Preface3.016 Mathematical Software3.016 Examination Philosophy3.016 Homework3.016 LaboratoryGradesHomework Calendar and WeightingLate PolicyTextbookLecture NotesLecture and Laboratory CalendarWeek of 4--8 SeptemberWeek of 11-15 SeptemberWeek of 18-22 SeptemberWeek of 25-29 SeptemberWeek of 2--6 Oct.Week of 9--13 OctoberWeek of 16--20 OctoberWeek of 23--27 OctoberWeek of 30 Sept--3 NovWeek of 6--10 NovemberWeek of 13--17 NovemberWeek of 20--24 NovemberWeek of 27 Nov--1 DecWeek of 4--8 DecemberWeek of 11--15 DecemberBeginners to Mathematica3.016 HomeJJ J I IIFull ScreenCloseQuitcW. Craig CarterLecture 1: Introduction and Course DescriptionSept. 6 2006These notes and all course materials will available at http://pruffle.mit.edu/3.016-2006. Studentsshould bookmark this site use it to download lecture notes, homework assignments, and reading as-signments for laboratories and lectures.The web materials for 3.016 are revised each year. This year I am doing substantial revision on howthe lecture notes are designed and s ome revision on lecture content. The site will develop throughoutthe semester.Previous years’ notes are available at http://pruffle.mit.edu/3.016 and may be useful to you.PrefaceThe subject is for undergraduate materials scientists and engineers who wish to learn about the math-ematics that is essential to their chosen field.Materials science and engineering is a discipline that combines knowledge of chemistry, mechanics,and physics and then applies them to the study of materials and their properties. It is a challengingand diverse enterprise—obtaining expertise in a large set of diverse subjects—but a career devoted todiverse study and applications will be very rewarding and fulfilling.Mathematics is the language that binds together disparate topics in physics, engineering, and chem-istry.While it is possible to become an excellent materials scientist and engineer without some workingknowledge of a large subset of mathematical topics, it is much easier to master this discipline withmathematics to guide you. Through mathematics, you will discove r that som e topics have similaritiesthat are not obvious—and not taught to you as being sim ilar. Such similarities and analogies will makelearning much, much easier—and I think much more enjoyable.MIT’s Department of Materials Science and Engineering has determined that students benefit froma background and a working knowledge of many more mathematics topics that pertain specifically toMS&E than are taught in a one-semester subject in the mathematics department. It is reasonable toask, “Is this subject a substitute for a mathematics subject such as linear algebra or partial differentialequations taught by a mathematics professor as part of the mathematics department?” No, this is not3.016 HomeJJ J I IIFull ScreenCloseQuitcW. Craig Cartera replacement for such a subject and I encourage you to take subjects in mathematics in the future.This subject is designed to be very broad in scope and therefore its depth in any one topic is limited.I do believe very strongly that you will enjoy studying math more after taking this introductionand that the mathematical background you will receive this semester will make your materials scienceeducation richer and more rewarding.I have designed this subject to help you learn as much essential mathematics as possible in a shorttime. To this end, this subject has several unusual aspects that you will need to know.3.016 Mathematical SoftwareSymbolic mathematical computer software is a tool used by almost every applied sc ientist. Suchsoftware helps produce results quickly, visualizes and documents the results, and minimizes the sillyerrors that creep into complicated mathematical manipulations. Although there are many other goodchoices, I have decided to use MathematicaR as a vehicle for learning and doing mathematics .It has a fairly steep learning c urve, but it probably repays the time investment with powerful (oncelearned) language syntax and packages. Such symbolic mathematical software is an aid to help youthink about and perform mathematics—it is not a replacement for mathematical understanding.MathematicaR is available for all MIT students, both on Athena (free) and via licenses for per-sonal laptop and desktop machines ($30 for students, a useful investment for other subjects). The pro-cess to access MathematicaR on Athena and the steps to download a license will be explained to you;the pertinent website is http://web.mit.edu/is/products/vsls/ http://web.mit.edu/is/products/vsls/.You will need MathematicaR for your first homework set and laboratory; you should try to get itworking someplace very soon. If you have a laptop, I suggest that you install MathematicaR on itas soon as possible.Laboratory as signments must be completed during the laboratory period and are to be emailed asan electronic copy of a MathematicaR notebook to the instructor and the TA.3.016 Examination PhilosophyTes ts and exams are powerful motivators to get students to take a subject seriously but I think thatworking through homework problems better promotes learning, particularly for self-motivated students.3.016 HomeJJ J I IIFull ScreenCloseQuitcW. Craig CarterTherefore, there will be no exams, tests, or quizzes in 3.016. Your grade will be based on yourhomeworks and laboratories. These will graded carefully (described below) and there will be about onehomework set every week and a half while the subject is meeting (i.e., no homework will be assignedduring the weeks that the laboratory 3.014 meets).3.016 HomeworkThe purpose of the homework is to help you solidify your understanding of mathematics applied toengineering and science problems by working through examples. Some examples may be exercises inmathematics; others will be exercises in application of mathematics to solving engineering and s cie nceproblems. I encourage you to use MathematicaR to solve your homework problems, and you mayturn in solutions as printed MathematicaR notebooks. Nevertheless to appreciate what symbolicmathematics programs can do for you, there will be some exercises that I will ask you to do with penciland paper. Howe ver, there is no harm in checking your “by-hand” results with MathematicaR .Of course when you do homework, you are not under the potentially menacing eyes of an examproctor. This means that you can receive help in the form of:Books Go to the library and find