University of Rhode Island    Department of Mathematics

MTH 243/2&4   Calculus III  

Fall 2010

Instructor: Dr. M. Kulenovic, Lippitt Hall 200A, 874-4436, mkulenovic@mail.uri.edu

Text:  McCallum, Hughes-Hallet, et. al., Multivariable Calculus, 5-th Edition

Prerequisites: MTH 142 or equivalent

Calculators: A graphing calculator is required

Office Hours: M, F 10-11; W: 1-2 and by appointment

Introduction
MTH 243 is a third calculus course, with the focus on functions of 2,3, or more variables and the extensions of the ideas of elementary calculus to higher dimension. The Mathematica software is available in the campus computer labs. Our work with will be organized into Mathematica projects  that you can download from this web site, or will be handed to you in class.

Objectives.  At the conclusion of this semester you will be able to:

  1. Read and interpret 3d plots and 2d/3d contour diagrams,  read and interpret tables of functions of several variables, and  plot by hand the graph of simple functions of 2 variables, and simple contour plots of 2 or 3 variables.
  2. do calculations with vectors that involve the concepts of addition, scalar multiplication, dot product, cross product, magnitude, projection, and use these concepts in geometry and physics applications.
  3. calculate partial and directional derivatives, gradients and differentials of function of several variables, use local linearization to approximate functions,
  4. Calculate critical points, use the second derivative test to determine local extrema and saddle points (for functions of two variables only),  use these concepts to solve unconstrained optimization problems, and use Lagrange multipliers to solve constrained optimization problems.
  5. Calculate double and triple integrals algebraically, change variables in integrals  from rectangular coordinates to polar, cylindrical, spherical coordinates (and viceversa).
  6. use the concept of parametrization to represent curves and surfaces
  7. represent and interpret plots of vector fields (including flow lines)
  8. use vector valued functions to do calculations of line integrals, flux integrals, divergence, and curl, apply these concepts and Green's and Stoke's theorems to problems in physics and geometry,
  9. Calculate flux integrals geometrically and algebraically over surface graphs, portions of cylinders, and portions of spheres.

Evaluation
There will be two exams and a comprehensive final.  The course grade will be computed as follows:

Course grade =  ( 20 E1 + 20 E2 +  30 FE + 20 CW +10Math) / 100

Key: E1, E2, and E3 correspond to Exams, FE = Final Exam, CW = Class Work(Quizzes), Math = Mathematica.
Class Work consists of quizzes.

How to get help
I may help you with questions, just stop by my office. Tutors will be available as well.

Special Accomodations
Students who need special accomodations and who have documentation from Disability Services (874-2098) should make arrangements with Dr. Kulenovic as soon as possible.

Tutoring

Multivariable Calculus Mathlets

WileyPlus codes:

Section 2: MWF 9-9:50:  http://edugen.wiley.com/edugen/class/cls182694/

Section 4: MWF 3-3:50:  http://edugen.wiley.com/edugen/class/cls182696/

Mathematica Notebooks

To follow soon

Illness due to Flu The H1N1 Flu Pandemic may impact classes this semester. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify your instructor of your status, and we will communicate through the medium we have established for the class. We will work together to ensure that course instruction and work is completed for the semester. The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view www.cdc.gov/flu/protect/habits.htm. UrI information on the H1N1 will be posted on the URI website at www.uri.edu/news/H1N1, with links to the www.cdc.gov site.

 

 

MTH 243-2&4  Calculus III Fall 2010

Day

 Event

Text  

Problems 

Wed, Sep 8

 

12.1

11,12,19,22, 29, 34 

 

 

12.2 

1,5,7,9,11,16,18,19 

 Sep 13

 

12.3 

1,4,5,7,10,20,28,30 

 

 

12.4 

1,2,8,10,11,23,2430 

 

 

12.5 

1,2,7,8,29 

 Sep 20

 

13.1 

1-6,8,14,29,30 

 

 

13.2 

11,14,19,28,30 

 

 

13.3 

1,4,8,14,16,19,27,37,42 

 Sep 27

 

13.4 

1,4,5,10,19,22,27 

 

 

14.1 

1,3,7,14,17,20

 

 

14.2 

1,4,5,14,22-28,35,41 

 Oct 4

 

14.3 

1-7,14,15,22, 

 

 

14.4 

1-11,19,22,29,35,49,58,64 

 

 

14.5 

1-11,14,19,23,28,35 

 Oct 11

 

14.6 

1,4,7,11,14,20,23 

 

 

14.7 

1-10,14,22,31,35 

 Oct 18

 TEST 1

15.1 

1-11,19-22 

 

 

15.2 

2,5,7,14-16,19-21,23

 Oct 25

 

16.1 

1-7,11-14,19,28-30,34-40

 

 

16.2

1-5,7-11,28-31,41,42

 Nov 1

 

16.3

1,4,5-11,14,16,17,20-23

 

 

16.4

1-7,14-16,20-23,31,32,35 

 Nov 8

 

16.5

1,4,5,7,10,11, 30, 31

 

 

17.1

1,4,8,11,19,20,28,32,35,41,47

 Nov 15

 

17.2

1-7,14-16,22-28,

 

 

17.4

1-10, 20

 Nov 22

 

18.1

1,3,5-10,14-16

 

 

18.2

1-11,16, 21, 23, 25, 31

 Nov 29

 TEST 2

18.3

1-6,11,14,19,22,28

 

 

18.4

1-7,16,19,22 

 Dec 6

 Review

 

 

 

 

 

 

 Dec 9

 Classes end