day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from

Page 1 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/1.jpg' width='140' height='200' /> Page 2 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/2.jpg' width='140' height='200' /> Page 3 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/3.jpg' width='140' height='200' /> Page 4 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/4.jpg' width='140' height='200' /> 1

First Order Partial Differential Equations

Page 5 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/5.jpg' width='140' height='200' /> Page 6 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/6.jpg' width='140' height='200' /> 2

Page 7 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/7.jpg' width='140' height='200' /> Page 8 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=8' data-page='8' class='cut-thumb lazyload' alt='Page 8: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/8.jpg' width='140' height='200' /> 3

Page 9 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=9' data-page='9' class='cut-thumb lazyload' alt='Page 9: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/9.jpg' width='140' height='200' /> Page 10 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=10' data-page='10' class='cut-thumb lazyload' alt='Page 10: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/10.jpg' width='140' height='200' /> 4

Page 11 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=11' data-page='11' class='cut-thumb lazyload' alt='Page 11: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/11.jpg' width='140' height='200' /> 5

Initial Data

Page 12 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=12' data-page='12' class='cut-thumb lazyload' alt='Page 12: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/12.jpg' width='140' height='200' /> Page 13 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=13' data-page='13' class='cut-thumb lazyload' alt='Page 13: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/13.jpg' width='140' height='200' /> Page 14 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=14' data-page='14' class='cut-thumb lazyload' alt='Page 14: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/14.jpg' width='140' height='200' /> Page 15 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=15' data-page='15' class='cut-thumb lazyload' alt='Page 15: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/15.jpg' width='140' height='200' /> 7

and Appropriate Initial Data

Page 16 <img data-url='document/day03-uh-jmorganmath4335lecturesday03pdf-2-9-s-b-so-although-we-can.html?page=16' data-page='16' class='cut-thumb lazyload' alt='Page 16: day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader040.cupdf.com/reader040/viewer/2022031219/5be339d509d3f2382f8cc955/html5/thumbnails/16.jpg' width='140' height='200' /> 8

day03 - UHjmorgan/Math4335/lectures/day03.pdf · 2 (9 S B So, although we can theoretically solve the initial value problem to obtain our characteristic curves as they eminate from

Documents