MA 213 Calculus III (Vector Calculus), Fall 2011

Course Calendar

See below for a calendar of topics to be covered and assigned problems. Apart from the midterm exam dates and academic holidays, the other items in the chart should be considered tentative until the day has passed. It is necessary to keep some flexibility in the schedule to account for adjustments in the pace of lectures. Check back frequently for updates. Below the calendar is an itemized list of some key dates, as well as the assigned problems.

Week Monday Tuesday Wednesday Thursday Friday
Aug. 22-26 First day of class
12.1 3D Coordinate Systems		 Introduction to WebWork 12.2 Vectors
Taylor's Theorem
Aug. 29-Sept. 2 12.3 The dot product Web HW 12.1 12.4 The cross product
Web HW 12.2		 Quiz 1 (12.1, 12.2)
Written HW 1 Due 		12.5 Equations of lines and planes
Web HW 12.3
Sept. 5-9 Labor Day Web HW 12.4 12.6 Cylinders and quadric surfaces
Web HW 12.5		 Quiz 2 (12.3, 12.4, 12.5)
Written HW 2 Due 		13.1 Vector functions and space curves
Sept. 12-16 13.2 Derivatives and integrals of vector functions Web HW 12.6 13.3 Arc length and curvature
Web HW 13.1 		Quiz 3 (12.6, 13.1)
Written HW 3 Due 		14.1 Functions of several variables
Web HW 13.2
Sept. 19-23 14.2 Limits and continuity
14.3 Partial derivatives 		14.3 Partial derivatives
Web HW 13.3
Web HW 14.1		 Quiz 4 (13.2, 13.3, 14.1)
Written HW 4 Due 		14.4 Tangent planes and linear approximations
Web HW 14.2
Sept. 26-30 14.5 The chain rule Web HW 14.3 14.6 Directional derivatives and the gradient vector
Web HW 14.4		 Quiz 5 (14.2, 14.3, 14.4)
Written HW 5 Due 		14.6 Directional derivatives and the gradient vector
14.7 Maximum and minimum values
Web HW 14.5
Oct. 3-7 14.7 Maximum and minimum values 14.8 Lagrange multipliers
Web HW 14.6		 Quiz 6 (14.5, 14.6, 14.7)
Written HW 6 Due 		15.1 Double integrals over rectangles
Web HW 14.7
Oct. 10-14 Review
Web HW 14.8		 Exam 1 15.2 Iterated integrals
Oct. 17-21 15.3 Double integrals over general regions Web HW 15.1 15.4 Double integrals in polar coordinates
Web HW 15.2		 Written HW 7 Due 15.5 Applications of double integrals
Web HW 15.3
Oct. 24-28 15.6 Triple integrals Web HW 15.4 15.8 Triple integrals in spherical coordinates
Web HW 15.5		 Quiz 7 (15.3, 15.4, 15.5)
Written HW 8 Due 		Catchup Day
Oct. 31-Nov. 4 16.1 Vector Fields Web HW 15.6 16.2 Line integrals
Web HW 15.8		 Quiz 8 (15.6, 15.8)
Written HW 9 Due 		16.2 Line integrals
16.3 The fundamental theorem for line integrals
Web HW 16.1
Nov. 7-11 16.3 The fundamental theorem for line integrals 16.4 Green's Theorem
Web HW 16.2		 Quiz 9 (16.1, 16.2)
Written HW 10 Due 		16.5 Curl and divergence
Web HW 16.3
Nov. 14-18 16.6 Parametric surfaces and their area Catchup Day
Web HW 16.4		 Quiz 10 (16.3, 16.4, 16.5)
Written HW 11 Due 		Review
Web HW 16.5
Nov. 21-25 Exam 2 Thanksgiving Holiday Thanksgiving Holiday Thanksgiving Holiday
Nov. 28-Dec. 2 16.7 Surface integrals 16.8 Stokes' Theorem
Web HW 16.6		 16.9 Divergence Theorem
Dec. 5-9 Catchup Day Review for Final Written HW 12 Due Last day of class
Review for Final

