University of Rhode Island    Department of Mathematics

MTH 243-1000  Calculus III  Summer 2004

MTWTh 8-10 a.m.

Instructor: Dr. Orlando Merino, Tyler Hall 220, 874-4442,
Text:  McCallum, Hughes-Hallet, et. al., Multivariable Calculus, THIRD EDITION
Prerequisites: MTH 142 or equivalent
Calculators: A graphing calculator is required

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. We will continue to use Maple V  in this course. The Maple software is available in the campus computer labs. Our work with Maple will be organized into Maple 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.

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

Course grade =  ( 15 E1 + 15 E2 +  30 FE + 40 CW ) / 100

Key: E1, E2, and E3 correspond to Exams, FE = Final Exam, CW = Class Work.
Class Work may include collected homework, quizzes, Maple assignments or special projects.
At least 50% of the Final Exam will consist of questions on the material discussed after the second exam.

How to get help
I may help you with questions, just stop by my office. However, ocasionally I won't be able to take walk-ins, it depends on what I am doing at the moment. To be sure, you may get an appointment, just call me at 874-4442. Also, I will answer all questions sent by electronic mail at

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

MTH 243-1000  Calculus III Summer 2004

Day  Event Text   Problems 
Monday, May 24   12.1 11,12,19-22, 29, 34 
    12.2  1,5,7,9,11,16,18,19 
Tuesday, May 25   12.3  1,4,5,7,10,20,28,30 
    12.4  1,2,8,10,11,23,2430 
Wednes, May 26   12.5  1,2,7,8,28 
    13.1  1-6,8,14,29,30 
Thursday, May 27   13.2  11,14,19,28,30 
    13.3  1,4,8,14,16,19,2736,37,42 
 Monday, May 31  No Class    
Tuesday, June 1   13.4  1,4,5,10,19,22,27 
    14.1  1,3,7,14,17,20
Wednes June 2  TEST 1 14.2  1,4,5,14,22-28,35,41 
Thursday June 3   14.3  1-7,14,15,22, 
    14.4  1-11,19,22,29,35,49,58,64 
Friday June 4  Monday Makeup 14.5  1-11,14,19,23,28,35 
    14.6  1,4,7,11,14,20,23 
Monday June 7   14.7  1-10,14,22,31,35 
    15.1  1-11,19-22 
Tuesday June 8   15.2  2,5,7,14-16,19-21,23
Wednes June 9   16.2  1-7,11-14,18,28-30,34-40
    16.3 1-5,7-11,28-31,41,42
Thursday June 10  TEST 2 16.4 1,4,5-11,14,16,17,20-23
Monday June 14   16.5 1-7,14-16,20-23,31,32,35 
    16.7 1-4,10,11
Tuesday June 15   17.1 1-11,19,20,28,32,35,41,47,58
    17.2 1-7,14-16,22-28,
Wednes June 16   17.4 1-7
    18.1 1,3,5-10,14-16
Thursday June 17   18.2 1-11,16
    18.3 1-6,11,14,19,22,28
Monday June 21   18.4 1-7,16,19,22 
    19.1 1-4,10,11,14,19 
Tuesday June 22   19.2 1-10
    20.1 1-11,14,19
Wednes June 23   20.2 2-7
    20.3 2-7
Thursday June 24  FINAL EX