MAT 211 Calculus III,Section 01, CRN 25751, Spring 2005

 

 

Class meets MW 10:00-11:10 in NSM A204, F 10:00-11:50 in WH F154.

 

Instructor:Serban Raianu

Office: NSM A-123; Office phone number: (310) 243- 3139

e-mail address: sraianu@csudh.edu; URL: http://www.csudh.edu/math/sraianu;

Office hours: MW: 11:15-12:45, F: 12:00-1:00, or by appointment.

 

Course Description: MAT 211, Calculus III,covers Chapters 13-17 from the textbook:

Multivariable calculus: analytic geometry, scalar and vector products, partial differentiation, multiple integration, change of coordinates, gradient, optimization, line integrals, Green's theorem, elements of vector calculus.

 

Text: James Stewart, Calculus, 5th edition, Brooks/Cole, 2003.

 

Objectives: After completing MAT 211 the student should be able to:

  • Gain an intuitive understanding of functions of several variables via level curves and surfaces, and related concepts of limit, continuity and differentiability.
  • Perform partial differentiation and multiple integration of functions of several variables.
  • Change from Cartesian co-ordinates to polar, cylindrical or spherical co-ordinates and vice versa, perform differential (partial or ordinary) and integration (multiple or single) in curvilinear co-ordinate systems and effect transformation via the Jacobian..
  • Utilize vectors to deal with spatial curves and surfaces, and calculus of several variables
  • Understand and use the concepts of vector calculus: gradient, curl, divergence, line and surface integrals, Green's, Stokes' and the divergence theorem.
  • Apply calculus of several variables to solve problems of optimization, differential geometry and physics

 

Prerequisites: MAT 193 or equivalent with a grade of "C" or better.

 

 

Grades: Grades will be based on three in‑class 70-minutes examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, attendance and other assignments (15%) for the remainder.

The exact grading system for your section is the following:

Each of the three 70-minutes exams will be gradedon a 100 scale, then the sum of the scores is divided by 5 and denoted by E.

Homework will be collected three times, on the days of the three exams, and each homework is worth 5 points. No late homework will be accepted. The average of all homework scores is denoted by H.

5 to 10 minutes quizzes will be given in principle every Friday, with the exception of the review and exam days, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q.

There are also 5 points awarded for attendance and class participation. This portion of the grade is denoted by A.

The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F.

To determine your final grade,compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

†††††††† A: 93‑100;††††† A‑: 90‑92;††††† B+: 87‑89;††††† B: 83‑86;†† B‑: 80‑82

††††††† C+: 77‑79;††††† C: 73‑76;††††††† C‑: 70‑72;††††† D: 60‑69;†† F: Less than 60.

 

WebWorK:There will be three WebWork assignments. You should go to my web site, follow the link, then log in using as user name your CSUDH email user name (i.e. first initial followed by last name), and the last 5 digits of your ID as password (change the password after the first log in). Each of the three assignments are due before 11pm of the day before each of the three exams. Completing an assignment will bring you 10 bonus points toward the grade of the following exam (this is 2 extra points toward your final grade).

 

Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with me, and I may then substitute the relevant score from your final examination for the missing grade.

 

Students with Disabilities: Students who need special consideration because of any sort of disability are urged to see me as soon as possible.

 

Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

 

Technology: Symbolic calculators, such as TI-89 or TI-92 are not acceptable for this course.

 

 

Tentative schedule and homework assignments

M 1/24: 13.1 Three-Dimensional Coordinate Systems. #13, 22, 30, 39, 40, 41

W 1/26: 13.2 Vectors. #4, 20, 27, 29, 30, 33, 43

F: 1/28: 13.3 The Dot Product. #21, 27, 34, 45, 49, 52, 53

M 1/31: 13.4 The Cross Product. #3, 11, 15, 24, 27, 29, 31, 36, 39, 41

W 2/2: 13.5 Equations of Lines and Planes. #3, 5, 7, 12, 23, 26, 33, 36, 51, 59, 66, 72