Key Dates

  • First day of class: August 24
  • Labor Day (academic holiday - no class): September 5
  • Last day to drop a class without it being reflected on the transcript, or to change grading option: September 14
  • Midterm grades posted: October 10-21
  • Last day to withdraw or reduce course load: November 4
  • Thanksgiving Break (academic holiday - no class): November 23-25
  • Last day of classes: December 9

Official academic calendars, final exam schedules and the 2010-2011 UK Bulletin may also be found at:

Textbook Assignments


This webpage contains textbook assignments. For web assignments, please click here and select your section.
  • Assignment 1
    To be handed in Thursday, Sept. 1: 12.1, #38, and 12.2, #34.
    Not handed in:
      12.1: 7, 11, 15, 27, 31.
      12.2: 7, 13, 19, 21, 29.
  • Assignment 2
    To be handed in Thursday, Sept. 8: 12.3, #50, 12.4, #28, and 12.5, #30.
    Not handed in:
      12.3: 5, 9, 17, 23, 37, 45.
      12.4: 3, 7, 19, 27, 29, 33.
      12.5: 3, 5, 7, 17, 21, 27, 33, 43, 51.
  • Assignment 3
    To be handed in Thursday, Sept. 15: 12.6, #10, and 13.1, #34.
    Not handed in:
      12.6: 3, 11, 19, 23, 39.
      13.1: 1, 5, 9, 17, 21, 27.
  • Assignment 4
    To be handed in Thursday, Sept. 22: 13.2, #32, 13.3, #12, and 14.1, #46.
    Not handed in:
      13.2: 7, 17, 23, 31, 35.
      13.3: 1, 11, 19, 31, 43.
      14.1: 5, 17, 30 (check your answers with a 3D plotter!), 43, 53.
  • Assignment 5
    To be handed in Thursday, Sept. 29: 14.2, #18, 14.3, #52, and 14.4, #20.
    Not handed in:
      14.2: 7, 9, 15, 31, 33.
      14.3: 5, 15, 23, 45, 55.
      14.4: 5, 7, 11, 15, 19.
  • Assignment 6
    To be handed in Thursday, Oct. 6: 14.5, #40, 14.6, #28, and 14.7, #38.
    Not handed in:
      14.5: 5, 7, 15, 21, 43.
      14.6: 5, 9 , 13, 23, 33.
      14.7: 1, 3, 15, 19, 23, 35, 37.
  • Assignment 7
    To be handed in Thursday, Oct. 20: 15.2, #16.
    Not handed in:
      15.1: 3, 7, 10, 11.
      15.2: 3, 15, 21, 25, 31.
  • Assignment 8
    To be handed in Thursday, Oct. 27: 15.3, #56, 15.4, #36, and 15.5, #16.
    Not handed in:
      15.3: 5, 11, 15, 23, 31.
      15.4: 5, 11, 17, 23, 31.
      15.5: 5, 7, 13, 27, 29.
  • Assignment 9
    To be handed in Thursday, Nov. 3: 15.6, #52, and 15.8, #26.
    Not handed in:
      15.6: 7, 13, 15, 31, 47.
      15.8: 1, 3, 15, 23, 25.
  • Assignment 10
    To be handed in Thursday, Nov. 10: 16.1, #36, and 16.2, #42.
    Not handed in:
      16.1: 3, 13, 17, 21, 27, 31.
      16.2: 5, 9, 15, 17, 19.
  • Assignment 11
    To be handed in Thursday, Nov. 17: 16.3, #20, 16.4, #18, and 16.5, #20.
    Not handed in:
      16.3: 5, 9, 17, 21, 33.
      16.4: 3, 7, 11, 17, 19.
      16.5: 7, 11, 13, 17, 33.
  • Assignment 12
    To be handed in Thursday, Dec. 8: 16.7, #42, 16.8, #18, and 16.9, #24.
    Not handed in:
      16.6: 19, 23, 33, 37, 39.
      16.7: 7, 9, 15, 19, 23.
      16.8: 3, 7, 9, 15, 17.
      16.9: 3, 7, 9, 13, 19.
Syllabus for “Ordinary Differential Equations”

Syllabus for MA213, Calculus III, Sections 3 and 4

 

University of Kentucky, Fall 2011

 

Course instructor and contact information: 

Instructor:  Dr. Alan Demlow, Associate Professor of Mathematics

            Office: POT 775, phone 257-6797

            E-mail:  alan.demlow@uky.edu

            Office hours:  Tuesdays 10-11 a.m., Wednesdays 3-4 p.m., and Fridays 9-10 a.m.   

