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Spring 2007 22M:028 Calculus III (Multivariable/Vector Calculus) and 22M:109 Classical Analysis MWThF 10:30 Room 105 MLH Prof. Jonathan Simon Office 1-D MLH Math Dept. office Phone 335-0768 14 MLH Email [email protected] Math Dept. phone335-0714 This is one of my favorite courses: The math is wonderful and the students are motivated. 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 of first and second semester calculus. If you got an A or B in Calc II, and work hard in this course, you can realistically aim for an A in Math 28. If you got a C in Calc II (and especially if you got a C in both 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 prerequisite material, you won't be able to focus on the new idea. You need to be comfortable and fluent in quick calculations of easy algebra, integrals and 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 you have a good understanding of the basic ideas of single-variable calculus, then you should be able to enjoy 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 a recommended co- (or pre-) requisite. Many ideas from multivariable calculus are echoed by ideas of linear algebra, so each course helps you understand the other. Our text uses matrices and vectors, and teaches the vector/matrix algebra it needs. Office hours t.b.a. (Meanwhile please see me, email, or phone, to make appointments.) Text: Vector Calculus (3rd ed.) by S. J. Colley We aim to cover nearly all of chapters 1-6, and part of ch. 7. The rhythm is usually one or two days per section (see Schedule). The overall goals of the course are for you to understand basic concepts and major theorems of multivariable calculus, and to acquire enough technical skills to use these ideas in subsequent courses (mathematics or physical/social sciences) and appropriate "real world" situations. This course will make some use of computers. You do not need to know how to program. I will provide handouts and informal guidance to help you learn how to use the package MAPLE, which is available in ITCs around campus. You are welcome to use any other system you know, such as MATHEMATICA or MATLAB. There will be occasional computer homework assignments.22M:28 Spring 05 J. Simon page 2 You can see the power of computer visualization in these illustrations of three of the major ideas of multivariable calculus: Slicing Stretching Linear Approximation A typical modern calculus text represents hundreds of years of thought and work by a large number of people, some brilliant and some just competent. I believe calculus is one of the great intellectual accomplishments of humankind. On a purely personal level, Multivariable Calculus is one of my favorite of all math courses: The material is powerful in its applications, beautiful in its internal construction 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 just at the level of difficulty where you have to work to understand it, but the understanding is achievable. There is a limit to how much of this world we can explore in one semester; so please interpret the phrases understand basic concepts and acquire enough technical skills with the reservation that this course is an introduction to the subject. Part of the joy and part of the frustration of mathematics is that as much as you learn, there always is more to be learned. Pace of the course: We have many ideas to encounter, and limited time. So… • Many topics will be covered, a few skipped or treated very lightly. For exams, I will make clear which sections are the basic requirements. • If you miss a class, get the assignment and notes (right away) from another student. We will move at a rapid pace. Also new material usually builds on what was covered before. And Homework usually gets assigned every day. Moral: Do not fall behind. If you miss a class, get the assignment and notes (right away) from another student.22M:28 Spring 05 J. Simon page 3 Exams and Homework: There will be two evening midterm exams and a comprehensive Final Exam I. Tuesday evening Feb. 20, 7-8:30 pm (room to be announced) Exam II. Wednesday evening March 28, 7-8:30 pm (room to be announced) Final Exam. Tuesday, May 8, 12-2 pm (our regular classroom) Special note: We will not have class on Wednesday, April 4 Homework will be assigned in class, almost every day, and collected each Wednesday at the beginning of class. The policy for unexcused late homework is "better late than never": you can submit it up to one week late for half-credit. [Exception: in May, the deadline is Friday May 4.] The course is not "curved". On each exam, and for cumulative homework, you will receive a grade, and these will be averaged. I will try to design the exams so the scale will be approximately 90 = A, 80 = B, 70=C, 60 = D, and below 58 = F. I will give A+ for averages 95 or above, and A-, B+/-, C+/-, D+ as appropriate. I do not believe in giving the grade “D-“ as a passing grade. I may give you a higher final grade than the strict average. Past justifications include: a student does strong work in all aspects of the course except for one bad midterm; a student's work shows a clear pattern of improvement through the semester; a student's average is near the border 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't attending regularly, sometimes taking attendance. A student who misses a lot of classes is not likely to receive any special consideration (previous paragraph) in computing the final grade. Your average will be computed with the following weights: Midterm Exam I 20% Midterm Exam II 25% Final Exam 30% Homework 25% Rules for exams and homework: All exams are


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UI MATH 2850 - Calculus III

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