F 2/4: 13.6 Cylinders and Quadric Surfaces. #4, 9, 11, 13, 15, 37, 40, 42

M 2/7: 13.7 Cylindrical and Spherical Coordinates. #9, 19, 23, 29, 31, 41, 50, 60, 64

W 2/9: 14.1 Vector Functions and Space Curves. #4, 9, 19-24, 39

F 2/11: 14.2 Derivatives and Integrals of Vector Functions. #5, 14, 19, 25, 33

M 2/14: 14.3 Arc Length and Curvature. #1, 5, 10, 14, 18

W 2/18: 14.4 Motion in Space: Velocity and Acceleration. #1, 7, 19, 21, 23, 24, 28, 29, 33, 40

F 2/20: Review

M 2/21: Presidentsí Day

W 2/23: Exam I

F 2/25: 15.1 Functions of Several Variables. #9, 30-32, 37, 53-58

M 2/28: 15.2 Limits and Continuity. #5, 9, 18, 26, 30, 37

W 3/2: 15.3 Partial Derivatives. #4, 8, 14, 15, 31, 47, 66, 67, 68d

F 3/4: 15.4 Tangent Planes and Linear Approximations. #1, 4, 13, 20, 23, 31, 33, 38

M 3/7: 15.5 The Chain Rule. #1, 5, 11, 14, 17, 23, 27, 31, 33, 38, 43, 47

W 3/9: 15.6 Directional Derivatives and the Gradient Vector. #1, 4, 9, 15, 24, 30, 34, 36, 41, 54

F 3/11: 15.7 Maximum and Minimum Values. #3, 5, 7, 27, 29, 41

M 3/14: 15.8 Lagrange Multipliers. #5, 9, 15, 17, 29

W 3/16: 16.1 Double Integrals over Rectangles. #7, 9, 13, 17

F 3/18: 16.2 Iterated Integrals. #3, 5, 7, 13, 19, 25

M 3/21: 16.3 Double Integrals over General Regions. #7, 11, 15, 21, 25, 31, 37, 41, 47

W 3/23:16.4 Double Integrals in Polar Coordinates. #7, 11, 17, 21, 25, 28, 29, 33

F 3/25: 16.5 Applications of Double Integrals. #5, 11, 14, 21

M 3/28: Spring Recess

W 3/30: Spring Recess

F 4/1: Spring Recess

M 4/4: Review

W 4/6: Exam II

F 4/8: 16.6 Surface Area. #1, 3, 7, 11, 24

M 4/11: 16.7 Triple Integrals. #7, 11, 13, 19, 31, 40

W 4/13: 16.8 Triple Integrals in Cylindrical and Spherical Coordinates. #7, 9, 17, 29

F 4/15: 16.9 Change of Variables in Multiple Integrals. #9, 11, 15, 17, 18, 19, 23

M 4/18: 17.1 Vector Fields. #3, 5, 6, 11, 25

W 4/20: 17.2 Line Integrals. #1, 5, 7, 11, 15, 17, 19, 21, 31, 37, 39, 41, 42

F 4/22: 17.3 The Fundamental Theorem for Line Integrals. #1, 3, 5, 13, 19, 29, 31

M 4/25: 17.4 Green's Theorem. #1, 7, 9, 12, 15, 17, 21

W 4/27: 17.5 Curl and Divergence. #7, 13, 15, 19, 25, 27, 33, 34

F 4/29: 17.6 Parametric Surfaces and Their Areas. #1, 3, 5, 7, 9, 11-16, 19, 22, 31, 37, 39, 45

M 5/2: 17.7 Surface Integrals. #9, 13, 19, 21, 23, 25, 27, 39, 41

W 5/4: 17.8 Stokes' Theorem. #1, 3, 5, 7 9, 11a, 13, 15, 17, 19

F 5/6: 17.9 The Divergence Theorem. #3, 5, 7, 9, 13, 15, 19, 25, 27, 29

M 5/9: Review

W 5/11: Exam III

F 5/13: Review

Final examination: Monday, May 16, 10:00-12:00.