 

Recitation instructor and contact information:

            Recitation instructor:  Wenwen Du

            Office:  POT 706, phone 257-6805

            E-mail:  wenwendu@ms.uky.edu

            Office hours:  Tuesdays and Thursdays 9-10 a.m. in POT 706 and Wednesdays 12-2 p.m. in the Mathskeller (CB063).

 

Lecture and recitation time and place:

            Lecture:  MWF 11-11:50 a.m., CB349

            Recitation Section 003:  TR 8-8:50 a.m., CB341

            Recitation Section 004:  TR 11-11:50 a.m., CB339

 

Course overview:   This course covers standard material concerning the calculus of functions of several variables. We will generalize many of the concepts developed for one-dimensional problems in Calculus I and Calculus II to several dimensions.  Because we live in a multi-dimensional world, vector calculus is an essential tool for describing many natural phenomena that we observe.  We will cover most of Chapters 12, 13, 14, 15, and 16 of the textbook.  Topics include vectors and the geometry of space (Chapter 12), vector functions (Chapter 13), differentiation and integration of functions of multiple variables (Chapters 14 and 15), and vector calculus (Chapter 16).  A tentative course schedule may be found at the course website. 

 

Textbook:  Calculus, 6th Edition Early Transcendentals), by James Stewart. 

 

Course website:  The course website will be linked to from http://www.ms.uky.edu/~demlow/ (click “Teaching” and then follow the link to the MA213/Fall 2011 site).  The website will contain a course calendar (which is subject to change and may be updated), homework assignments and other important information, so please bookmark it and return to it often.

 

Homework:   Two types of homework will count towards your grade:

1.     Online homework using the web homework system WeBWorK will be assigned and due roughly three times per week (on Tuesdays, Wednesdays, and Friday).  Online homework will make up 10% of your course grade.  Late online homework will not be accepted.    If a documented emergency or illness takes you away from school and you are unable to complete a web assignment on time, you will be given the option of having the assignment excused or completing a makeup assignment.  If you have a scheduled absence (travel or authorized university absence), you must still submit the web homework by the deadline.  The URL for the WeBWorK system is http://mathecon.ms.uky.edu/webwork2.  In order to access your section’s site, click on the link containing your section number (so, sections 3 and 4 click on “ma213_0304”). 

2.     You will be assigned roughly three written problems per week to be handed in the following Thursday at the beginning of your recitation section.  One or two of these problems will be graded per week.  Late assignments will not be accepted except with a documented excuse (see “Attendance” below).  Your lowest two homework scores will be dropped.  Written assignments will be worth 5% of your final grade. 

Additional homework problems from the textbook will be assigned regularly.  While these additional problems will not be handed in or graded, you are responsible for the material that they cover, and it is strongly recommended that you complete them.

 

Exams:  There will be two one-hour in-class preliminary exams during the course of the semester, each worth 20% of your final grade.  The final exam will be comprehensive, though it may emphasize material not covered on the preliminary exams, and it will be worth 35% of your final grade.  The date and time of the final exam follows the standard university schedule and is given below.  Below is a tentative exam schedule with an approximate breakdown (subject to change!) of material covered on each.

 

            Prelim 1:         Wednesday, Oct. 12                Chapters 12, 13, and 14

            Prelim 2:          Monday, Nov. 21                    Chapter 1, Sections 16.1-16.5

            Final Exam:     Friday, Dec. 16, at 1 p.m.        Comprehensive

 

Makeup exams are allowed only for sanctioned university activities or legitimate emergencies and only with written documentation (see “Attendance” below).  If you feel that your situation warrants a makeup exam, please check with your instructor as soon as possible to request one. 

 

Accommodations due to disability:  If you have a documented disability that requires academic accommodations, please see me as soon as possible during scheduled office hours.  In order to receive accommodations in this course, you must provide me with a Letter of Accommodation from the Disability Resource Center (Room 2, Alumni Gym, 257-2754, jkarnes@email.uky.edu) for coordination of campus disability services available to students with disabilities. 

