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UW-Madison MATH 320 - MATH 320 Syllabus

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SyllabusMath 320 - Linear Algebra and Differential EquationsFall 2007Lecturer: Dr. Jeff ViaclovskyOffice Hours: Tue 2:30–3:30, Thurs 2:30–3:30.Office: 803 Van VleckPhone: 263-1161Email: [email protected]: Bing Wang Email: [email protected]: Melanie Ruiz Email: [email protected] Web Site:∼jeffv/courses/320 F07.htmlText: Edwards and Penney, Differential Equations and Linear Algebra, 2nd ed., Prentice Hall.Lecture: TR 1:00–2:15PM, Ingraham 19Discussion Sections:331 (Bing Wang) M 11:00–11:50 AMin Van Vleck B123332 (Bing Wang) W 11:00–11:50 AMin Van Vleck B123333 (Bing Wang) M 12:05–12:55 PMin Van Vleck B219334 (Bing Wang) W 12:05–12:55 PMin Van Vleck B341335 (Melanie Ruiz) M 14:25–15:15 AMin Van Vleck B219336 (Melanie Ruiz) W 14:25–15:15 AMin Van Vleck B219Exam schedule:Exam 1: 1:00–2:15 PM Thursday, October 4Exam 2: 1:00–2:15 PM Thursday, November 8Final Exam: 5:05–7:05 PM on Monday, December 17 (room TBA)Acceptable excuses for missing an exam include only official university excuses, with a note from an appropriateuniveristy official. The location of the final will be announced on the Registrar’s homepage in early December.The final exam is cumulative.Prerequisite: The prerequisite for Math 320 is Math 222, and we will use ideas from Math 222 in afundamental way in many parts of Math 320. Credit may not be received for both Math 320 and Math 340.Course Content and Goals: Differential equations are equations describing a function in terms ofits derivatives. They are the basic tool that scientists and engineers use to model physical reality. Given anunknown functional relationship one wishes to model, one chooses an appropriate differential equation thatthe function should satisfy, and one wants to recover the function; doing so is called solving the differentialequation. The importance of this process to science and engineering cannot be over-emphasized. The crucialquestions regarding differential equations that we seek to answer in this course are:1. When does a differential equation have a solution? When is that solution unique?2. Can one construct the (unique) solution of a differe ntial equation in terms of elementary functions? Ifnot, can one approximate its solution numerically and/or understand it qualitatively?3. How does one choos e the differential equation(s) used to model a physical system? What are the s trengthsand limitations of such models? Specifically, what is the significance of linearity in our models andapplications?Math 320 Syllabus 2Linear algebra is the part of mathematics that grows out of solving systems of linear equations. It blossomsinto a general theory of linear objects, namely vector spaces, and concerns itse lf with transformations thatpreserve this linear structure, which can all be described by matrices. In this clas s, we will see that solutionsof certain differential equations in fact form a vector space, and techniques from linear algebra will allow us tosolve systems of linear differential equations.These two subjects are frequently studied separately, with little note made of their connection. We willstudy them together and in so doing will see that1. The viewpoint of linear algebra is immensely helpful in uncovering the order underlying the topic ofdifferential equations; it helps us understand the why and not just the how of our calculations;2. Conversely, seeing immediately the applications of linear algebra to differential equations helps to motivatemany of the ideas of linear algebra, which can seem overly abstract by themselves.3. Linear algebra is crucial to the computer approximations which are often the only way to solve the mostchallenging differential equations.Thus you should emerge from this course with a better understanding of both differential equations andlinear algebra, and a sense of how they motivate and enrich each other.Grades: Course grades will be based on a possible total of 500 points, determined as follows:Homework + Discussion 150 pointsExam 1 100 pointsExam 2 100 pointsFinal Exam 150 pointsThe Homework + Discussion score is broken down as follows: approximately 120 points for homework, and30 points for participation. Students who attend nearly all the sections and come prepared with questions willreceive the full 30 points. Those who miss many sections or are conspicuously not participating (e .g. sleeping,surfing the internet, etc.) will lose points.Homework: The homework exercises are the most critical component of your learning in thiscourse. The best way to cement your understanding of this subject is to work through a wide variety ofproblems, so it is vital that you do the homework. Moreover, the questions on the exam will be very similar tothe kinds of exercises given in the homework.Homework assignments are posted on the course web site, which will be updated often. Homework is duein the folder outside your TA’s office by 5 pm each Friday. Late homework is not accepted. It is essential thatyou begin the homework early – do not expect to do it all the two days before it’s due!Learning often happ ens best when we are forced to explain our work or thinking to someone else. Sometimesjust verbalizing your mathematical thoughts can deepen your understanding. Thus, I encourage group workingon the homework (groups of two or three tend to be most effective). However, you must still each write theproblems up on your own. And of course there will be no group consultations during exams.Please prepare your written homework according to the following rules (failure to do so may result in yourgetting no credit for the assignment):1. Write your name clearly at the top of the first page.2. Put the problems in order, indicating clearly any you have skipped.3. STAPLE your homework. Paper-clips, folded corners, etc. are not accepted. No matter how sturdythe corner-fold seems, while the grader is flipping through your homework during grading, it will c omeundone.Math 320 Syllabus 34. Write clearly.5. If you naturally do the problems out of order or with very messy script, then seriously consider rewritingthem neatly on a new sheet of paper after you are done and turning that in.Also, note that a correct solution to a homework problem consists of more than just writing the correctanswer. Homework solutions should also include a convincing a rgument that your solution is the correct answer.Write enough steps and work that your thought processes are

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