank">Panopto</a> 596 597</td> 598 599<td> 600<font color="#008000">Textbook reading:</font> 6.4<br> 601<font color="#008000">Keywords:</font> equations with discontinuous nonhomogenous term (driving force)<br> 602 603</td> 604 <td> <a href="22DiscontinousDrivingForce.pdf" target="_blank">Notes</a> 605 606</td> 607</tr> 608 609<tr> 610<td> L23 611 612</td> 613 614<td> <a href="https://www.youtube.com/watch?v=es7qKD8XRSc&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=c5545d0c-e485-492e-b2d5-abc201659df8" target="_blank">Panopto</a> 615 616</td> 617 618<td> 619<font color="#FFA500">Note:</font> I added a quick exercise at the end of the lecture notes after the video ended. <br> 620 621<font color="#008000">Textbook reading:</font> 6.5<br> 622<font color="#008000">Keywords:</font> Impulse (Dirac delta) function driving force<br> 623<font color="#008000">Objectives:</font> <ul> 624(1) Laplace transform of impulse functions <br> 625(2) Solve initial value problems with impulse functions as the driving force<br> 626(3) Graphing the solution 627</ul> 628 629</td> 630 <td> <a href="23ImpulseFunction.pdf" target="_blank">Notes</a> 631 632</td> 633</tr> 634 635<tr> 636<td> L24 <br><font color="#FFA500">8min</a> 637 638</td> 639 640<td> <a href="https://www.youtube.com/watch?v=DwZyQrlLhAM&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=5b7bb68a-025e-4543-a0d1-abc70185f557" target="_blank">Panopto</a> 641 642</td> 643 644<td colspan="2"> 645Brief comments on the <a href="LaplaceTableComment.pdf" target="_blank">table of Laplace transforms</a> 646</td> 647</tr> 648 649<tr> 650<td> L25 651 652</td> 653 654<td> <a href="https://www.youtube.com/watch?v=pkuqVfKNFjU&feature=youtu.be&ab_channel=HeatherLee" target="_blank">Youtube</a> <br> <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=d700b841-8263-4d
65454-8175-abc801174464" target="_blank">Panopto</a> 655 656</td> 657 658<td> 659<font color="#008000">Textbook reading:</font> 6.6<br> 660<font color="#008000">Keywords:</font>convolution<br> 661</td> 662 <td> <a href="25Convolution.pdf" target="_blank">Notes</a> 663 664</td> 665</tr> 666 667 668 669 670 671 </table> 672 673 674 675 676 677 678 679<h2><font color = ``228B22''> Numerical Resources <a name="numerical"> </a></font> </h2> 680None are required, and we won't be using them very much in this class, but feel free to play around with any of these as you like. 681 682<li><a href="https://www.wolframalpha.com/"target="_blank">WolframAlpha</a> </li> 683 684 685<li><a href="https://www.geogebra.org/"target="_blank">Geogebra</a>: a nice graphing tool </li> 686 687<li><a href="https://itconnect.uw.edu/wares/uware//"target="_blank">UW IT Connect</a> has a list of softwares you can install on your personal computer, e.g. Mathematica and Matlab are free for students. </li> 688 689 690<li> Python: you can run Python from a browser using <a href="https://alpha.iodide.io/"target="_blank">iodide</a>, or you can download Python from <a href="https://www.anaconda.com/"target="_blank">Anaconda</a>. 691</li> 692 <ul>Some references: <a href="https://www.scipy.org/docs.html"target="_blank">Scipy documentation</a>, <a href="http://scipy-lectures.org/"target="_blank">Scipy lecture notes</a>, <a href="https://docs.python.org/3/tutorial/introduction.html#using-python-as-a-calculator"target="_blank">Python as a calculator</a>, <a href="https://www.geogebra.org/"target="_blank">mathematical functions</a>, <a href="http://math.jacobs-university.de/oliver/teaching/scipy-intro/scipy-intro.pdf" target="_blank">introductory notes</a>. 693 </ul> 694 695<li> <a href="https://www.sagemath.org/"target="_blank">Sage</a>, which can be run from a web browser using <a href="https://cocalc.com/"target="_blank">CoCalc</a>. Sage is mostly built on Python but not the same, e.g. it's easier to type math expressions in Sage and and it has more math specific codes/routines built in. Its founder is a former UW math professor, <a href="https://wstein.org/"target="_blank">William Stein</a>. Thomas Judson's book, <a href="http://faculty.sfasu.edu/judsontw/ode/"target="_blank">The ODE Project</a>, teaches differential equations and Sage. 696 </ul> 697 698<li>Slope field and integral curves: 699 <ul> 700 - <a href="http://slopefield.nathangrigg.net/" target="_blank">Slope field plotter</a> created by a former UW math graduate student, <a href="https://nathangrigg.com/about/" target="_blank">Nathan Grigg</a>.<br> 701 - <a href="https://https://en.wikipedia.org/wiki/Slope_field#Software_for_plotting_slope_fields" target="_blank">Other software codes </a> for plotting slope fields. 702 </ul> 703</li> 704 705<li>Euler's method with Python: <a href="eulerExp.py"target="_blank">eulerExp.py</a> and <a href="euler_method.pdf"target="_blank">explanations</a> written by William Casper. 706 707</li> 708 709</body> 710</html>
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