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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&#x40;<!--
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>  &nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp </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&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp &nbsp&nbsp</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 &#8477<sup>2</sup>, write in terms of the Cartesian coordinate (c<sub>1</sub>, c<sub>2</sub>) and the polar coordinate (A, &delta;). <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 &sect;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 &sect;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 &sect;3.8, and the rest is on section &sect;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>,&nbsp <a href="SylvesterT2soln.pdf" target="_blank">Q1soln</a>,&nbsp  <a href="SylvesterT2p.pdf" target="_blank">
503Q2</a>, &nbsp <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 &sect;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>, &nbsp  <a href="https://uw.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=c911a7cf-bfde-42ad-aa1d-abbb0156b893" target="_blank">Panopto</a>), &nbsp <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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