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Prerequisites Math 116, 156 or 186
Credits 4 credits
Alternatives Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material.
Subsequent
Courses
For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Introduction to Differential Equations)
Textbook You can use either one of the following two books (if you have the 6th edition of this book, see here):
• Calculus (an excellent textbook, can be a good reference for single-variable calculus)
• Multivariable Calculus (Later chapters of the Calculus book, lighter and easier to carry around)
by James Stewart, Seventh edition, Brooks/Cole; 2008
Course
Description
The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.
Course
Outline
 Vectors Parametric Curves Functions of Two and Three Variables. Partial Derivatives. Multiple Integrals. Calculus of Vector Fields. Curl and Divergence. Green's, Stokes', and Divergence Theorems
Course
Components
• Web Homework: 10%
• Written Homework: 10%
• First Exam (12.1-14.7): 25%
• Second Exam (14.8-16.3): 25%
• Final Exam (cumulative, emphasis on Chapter 16): 30%

Exam
Policies

• Calculators and Notes are not allowed on the midterms and final.
• You can reschedule an exam only due to a serious conflict, illness, or family emergency. If possible, you should discuss any such conflict with your instructor well in advance of the exam date.
• If you need any special arrangements for the exams, you should let your instructor know about it during the first two weeks of the semester.
Gateway There is a gateway test for this course, covering integrals for single variable calculus. If you master the skills needed to pass the gateway test, you have a much better chance to do well in the course.
Maple
Laboratory
The geometry underlying multivariable calculus is three-dimensional. Therefore, we meet once a week in a computer lab to use the Computer Algebra System Maple to create graphs of curves and surfaces in space that are otherwise very difficult to visualize, and to evaluate some of the mathematical expressions we obtain. You will use Maple in most of the lab periods, and on some of the written homework problems. You will not be evaluated on your understanding of Maple on exams. Maple is installed on any of the SITEs labs on campus. You can also use VirtualSites (http://virtualsites.umich.edu) to get a remote desktop on a campus server that will have Maple.
Web
Homework
There are several on-line problem sets (including "Set 0", an introductory set explaining how to use the system, which is also graded). You should start on web homeworks early. Homeworks start at 8 am on the day that they open and close at 11:59 pm on the day they are due. You are allowed six attempts for each problem. You can get partial credit on a multiple parts problem. Each set consists of 5-10 problems. More answers to commonly asked questions can be found in Web Homework FAQ. About a day after the due date the correct answers to the set are available. You must complete all of each web homework set for full credit on the web homework.
Written
Homework

In addition to web homework, there are written homework sets due approximately weekly. These assignments are due to your GSI in lab. Due dates can be found on the course syllabus.

Administrative overhead prevents us from grading all problems on each set, but you should complete them all. On each set, three problems will be selected at random and graded (out of 5 points each). You will get another 5 points if you complete all other problems. Thus each homework set will be worth 20 points. The written homework on which you get the lowest score will be dropped when calculating your course average.

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