MAT240 Section 3323:  Calculus with Analytic Geometry III

Instructor:  James Sousa

 

Course Description

                Vector-values functions of several variables, multiple integration, introduction to vector analysis.  Prerequisite:  Grade of “C” or better in MAT230 or MAT231.

 

Course Competencies

ุ       Perform operations on vectors.

ุ       Use vector operations in applied problems.

ุ       Use plane and space vectors to solve geometry and physics problems.

ุ       Use contour diagrams to analyze the behavior of a function of several variables.

ุ       Use partial derivatives to solve optimization problems.

ุ       Set up and compute double and triple integrals in any order of integration using rectangular coordinates.

ุ       Set up and compute double and triple integrals in polar, cylindrical, and spherical coordinates.

ุ       Use line integrals to compute the work done by a vector field along a curve.

ุ       Use surface integrals to compute the flux of a vector field through a surface.

ุ       Use multiple integrals to calculate line and surface integrals.

 

Class Time and Location

                Monday – Thursday in Room B208 from 7:45am – 8:50am

 

How to Contact The Instructor:        

Phone:  602-285-7154                                            Email:  james.sousa@pcmail.maricopa.edu

Office:     A236                                                       Office Hours:  Mon – Fri. 10:00am – 10:50am or by appointment

                                               

Math Help Resources:

ุ       I highly recommend getting to know your classmates and forming study groups.  Your classmates are your best resources.

ุ       The “Math Zone” located in building A on the second floor is open Mon – Saturday and offers free tutoring.

ุ       The Learning Center and the Math and Science Center also offers free tutoring.

ุ       My office is also in the “Math Zone”.  If my door is open I’m available for questions.

ุ       Check the class website for useful resources online at http://www.pc.maricopa.edu/Mathematics/faculty/jsousa/

ุ       The Disability Support Services (DDS) office coordinates services, which will ensure students with disabilities have equal access to college programs.

 

Materials:

ุ       Text:  Calculus:  Early Transcendental Functions, 3e, Larson, Hostetler, Edwards

ุ       Calculator:  TI-89 (recommended)  Other graphing calculators can be used but will not be demonstrated in class.

 

Attendance and Classroom Policies:

ุ       You are expected to attend and participate in every class.  If for some reason you will not be in class you should call me and let me know before the class meeting.  You are still responsible for turning in all assignments when due.   

ุ       No make-up tests/quizzes will be given.  If you can not make a scheduled test or quiz, you must arrange a time to take it early. 

ุ       Turn off all pagers and cell phones before entering the classroom to minimize interruptions.

 

Grading Policy:

 

Quizzes/Maple Labs:  15%                                  Tests:  65%                                            Final:  20%

 

ุ       Assignments will not be collected, but are recommended to be completed daily.  Doing the homework is the best way to prepare for tests and quizzes.  If you are able to answer student homework questions on the board, you can receive extra points, up to 5 points per test.   

ุ       Quizzes/Maple Labs:  Quizzes will be given weekly.  Quizzes may be individual, group, in class or take home. Some quizzes may be unannounced. Maple Labs will be assigned throughout the semester.  Class time may or may not be given to complete the labs.  

ุ       Tests:  Tests will be given in a variety of ways.  There may be no calculator parts, calculator parts, and take-home parts. 

ุ       Final:  A comprehensive final exam will be given at the end of the semester.  It can also take the place of your lowest test if you score better on the final than your lowest test.  The final exam is Monday, December 12th from 7:00am – 8:50am. 

 

Cheating Policy:

                Cheating of any kind will not be tolerated.  A student caught cheating will get an automatic zero on the given assignment/quiz/test.  You may receive an F in the class.     

               

 

Drop Policy:

                If for some reason you need to drop this course please take proper action.  You must fill out a drop for before October 7th without my signature.  You must fill out a drop form by Novemeber 25th with my signature.  Don’t just stop coming.  However, the instructor reserves the right to drop you after missing 2 weeks worth of classes.

Assignment Problems:  Problems are subject to change.  Additional Assignment may be given. 

You can always check online for when assignments are assigned at  http://www.pc.maricopa.edu/Mathematics/faculty/jsousa/  .

 

MAT240:  Calculus III Assignments

The following are a list of assignments for each section.  The assignments are subject to change. 