 

Quizzes: You will have written quizzes most Thursdays in recitation, with a total of roughly 10 during the semester (see the course schedule for precise dates).  These will be graded out of 10 points, and the score that is recorded will be the minimum of 10 and 3 more than your raw quiz score.  (So, you will automatically receive 3 points just for taking the quiz, and you will receive full credit if you score at least 7/10 on the quiz.)  Quizzes will make up 10% of your final grade. 

 

Grading:  Your final grade will be determined as follows:

                       

                                    Written Homework                 5%

                                    Online Homework                   10%

                                    Quizzes                                   10%

                                    2 hourly exams (20% each)     40%

                                    Comprehensive final                35%

 

A standard grading scale will be used (90-100% A, 80-89% B, 70-79% C, 60-69% D, and under 60% E).   The final course grade may be curved up (but not down) in order to ensure that the overall average for sections 3 and 4 is at least 75%. 

 

Calculators:   You are allowed to use computational aids such as calculators on homework assignments, but they will not be allowed during exams. 

 

Attendance:  Attendance is required, and you are responsible for all lecture material and announcements made in class.  However, lecture and recitation attendance will not be recorded.   Legitimate reasons for missing class include serious illness, illness or death of a family member, university-related trips, and major religious holidays.  Students asking for makeup exams or quizzes or extensions of written homework due dates should let their instructor know of any conflicts as soon as possible (but in any case no more than a week after the absence) and be prepared to provide written documentation. 

 

Academic integrity:  Violations of academic integrity will be taken seriously and dealt with according to university regulations.   Instances of cheating on exams and quizzes include (but are not limited to) copying from or communicating with another student, bringing any kind of notes into the exam unless expressly permitted, and using any type of electronic aid.  You are encouraged to work together on homework, but you are required to write up and submit your own solutions to all assignments.  Students caught cheating will be prosecuted according to university guidelines.

 

Classroom Decorum:  Students are expected to be attentive and courteous during class.  During class, please put away newspapers, turn off cell phones, and refrain from using laptops or other electronic devices except for note-taking purposes. 


Links to demonstrations, etc.


Vector calculus is a highly geometric subject. You are STRONGLY encouraged to use software tools to help you visualize concepts. Here are some links to online and software resources that might find helpful.

General graphics and calculus tools:
  • If you have a Mac, I highly recommend the Grapher utility (found in the Applications/Utilities/ folder in Mac OS 10.4 and later).
  • Gnuplot is a free, open-source plotting package. Installations are available for a variety of platforms. Google to find it.
  • Winplot is a free Windows-specific plotting package. As above, Google to find it.
  • Wolfram Alpha has some basic plotting functionality, along with some symbolic manipulation capability. Click here for examples of plotting inputs (including 3D and parametric plots) and here for calculus examples.
  • High-powered general-purpose commercial packages such as Mathematica and Maple can carry out 3D plotting and lots more.

Vector calculus demonstrations:
  • The Wolfram Demonstrations Project has a wide range of demonstrations on mathematical topics, including multivariable calculus. Browse at your leisure. I may use some of these in class and/or add links below to specific demonstrations during the semester. Note that you might have to download a plugin to view these demos.
  • The Exploring Multivariable Calculus website also has graphical demonstrations. Have a look around.

Exam review materials

Final Exam
  • The Final Exam review sheet contains information about the exam and some sample problems.
  • Please note that office during exam week will be Tuesday and Thursday 2-4 p.m., and that I will NOT necessarily be available during the office hours that I scheduled during the semester.

Exam 2

Exam 1

General exam resources
  • There is not a UK MA213 test bank. Robert Molzon has posted a few of his old exams on the web (check the bottom of the web page). His exams will not cover exactly the same material as ours but still can provide you with some good practice problems.
  • If you look around the web a little bit, you can probably find practice vector calculus exams from other schools. For example, the University of Michigan has a website with old multivariable calculus exams. However, the level of difficulty of the exams and the material covered on each might be substantially different than what you can expect on your exam.