Calculus III  Spring 2006
(last updated 05/02/2006)
Instructor: S. M. Mintchev
Meeting Time: TR 6:20pm  8:00pm
Location: Tisch Bldg., Rm. UC55
Instructor Information:
email address: mintchev@cims.nyu.edu
office: Warren Weaver Hall, Rm. 718
telephone: 2129983107
office hours: M 10:00am  11:00am; 2:00pm  3:00pm; T 11:00am  12:00pm
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
vectorvalued 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, approximatelybiweekly 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. inclass 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 endofsemester 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 eachother 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 46 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 
13.113.3 
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 