Spring 2005 22M:028 Calculus III(Multivariable/Vector Calculus)and22M:109 Classical AnalysisMWThF 9:30Room 113 MLHProf. Jonathan SimonOffice 1-D MLHMath Dept. officePhone 335-076814 MLHEmail [email protected] Dept. phone335-0714This is one of my favorite courses to teach. The math is wonderful and the students usually areinteresting and rewarding to work with. Expect to work hard and learn a lot.Are you prepared for this course?The prerequisite for this course is second-semester calculus. To me, that means "solid knowledge offirst and second semester calculus". If you got an A or B in Calc II, and work hard in this course, youcan realistically aim for an A in Math 28. If you got a C in Calc II (and especially if you got a C inboth I and II), then I believe you will have some trouble with Calc III; if you got a D in Calc I or II,then I do not recommend Math 28.Why? Each time we introduce a new idea, we work examples to illustrate/practice/apply it.If you get bogged down in elementary calculations, you won't be able to focus on the newidea. You need to be comfortable and fluent in quick calculations of easy algebra, integralsand derivatives (including trig, log, exp).At the same time, all the core ideas in Calc III are extensions of ideas developed in Calc I. If youhave a good understanding of the basic ideas of single-variable calculus, then you should be able toenjoy extending those ideas to multi-variable settings.Linear Algebra (e.g. 22M:27) is not required for this course; however I view Linear Algebra as arecommended co- (or pre-) requisite. Many ideas from multivariable calculus are echoed by ideas oflinear algebra, so each course helps you understand the other. Our text uses matrices and vectors,and teaches the algebra it needs.Office hours t.b.a. (Meanwhile please see me, email, or phone, to make appointments.)Text: Vector Calculus (2nd ed.) by S. J. ColleyWe aim to nearly all of chapters 1-6, and part of ch. 7.The rhythm is approximately two days per section (see Schedule).The overall goals of the course are for you to understand basic concepts and major theorems ofmultivariable calculus, and to acquire enough technical skills to use these ideas in subsequentcourses (mathematics or physical/social sciences) or appropriate "real world" situations.This course will make some use of computers. You do not need to know how to program. I willprovide handouts and informal guidance to help you learn how to use the package MAPLE, which isavailable in ITCs around campus. You are welcome to use any other system you know, such asMATHEMATICA or MATLAB. There will be occasional computer homework assignments.22M:28 Spring 05 J. Simon page 2You can see the power of computer visualization in these illustrations of three major ideas ofmultivariable calculus are:Slicing StretchingApproximatingA typical modern calculus text represents hundreds of years of thought and work by a large numberof people, some brilliant and some just competent. I believe calculus is one of the great intellectualaccomplishments of humankind. On a purely personal level, Multivariable Calculus is one of myfavorite of all math courses: The material is powerful in its applications, beautiful in its internalconstruction and the way it unites different kinds of mathematics (see e.g. Sec. 2.5 for derivatives +matrix multiplication, and Sec. 5.5 for integrals + determinants), and right at the level of difficultywhere one really has to work to understand it, but the understanding is achievable.There is a limit to how much of this grand edifice one can explore in just one semester; so pleaseinterpret the phrases understand basic concepts and acquire enough technical skills with thereservation that this course is an introduction to the subject. Part of the joy and part of thefrustration of mathematics is that as much as you learn, there always is more yet to be learned.Pace of the course: We have many ideas to confront, and limited time; this has several implications:o Many topics will be covered, a few skipped or treated very lightly. For exams, I will make clearwhich sections are the basic requirements.The course moves at a rapid pace. Also new material often builds on the material previouslystudied. Also Homework usually gets assigned every day. So is important for you not to fallbehind. If you miss a class, get the assignment and notes (right away) from another student.22M:28 Spring 05 J. Simon page 3Exams and Homework: There will be two evening midterm exams and a comprehensive FinalExam I. Wednesday evening Feb. 23, 7-8:30 pm (room to be announced)Exam II. Wednesday evening March 30, 7-8:30 pm (room to be announced)Final Exam. Wednesday, May 11, 12-2 pm 113 MLH (our regular classroom)Special note: We will not have class onMonday April 25Homework will be assigned in class, almost every day, and collected each Wednesday at thebeginning of class. The policy for unexcused late homework is "better late than never": youcan submit it up to one week late for half-credit. [Exception: in May, the deadline is Friday May 6.]The course is not "curved"; on each exam, and for cumulative homework, you receive a letter grade(usually expressed as a number, e.g. 4.3 = A+, 2.7 = B-), and these will be averaged.Occasionally, circumstances justify a higher final grade than the strict average. For example: (a) astudent does strong work in all aspects of the course except for one bad midterm; (b) a student'swork shows a clear pattern of improvement through the semester; (c) a student's average is near theborder between two final grades and her/his class participation has been strong.There is no formal attendance requirement, but I try to pay attention to who is and who isn'tattending regularly. Sometimes I will take attendance. A student who misses a lot of classes is notlikely to receive any special consideration (previous paragraph) in computing the final grade.Your average will be computed with the following weights:Midterm Exam I20%Midterm Exam II25%Final Exam30%Homework25%Rules for exams and homework: All exams and quizzes are "closed book". You should have nobooks or papers of your own available during an exam. Calculators and computers will not bepermitted for exams.If you have an exam conflict, please notify me well ahead of the exam date so we can decideon appropriate arrangements. If you miss a test or