MATH361- Multivariable Calculus

Spring 2010


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Course Description:   Multivariable Calculus is the third and final course of the calculus sequence.  Material covered will include vectors and the geometry of space; vector-valued functions and the calculus of these functions; functions of several variables and the calculus of these functions; coordinate systems including polar, cylindrical, and spherical;  and vector fields and their calculus.  In order to increase the likelihood of success in this course it is recommended that the student attend class without fail, religiously work the homework, read the textbook, focus on understanding the concepts (not just the rote computations), and seek help from the professor and other sources (tutoring, library, textbook website, etc.) when needed. 

Course Objectives:

  •  The student will be able to work with vectors and understand the geometry of space.  This includes using the dot and cross products as well as understanding and being able to graph equations of line, functions and surfaces in space. 

  •  The student will be able to work with polar, cylindrical and spherical coordinates.

  •  The student will be able to perform calculus with vector-valued functions.

  •  The student will be able to understand and perform the calculus on functions of several variables.

  •  The student will be able to compute multiple integrals in rectangular, polar, cylindrical and spherical coordinates.

  •  The student will be able to understand and work with vector fields including using Green's and Stokes' theorems.

  •  The student will be able to use MAPLE to solve applied problems using integrals and series. 

Prerequisites:  Completion of MATH 262 with a grade of C or better OR placement via the AP Statistics exam.  Please see me as soon as possible if you think you may not meet the prerequisites for this course!

Professor:  Dr. M. Leigh Lunsford.  For Dr. Lunsford's office location, phone number, email address, schedule (including office hours), and other general information, go to her homepage:  http://www.mathspace.com/Lunsford/

Meeting Times and Locations:   Please note that this course includes a required laboratory component which is in a different meeting place and at a different meeting time.

  • MATH361-01 - Multivariable Calculus, MWF 9:00-9:50, Ruffner 352

  • MATH262-01-LAB - Lab, R 9:15-10:45, Ruffner G56

Required WebAssign On-Line Homework System:  You will be required to use WebAssign to complete on-line homework assignments.  Please see the class homepage for directions on how to access WebAssign.

Required Course Textbook:  There are two options available for you when purchasing your textbook.  Hopefully you already have a copy of Calculus Concepts and Contexts, 3rd Edition by James Stewart.   Otherwise I recommend that you buy Multivariable Calculus Concepts and Contexts, 3rd Edition by James Stewart.  The book store should sell copies of both.  If you have purchased a new textbook it should be bundled with an access code to WebAssign.

Textbook Website:  The textbook website contains many resources including the Tools for Enriching Calculus (TEC).   The TEC applets help you understand and visualize calculus by exploring concepts through interactive modules and animations.  TEC icons in the text direct you to the appropriate module for exploration.  TEC also has homework hints for specially marked exercises (numbered in red such as 23) in each section.  Also, in order to help you evaluate your progress, for each section of the textbook there is a Web quiz with answers. 

Required Technology/Computer Configurations: 

  • A calculator is not required for the course.  However, for routine computations, I highly recommend that you use the TI83 or TI83-Plus or TI84 or TI84-Plus.  Note that you will not be allowed to use any calculator that performs symbolic computations!

  • Make sure your computer is configured to run WebAssign and the applets on the textbook website and .

Supplements to the Text:  See pages xxii and xxiii of your textbook for a complete list of ancillaries available. 

Determination of Course Grade:

45% - Two In-Class Exams

10% - On-Line Homework

15% - In-Class Quizzes and Lab Assignments

  5% - Mathematics Cultural Points (cults)
25% - Comprehensive Final Exam

Grades will be assigned on a ten point scale (90's A; 80's B; 70's C; 60's D; 50's and below F).

In-Class Exams:  A minimum of a one week notice will be given for exam dates.  Please see the class schedule below for the tentative exam dates (for more detailed information about test dates see the Calendar in WebAssign).  Except in the case of an emergency, a make-up exam must be scheduled before the scheduled exam date.  If the exam has already been given and you have not previously scheduled a make-up, then you will receive a zero on that exam.  Please see the make-up policy below for additional information.

On-Line Homework:   Just like with anything else worthwhile in life, one must practice to become proficient at mathematics.   For this purpose you will have on-line homework due after every class period.  Your on-line homework problems will be graded and given through WebAssign.   Each day after class I will assign problems from the text to work on-line via the WebAssign system.  These will be due before the next class period.  You will only get two attempts to submit your WebAssign homework.  The on-line problems assigned will typically be the even problems in the book.  It is strongly suggested that you work similar odd problems in the book (which have an answer in the back of the book) for practice before attempting to work the on-line problems.

In-Class Quizzes:   Approximately each week a short (15 to 20 minute) quiz will be given in class.  Generally, quizzes will be given at the beginning of the lab period.  These quizzes will be based on your homework assignments and our class discussions.  I will try to give at least one class period notice for an in class quiz (please see the Calendar on WebAssign for the latest information on quiz dates).  Once a quiz has been graded and returned to the students, there will be no make-ups for that quiz, period.  Except in the case of an emergency, a make-up quiz must be scheduled before the scheduled quiz date.  Thus, contact me ASAP if you have an excused absence and need to make up a quiz.  Please see the make-up policy below for additional information.  All quizzes must be pledged.  

