MATH 21D (Vector Analysis) - Fall 2011, UC Davis

Lectures: MWF 8:00-8:50am, 106 Wellman (Anne Schilling)
Discussion Sessions: MAT 21D-A01, CRN 69465, T 7:10 - 8:00 PM in Olson 205 (Chris Westenberger)
MAT 21D-A02, CRN 69466, T 6:10 - 7:00 PM in Olson 205 (Brady Smith)
Instructor: Anne Schilling, MSB 3222, phone: 554-2326,
Office hours: Mondays 12pm-1pm, Fridays 11am-12pm
T.A.: Brady Smith, Kemper Hall 3120,
Office hours: Tuesdays 2-3pm and Wednesdays 3-4pm
Christopher Westenberger, MSB 2141,
Office hours: Tuesdays 11am-12pm and Thursdays 2-3pm
Text: Thomas' Calculus: Early Transcendentals, 12th Edition" by Weir/Hass (ISBN #978-0-321-58876-0).
We will cover most of Chapters 15, 12, 13, 16.
Pre-requisite: MAT 21C
Problem Sets: There will be weekly homework assignments due on Wednesdays before class.
Homeworks consist of two components: WebWork homeworks and written homeworks from the book.
WebWork is an online homework system, for more information see the WebWork Wiki. The WebWork problems are graded and comprise the homework grade. No late homeworks will be accepted.
The written homework from the book is assigned on a weekly basis, but is not collected for grading. Make sure to work through all the problems, however, and ask your TA to discuss the problems in the discussion sessions. A selection of these problems will appear on the midterms.
Computing: During class, I will illustrate some results using the open source computer algebra system Sage. When you follow the link, you can try it out yourself using Sage Online Notebook. Or you can sign up for a Class Account with the math department. Log into and type the command `sage` to launch a Sage session in the terminal.
Exams: There will be two Midterms on October 14 and November 4 in class. The Final exam will be Thursday, December 8, from 6:00-8:00pm.
There will be no make-up exams!
Grading: The final grade will be based on: Problem sets 10%, Midterms 25% each, Final 40%.
Grades will be recorded on SmartSite.
Course Grade: The course grade will be determined on an absolute scale with slight modifications using the normal distribution curve if appropriate. An approximate guideline is
        85% - 100% = A-, A, A+
        70% - 85% = B-, B, B+
        55% - 70% = C-, C, C+
        45% - 55% = D-, D, D+
        Less than 45% = F

Course description

This course is the last of the four-quarter sequence on Differential Calculus. It focuses on vector analysis which is a branch of mathematics concerned with differentiation and integration of vector fields, in particular in 3 dimensional Euclidean space. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields and fluid flow. The highlights of this course will be Green's theorem, Stoke's theorem, and the Divergence theorem.
We will cover most of Chapters 15, 12, 13, 16 of Thomas' Calculus.

Sage Examples

Worksheet on the geometric illustration of double integrals (pdf)
Worksheet on the geometric illustration of boundaries in triple integrals (pdf)

Problem sets

Homework 0: due September 28, 2011 before class:
ReviewHomework on WebWork
Read sections 15.1-15.2
Problems section 15.1 #1,11,14,26
Problems section 15.2 #5,13,21,25,28,36,57,69,77

Homework 1: due October 5, 2011 before class:
Homework 1 on WebWork
Read sections 15.3-15.5
Problems section 15.3 #1,5,11,16,24
Problems section 15.4 #6,10,17,23,28,41
Problems section 15.5 #5,16,19,24,28,40

Homework 2: due October 12, 2011 before class:
Homework 2 on WebWork
Read sections 15.6-15.7
Problems section 15.6 #3,7,13,18,25,33
Problems section 15.7 #6,11,15,31,34,51,70

Midterm 1: October 14, 2011 in class. Please bring your student ID!
The midterm will cover Sections 15.1-15.7 of the book and Homeworks 0-2.
There will be at least one of the book homework problems on the test.
WebWork Homework 3 will open early and provides review problems for Section 15.
You may do these problems before the midterm as practice problems.

Homework 3: due October 19, 2011 before class:
Homework 3 on WebWork
Read section 15.8
Problems section 15.8 #1,5,12,22

Homework 4: due October 26, 2011 before class:
Homework 4 on WebWork
Read sections 12, 13.1-13.4
Problems section 13.1 #3,7,8,19,27
Problems section 13.2 #13,16,18
Problems section 13.3 #6,9,13,19,20
Problems section 13.4 #4,5,6,18

Homework 5: due November 2, 2011 before class:
Homework 5 on WebWork
Read sections 13.5, 16.1, 16.2
Problems section 13.5 #4,21,23
Problems section 16.1 #11,12,34,39
Problems section 16.2 #2,9,14,21,24,25,30,43,45

Midterm 2: November 4, 2011 in class. Please bring your student ID!
The midterm will cover Sections 15.8, 13.1-13.5, 16.1-16.2 of the book and Homeworks 3-5.
There will be at least one of the book homework problems on the test.

Homework 6: due November 9, 2011 before class:
Homework 6 on WebWork
Read section 16.3
Problems section 16.3 #1,6,10,15,18,31,33

Homework 7: due November 16, 2011 before class:
Homework 7 on WebWork
Read section 16.4
Problems section 16.4 #1,3,12,20,21,26,30,35,37

Homework 8: due November 23, 2011 before class:
Homework 8 on WebWork
Read sections 16.5, 16.6
Problems section 16.5 #3,4,9,17,27,31,37,49,56
Problems section 16.6 #1,6,8,19,21,25,43,46

Homework 9: due November 30, 2011 before class:
Homework 9 on WebWork
Read sections 16.7, 16.8
Problems section 16.7 #1,7,10,11,13,19a,26
Problems section 16.8 #1,2,8,13,17,18,19,20,25,27,29,30

Practice Problems:
WebWork (not graded! just for practice)

Final Exam: Thursday, December 8, 6:00-8:00pm in 106 Wellman. Please bring your student ID!
The final exam will be comprehensive. There will be at least two of the book homework problems on the test (from after the second midterm, that is, Book Homeworks 6-9). You are allowed to bring one letter sized piece of paper with formulas/theorems/definitions from the lecture and the book. Only write on one side! Do not write homework solutions on that piece of paper!
Here is a practice final with 8 problems: 15.2 #57, 15.6 #33, 15.8 #23, 16.2 #27, 16.3 #29, 16.6 #45, 16.7 #17, Chapter 16 Practice Problem #54 (pg. 1004)
Solutions (written by Christopher)

Office hours during final's week: Monday 2-3pm Anne Schilling; Tuesday 12-1 and Thursday 2-3 Christopher Westenberger; Wednesday 6-8pm Brady Smith