M427K Handout: First Day HandoutSalman ButtJanuary 17, 2006This handout serves as an informal syllabus for the class, as well as specifically addressing thediscussion sections.Class in formationClass number: 57035Professor: Thomas Cecil - [email protected] - RLM 10.132 - Office hours:TA: Salman (Sal) Butt - [email protected] - RLM 11.114 - Office hours:Schedule:Lectures - MWF - 9-10am - RLM 4.102Discussion Sections - TTh - 3:30-4:30pm - RLM 4.102Textbook: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Prob-lems, 8th ed.Grading: There will be weekly homework, 2 midterms, and 1 final exam:Midterm 1 - Wed, 02/15/06 - in class - 22.5%Midterm 2 - Wed, 04/05/06 - in class - 22.5%Final Exam - Fri, 05/12/06 - location TBA - 35%Weekly homework - due by the end of the day on their due date stapled - 20% [Note: latehomework will be accepted but will be reduced by half for every additional week it is late.]Note that make up exams are not allowed except for religious holidays when 2 weeks of priornotification is given to Professor Cecil.Class webpage: http://www.ma.utexas.edu/˜tcecil/M427K spring 2006.htmlDepartment syllabus: http://www.ma.utexas.edu/text/syllabi/syllabi33.html [Note: we willnot strictly be adhering to this syllabus.]Discussion SectionsI want to list major pitfalls many students, especially undergraduates, seem to have. Duringthe semester, I hope to help you overcome these pitfalls as well as develop your understanding ofthe course material.Misconception 1: Your knowledge of the material is acc urately determined by your ability tofollow lecture and/or discussion sec tions. This is incorrect. It is relatively easy to follow someoneelse’s train of thought in solving a problem, especially when that person explains their ideas lucidly.Generating one’s own ideas and solutions to problems is a whole different matter. And indeed yourknowledge of the material is best determined by your ability to solve a problem from scratch byyourself, as well as explain your reasoning to fellow peers.Misconception 2: The only answer that matters is the right answer. Years and years ofschooling have shoved this skewed notion into your head, especially in your mathematics classes,where many people perceive there to be an absolute truth – where there is always a right and wrong1answer. Although this is partly true, mathematicians do not have a “back of the book” where theycan look up the right answers. To do mathematics is to struggle with a problem and its subtleintricacies, following many errant paths (possibly for years) and trying to make slow progress to asolution. I emphasize the importance of taking errant paths: misunderstandings are only discoveredby making mistakes.Misconception 3: You are empty vessels into which I am meant to pour all my knowledge ofthe course material. This viewpoint is taken by many students and teachers. It is patently absurd,especially in mathematics. Mathematics (and many would argue any pursuit) is about doing –knowing what the derivative of cos( x) is meaningless unless you can do something with it. It iscritical that you enter the classroom with an engaged, active mind – not a passive one that will sitthere quietly and not attempt to process what is being discussed. Discussion section is a great timeto ask questions and clear up misunderstandings, but that can only happen if you listen actively.Misconception 4: It is acceptable to make small errors (often in computation) on an exam.Although little mistakes will not cost you many points, this idea could not be further from thetruth especially in the real world. Little mistakes can cost millions of dollars – just ask the NASAengineers working on the Mars orbiter project who used the wrong units in their calculations. Thereason we practice – in class and in homework – is so that when your work really matters, e.g. ona test or in your future career, you execute flawlessly.A few notes: Undergraduates (myself included) often have very poor study habits – crammingespecially. This class has real-world applications for you in your other classes as well as in yourfuture. Many of you will go on to a career in engineering or physics, and being able to solvedifferential equations is critical to your success. Thus your ability to retain material beyond theend of this class is significant. Poor study habits – and, again, cramming especially – only hinderyour ability to retain the knowledge you gain even if they help you in the short-term (i.e. doing wellin this class). So I strongly encourage you to keep up with class and all the homeworks. Studyingfor an exam should mainly consist of reviewing material – not learning it anew.I refuse to do homework problems in discussion sessions and in office hours from scratch. I willonly talk about a homework problem in discussion before it is due if there is an especially thornytrick you need. Office hours is the proper place to talk about homework problems. And even there,I refuse to do a problem from the beginning. I expect you to have thought about the problem fora while and tried a few things. We will work out the problem together – I will not work it out foryou.Finally writing and speaking mathematics is crucial if anyone is going to understand yourarguments in a technical field. Thus I want to stress the importance of logical, coherent arguments.This is especially true on your homework. A string of equations without any sort of logical orderis unacceptable. I am not asking for much – merely write down or say what you are thinking inyour head. If you have some confusion about what you are thinking, the only way to correct it isfor you to make it explicit by writing or saying what is on your mind.By the end of the semester, I hope that you not only are able to solve differential equations, butthat you have also developed your learning ability. Your undergraduate career is about developingthis skill more than any other. Becoming an expert in any field after a few years of undergraduatework is absurd, but developing yourself into a capable learner is the key skill necessary for futuresuccess and expertise in any