2018 June 7,

Math 210: Calculus 3

Carleton College, Spring 2018, Joshua R. Davis, , CMC 325, x4095


This course continues your education in calculus — a subject on which much of our modern technological world is based. Specifically, this course extends the vector techniques, that you learned in Math 120, from 2D to 3D. That's important, because our world isn't 2D. The course then develops the calculus of vector fields, which underlie applications such as electromagnetism, fluid dynamics, and structural geology. Finally, it presents sequences and series, which find applications throughout statistics, physics, and other fields. The course materials are

Our class meets in CMC 319 during period 2A (MonWed 9:50-11:00, Fri 9:40-10:40). If you want to meet with me outside class, then try to make my office hours, which are

If you cannot make my office hours, then e-mail me to make an appointment, listing several possible times.


Final grades (A, B, C, etc.) are assigned according to an approximate curving process. By this I mean that there are no predetermined percentages (90%, 80%, 70%, etc.) required for specific grades. The advantage of this system is that student grades don't suffer when I write a difficult exam. The disadvantage is that you cannot compute your own grade. Visit me in my office, if you want me to estimate your current grade for you. The following elements contribute.

You are expected to spend about 10 hours per week on this course outside class. Some students need to spend more than 10 hours. If you find yourself spending more than 15 hours, then talk to me.

Standards for Work

On homework, you are encouraged to figure out the problems with other students. However, you should always write/type your solutions individually, in your own words. You may not copy someone else's work or allow them to copy yours. Presenting someone else's work as your own is a violation of Carleton's Academic Integrity standards.

Writing is not just for English and history majors. Written and oral communication skills are essential to every academic discipline and are highly prized by employers. In this course, your written work is evaluated both for correctness and for presentation.

Although homework is assigned every day, it is usually collected only on Fridays. When handing in a week's homework, staple your pages into a single packet, in the correct order. Multi-sheet packets that are not stapled are unacceptable. I will not accept packets that are not stapled. Is there a stapler in the classroom? Often not, so staple ahead of time. Is a paper clip okay? No.

Depending on time constraints in any given week, perhaps not all of your homework will be graded. In order to ensure full credit, do all of the assigned problems.

Special Accommodations

During the term, you have one free pass to hand in a week's homework packet late, no questions asked. Simply hand in your late packet when the next packet is due, writing "Late Pass Used" prominently at the top of the late packet. Once you have used your late pass, no late assignments are accepted, except in extreme circumstances that typically require documentation by physicians or deans.

If some medical condition affects your participation in class or your taking of exams, let me know in the first week of class. You may need to make official arrangements with Disability Services for Students.


This schedule is tentative. It will be adjusted as we proceed. To help you decode the schedule, here is an example. On Day 2 we discuss triple integrals. Section 15.6 of the textbook covers that material; read it if you want another treatment. You have six homework problems, which are due on Day 3.

M 3/261reviewDay 11, 2
W 3/28215.6triple integrals15.6 #10, 12, 22, 28, 32, 48ab3
F 3/30315.7cylindrical coordinates15.7 #7, 10, 16, 28, 30, 316cylindricalSpherical.pdf
M 4/02415.8spherical coordinates15.8 #6, 13, 18, 22, 28, 466
W 4/0454.4, 7.8L'Hopital's rule, improper integrals4.4 #16, 18, 24, 80; 7.8 #10, 16, 40, 699
F 4/06613.1vector functions, space curves13.1 #8, 18, 21-26, 329
M 4/09713.2derivatives, integrals of vector functionsDay 79
W 4/11813.3arc length but not curvature13.3 #4, 15, 16, 6712
F 4/13916.1vector fieldsDay 912
M 4/161016.2line integralsDay 1012
W 4/181116.3fundamental theorem for line integrals16.3 #1, 4, 18, 20, 25, 26, 28, 36c15
F 4/201216.4Green's theorem16.4 #1, 6, 12, 21, 2715
M 4/2313review
W 4/2514Exam A
F 4/271511.1sequences11.1 #3, 14, 24, 26, 28, 38, 46, 6817
M 4/30Midterm Break
W 5/021611.2seriesDay 1617, 20
F 5/0417catching upnone
M 5/071811.3integral testDay 1819, 20
W 5/091911.4comparisons11.4 #4, 6, 14, 16, 24, 30, 3823
F 5/112011.5alternating series11.5 #6, 7, 18, 20, 26, 3423
M 5/142111.6absolute convergence, ratio test, root testDay 2122, 23
W 5/162211.8power series11.8 #4, 10, 22, 24, 26, 30, 36a, 38, 4226
F 5/1823review
M 5/2124Exam B
W 5/232511.9power series as functions11.9 #8, 14, 16, 18, 26, 36a, 3828arctan.nb
F 5/252611.10Taylor series11.10 #10, 18, 20, 22, 26, 44, 5428
M 5/282717.4series in differential equationsa few of 17.4 #1-#12never
W 5/3028series in probability, conclusion
S 6/02Exam C, 3:30-6:00