Calculus III - Spring 2006

(last updated 05/02/2006)



Final Exam Notice: The final examination for this course is scheduled for Thursday, May 4, 2006. It will be held from 6:00pm to 7:50pm in Silver Center Rm. 509. Please arrive 5 - 10 minutes early to allow for seating and exam distribution.

Instructor: S. M. Mintchev

Meeting Time: TR 6:20pm - 8:00pm

Location: Tisch Bldg., Rm. UC55

Instructor Information:

General Information about the Course: This course is a continuation to the Calculus II course taught at New York University. The topics covered build on the previously developed concepts of continuity, differentiation, and Riemann integration on the real line and extend these to functions of several variables, and further to vector-valued functions. While not required, completion of the Calculus I and II courses at NYU or equivalent is strongly recommended.

Text: Calculus III: Multivariable (Materials Excerpted from "Calculus. Ninth Edition." by Salas, Hille, and Etgen), J. Wiley Publications - Custom Services.

Grading Policy: There will be six, approximately-bi-weekly homework assignments, posted on this website at the beginning of the discussion period for the required material, and due at the beginning of class on the posted date (see below for the list of assignments). Usually, about 30 problems will be assigned at a time. Of these, the grader for the course will choose about 7 at random and grade them. Late homework will NOT be accepted, except with a relevant doctor's note, etc. Some of the homework assignments (specificity left to the instructor's discretion) will be followed by a 20 min. in-class quiz consisting of two or three problems related to the homework material. In addition to these assessments, there will be two exams for the course. A midterm exam will be given approximately in the first week of March. The midterm will cover the first half of material for the course - in particular, this will be the material from the first three homework assignments. There will also be a final examination administered during the end-of-semester examination period; this exam will cover the second half of material taught in the course. The values of these components towards the final grade in the course are presented below:

Component

Value

Homework

15 %

Quiz Total

25%

Midterm Exam

30 %

Final Exam

30 %

Students are advised to solve homework problems carefully and to write up neat presentations of their solutions. While collaboration is encouraged, students should make a strong individual (meaning: separated from each-other in space, and entirely independent) effort on a problem before attempting collaboration with peers. Such work will be key to placing the student in a position to perform well on the examinations. In addition, since there will be no examinations before the ADD/DROP deadline for most NYU programs, the first two homework assignments should be interpreted as being illustrative of the workload required for passing the course; the grades on these, as well as on any quizzes given during the first 4-6 weeks should be used to make the ADD/DROP decision if necessary.

Syllabus (please note that this schedule is tentative and will likely be adjusted as the semester progresses):

Date

Chapter.Section

Topic

01/17/2006

12.1 - 12.3

Cartesian Coordinates, Vectors

01/19/2006

12.4, 12.5

Dot Product, Cross Product

01/24/2006

12.6, 12.7

Line, Planes

01/26/2006

13.1-13.3

Vector Functions, Differentiation Formulas

01/31/2006

13.4, 13.5

Curves, Arc Length, Curvature

02/02/2006

14.1 - 14.3

Local Curves, Level Surfaces

02/07/2006

14.4, 14.5

Parial Derivatives, Limits

02/09/2006

14.6

Continuity

02/14/2006

15.1, 15.2

Gradient, Directional Derivative

02/16/2006

15.3

 Chain Rule

02/21/2006

15.4 Normal, Tangent Line, Tangent Plane

02/23/2006

 15.5 Maxima and Minima

02/28/2006

 15.6, 15.7 -same-

03/02/2006

 15.8, 15.9 Differential of a Function

03/07/2006

 16.1, 16.3 Double Integrals, Iterated Integrals

03/09/2006

Midterm Examination
03/14/2006
 SPRING
 BREAK
03/16/2006
 SPRING BREAK

03/21/2006

16.4, 16.5

Double Integrals in Polar Coordinates
03/23/2006

16.6, 16.7

Triple Integrals
03/28/2006

16.8, 16.9

Cylindrical and Spherical Coordinates
03/30/2006

16.10

Change of Variables
04/04/2006

17.1, 17.2

Line Integrals
04/06/2006

17.4, 17.5

Green's Theorem
04/11/2006

17.5

-same-
04/13/2006

17.6

Surface Area
04/18/2006

17.7

Surface Integrals
04/20/2006

17.8

The "Grad" Operator
04/25/2006

17.9

Divergence Theorem
04/27/2006

17.10

Stokes Theorem

Homework Assigments (please see grading policy section for requirements):

Assigned

Due

Homework Exercises

01/17/2006

01/31/2006

 Section 12.1: 38, 48
Section 12.3: 20, 38, 42
Section 12.4: 11, 44, 53, 56
Section 12.5: 17, 19, 40, 42
Section 12.6: 17, 18, 40, 44
Section 12.7: 43, 45, 46

02/02/2006

02/14/2006

 Section 13.1: 18, 40, 58
Section 13.2: 28, 36
Section 13.3: 27, 28, 44
Section 13.4: 16, 17, 19, 22
Section 13.5: 24, 50, 58
Section 14.1: 38, 39
Section 14.2: 27, 28, 30, 38, 42, 44, 53 (a)
Section 14.3: 40

02/21/2006

02/28/2006

 Section 14.4: 38, 61
Section 14.5: 10, 19, 20
Section 14.6: 18, 20, 32
Section 15.1: 5, 6, 12, 32, 42
Section 15.2: 2, 22, 36, 40
Section 15.3: 12, 18, 24, 36
Section 15.4: 6, 34

03/22/2006

04/04/2006

 Section 15.5: 22, 24, 26
Section 15.6: 16, 20, 30
Section 15.7: 30, 32
Section 15.8: 16, 34
Section 15.9: 24, 31, 32
Section 16.1: 4, 8, 10
Section 16.3: 14, 16, 18, 55, 60
Section 16.4: 12, 16, 26
Section 16.5: 6, 18, 25, 26

04/10/2006

04/25/2006

Section 16.6: 4, 7, 9
Section 16.7: 4, 7, 36, 50
Section 16.8: 12, 16, 26
Section 16.9: 18, 34
Section 16.10: 15, 26
Section 17.1: 4, 6, 20, 28
Section 17.2: 10, 22, 24
Section 17.4: 28
Section 17.5: 22, 24
Section 17.6: 5, 6, 8, 16, 29, 32(a)(c), 38 (*)


Section 17.7: 9, 10, 12, 28, 31, 32
Section 17.8: choose 6 from 1 - 14
Section 17.9: 12, 14, 20, (23, 24 physics *)
Section 17.10: 5, 6, 7, 12, 18