Lab Assignments:  Occasionally we will have a laboratory assignment to enhance the material we are learning in class.  Generally you will be allowed to work on a lab assignment with a partner.  Lab assignments may also emphasize the use of computer software such as Maple or Excel.  Late lab assignments will not be accepted and there will be no make-up lab assignments.

Mathematics Cultural Points (cults):  In order to receive the full 5% credit for mathematics cultural points you must earn at least 8 cults.  To determine how to earn cults please click here.  All cult submissions must be received by Friday, December 4 (the last day of class).  In addition, any cults that you submit as a write-up to a planned event (e.g., a colloquium), must be received no later than 2 class days after the event occurs.  Please note the deadline for obtaining approval for an article to present is Friday, November 20.

Final Exam:  The final exam for this course will be comprehensive.  You cannot miss the final - failure to take the final exam will automatically result in an F grade for the course.   Please see me as soon as possible if you may have a conflict with the final exam date.

Final Exam Date:   Thursday, April 29, 2010 from 11:30 a.m. -2:00 p.m.

Honor System:  I expect you to conform to the Longwood University Honor System as contained in the Student Handbook.  All material handed in to me (quizzes, tests, etc.) must be pledged.

Extra Credit:  Extra Credit will NOT be given - period.

Attendance & Excused Absences:   You are expected to attend every class.  If you miss classes it will most likely be reflected in your grades (i.e. you will perform poorly).  The following college attendance policy will be followed per the Class Attendance section of the Academic Regulations chapter of the Longwood University Undergraduate Catalog:  Missing 10% of class meetings may result in a lowering of one letter grade.   Missing 25% of class meetings for any reason will result in an automatic “F” for the course.  Absences are excused only for college sponsored activities and recognizable emergencies.  You must have the proper documentation for an excused absence.  Student Health Services can provide documentation only for students hospitalized locally or absent at the direction of Student Health Services personnel You must also assume full responsibility for all material covered during your absence, including scheduling any make-up quizzes or exams.  A grade of "0" will be assigned for all work missed due to unexcused absences.

Make-up Policy:    Make-up assignments will be given only when the reason for missing the assignment meets the criteria for an excused absence (see above).  Except in the case of emergencies, make-up assignments must be scheduled and/or turned-in before the due date of the assignment being made-up (i.e. you should plan ahead if you know you are going to miss class).  As a general rule, you can expect that make-up tests will more difficult than regularly scheduled tests.  If you have a recognizable emergency, please contact me as soon as you can to discuss your make-up options.

Resources for Students Learning Calculus:  

  • Me!  I want you to consider me to be your number one resource!  In addition to seeing me during my office hours, you are welcome to call me or send me email if you have questions about your homework.  If you are unable to see me during my office hours please make an appointment with me! 
  • Longwood's Academic Support Center:  The Academic Support Center offers tutoring for MATH262 - please see their website for more details. 
  • Textbook Resource:  There is a website that accompanies your textbook which also has practice Web quizzes and detailed solutions to problems. 

Office of Disability Services:  Any student who feels s/he may need an accommodation based on the impact of a physical, psychological, medical, or learning disability should contact me privately. If you have not already done so, please contact the Office for Disability Services  (103 Graham Building, 395-2391) to register for services.

Class Schedule:  Below is a tentative class schedule.  This schedule may change due to class pace, etc.  However, it is provided here for your information.  For a more detailed schedule depending on our actual classroom interaction please see the Calendar in WebAssign.

Week of Class Topics Covered Corresponding Sections in Textbook
1

Three-Dimensional Coordinate Systems; Vectors; Dot and Cross Products

9.1 - 9.4

2

Equations of Lines and Planes in Space; Functions and Surfaces

9.5, 9.6

3

Polar, Cylindrical, and Spherical Coordinates

Appendix H, 9.7

4

Vector Functions and Space Curves; Derivatives and Integrals of Vector Functions; Arc Length

10.1 - 10.3

5 Curvature; Motion in Space (Velocity and Acceleration); Parametric Surfaces

10.3 - 10.5

6

Functions of Several Variables; Limits and Continuity

Review for Test 1

Test 1

11.1, 11.2

7

Partial Derivatives and Tangent Planes

11.3, 11.4

8

The Chain Rule; Directional Derivatives and the Gradient Vector

11.5, 11.6

9

Maximum and Minimum Values; Lagrange Multipliers

11.7, 11.8

10

Double Integrals over Rectangles; Iterated Integrals; Double Integrals over General Regions

12.1, 12.2, 12.3

11

 Double Integrals in Polar Coordinates; Applications of Double Integrals; Surface Area

12. 4 - 12.6

12

Triple Integrals; Triple Integrals in Cylindrical and Spherical Coordinates; Vector Fields

12.7, 12.8, 13.1

13

Line Integrals; The Fundamental Theorem of Line Integrals; Green's Theorem

Test 2

13.2 - 13.4

14

Curl and Divergence; Surface Integrals; Stokes' Theorem

13.5 - 13.7

15 Final Exam  
 

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