 

Chapter 10:  Vectors and Geometry of Space

10.1:  Vectors in a Plane (15)                                                                  1,5,9,17,21,25,33,41,53,61,65,69,73,77,81

10.2:  Space Coordinates and Vectors in Space(16)                                3,7,11,15,19,31,35,39,43,47,51,63,67,71,81,93

10.3:  Dot Product of Two Vectors (11)                                                 1,5,13,17,21,25,33,45,47,63,67

10.4:  Cross Product of Two Vectors(10)                                               1,5,9,13,29,37,41,43,45,47

10.5:  Lines and Planes in Space (14)                                                     5,9,13,17,21,33,37,41,45,49,53,69,73,81

10.6:  Surfaces in Space (16)                                                                  1,3,5,7,9,11,13,15,19,23,25,41,45,47,49

10.7:  Cylindrical and Spherical Coordinates (18)                   5,9,13,17,21,29,33,45,47,51,59,63,81,83,85,91,95,99

 

Chapter 11:  Vector-Valued Functions

11.1:  Vector-Valued Functions:                                                             1,3,5,9,13,15,21,33,37,45,49,63,67,69,71

11.2:  Diff/Int of Vector-Valued Functions:                                            3,9,11,19,27,33,37,45,47,49,51,53,59

11.3:  Velocity and Acceleration:                                                            3,5,13,17,19,25,27,41

11.4:  Tangent Vectors and Normal Vectors                                           1,3,9,17,19,21,23,25,31,33,49,57

11.5:  Arc Length and Curvature                                                             7,9,17,19,25,27,35,37,39,51,55

 

Chapter 12:  Functions of Several Variables

12.1:  Functions of Several Variables:                                                    7,11,17,19,21,23,31,33,35,45-48,49,51,73,75

12.2:  Limits and Continuity:                                                                   7,9,11,15,17,19,21,25,27,31,33,37,41

12.3:  Partial Derivatives:                                                                        7,9,11,13,15,25,35,37,47,51,55,61,75,(93)

12.4:  Differentials:                                                                                 1,7,9,11,13,31,37   

12.5:  Chain Rule for Functions of Several Variables:                            1,7,11,15,17,19,21,23,27,29,33

12.6:  Directional Derivatives and Gradients:                                          1,5,7,11,13,19,21,31,33,39,41,43,55

12.7:  Tangent Planes and Normal Lines:                                                5,9,11,15,17,25,27,29,41,49

12.8:  Extrema of Functions of Two Variables:                                      5,7,9,11,23,25,27,31,33,47,51

12.9:  Applications of Extrema                                                                3,5,9,19,29,47

12.10:  Lagrange Multipliers:                                                                  1,7,9,17,21,23

 

Chapter 13:  Multiple Integration

13.1:  Iterated Integrals and Area in the Plane:                                        3,7,11,15,19,23,27,29,31,35,39,43,47,51,55

13.2:  Double Integrals and Volume:                                                      7,9,11,15,21,23,25,33,35,43,49,55

13.3:  Change of Variables:   Polar Coordinates                                     1,5,9,11,15,17,21,23,27,29,39,41,(55)

13.4:  Center of Mass and Moments of Inertia:                                       (5,11,17,27,35)

13.5:  Surface Area:                                                                                3,11,15,21,23,31

13.6:  Triple Integrals and Applications:                                 3,5,7,13,17,23,25,29,31,47

13.7:  Triple Integrals in Cylindrical/Spherical Coord.:                           5,7,9,11,13,15,21,31

 

Chapter 14:  Vector Analysis

14.1:  Vector Fields:                                                                                1,3,5,7,9,13,21,19,31,35,37,43,51,55,59,69

14.2:  Line Integrals:                                                                               1,3,7,9,11,15,21,23,29,33,43,47

14.3:  Conservative Vector Fields                                                           3,5,7,11,15,19,35

14.4:  Green’s Theorem                                                                          3,5,7,11,13,21,27

 

Course Timeline (subject to change)

 

Week #1  (8/22 – 8/ 26)  10.1 – 10.4                                                      Week #2  (8/29 – 9/2) 10.4 – 10.7

Week #3   (9/5 – 9/9)  10.7, Maple, Ch10 Test                                       Week #4  (9/12 – 9/16) 11.1 – 11.2, Maple

Week #5  (9/19 – 9/23)  11.3 – 11.5                                                       Week #6  (9/26 – 9/30)  Ch 11 Test, 12.1-12.2

Week #7  (10/3 – 10/7)  Maple, 12.3 – 12.4                                           Week #8  (10/10 – 10/14)  12.5 – 12.7

Week #9  (10/17 – 10/21) Ch 12 Test , 12.8                                           Week #10 (10/24 – 10/28)  12.9-12.10, Maple

Week #11  (10/31 – 11/4)  13.1 -13.3                                                     Week #12  (11/7 – 11/11) 13.5

Week #13  (11/14 – 11/18)  Ch 12-13 Test, 13.6-13.7, Maple               Week #14  (11/21 – 11/25)  13.7, 14.1

Week#15  (11/28 – 12/2)  14.2 – 14.4                                                    Week #16:  (12/5 – 12/8)  Ch 14 Test, Final Exam Review

Week #17:  12/12 Final Exam:  7:00-8:50am

 

Closing Remarks:

This class will be a challenging but hopefully rewarding experience for you.  It is very important to stay current on all assignments and seek help whenever you need it.  For every 1 hour of class it is expected that you may need to spend 2-3 hours of work outside the class to succeed.  I hope that if you have any concerns or comments throughout the class you will come and talk to me.  I am here to help you be success.  I look forward to a rewarding semester working with you.

 

 

The greatness of a nation can be judged by the way its animals are treated.                         Mohandas Gandhi