Calculus II - Spring 2005


NOTICE: The Final Examination for this course is scheduled for Wednesday, May 4, 2005, and will be administered in SILV 207. Please note that the room for the final exam is different from the room for the section's regular class time meetings. The exam starts at 8:00AM and will last until 9:50AM. Please arrive 5-10 mins. early in order to allow for seating and exam distribution.

Instructor: S. M. Mintchev

Meeting Time: TR 2:00pm - 3:50pm

Location: Waverly Bldg., Rm. 435

Instructor Information:

General Information about the Course: This course is the official continuation to the Calculus I 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. While some material may occasionally look familiar to that of the Calculus I course, most of the material covered will be brand new. The approach for this course is to introduce the student to a more rigourous framework, where a growing understanding of reading and composing logical proofs will be expected in addition to the usual mastery of computational problems required in an introductory calculus sequence.

Grading Policy: There will be weekly homework assignments, posted by 6:00pm Thursday on this website, and due at the end of class on the following Tuesday. Usually, about 18 problems will be assigned each week. Of these, the grader for the course will choose about 6 at random and grade them. Late homework will NOT be accepted. In addition to these assigments there will be two exams during the semester; the exams will be administered at the one third, resp. two thirds, marks of the semester. The first exam will cover the first third of the material; the second will cover the second third. There will be a final examination administered during the end-of-semester examination period; this exam will cover the last third of material taught in the course. The values of these components towards the final grade in the course are presented below:

Component
 Value
Homework
 20 %
Exam 1
 20 %
Exam 2
 20 %
Final Exam
 40 %

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

Date
 Chapter.Section
 Topic
01/18/2005
 8.2; 8.6
 Review of Integration
01/20/2005
 8.7
 Numerical Integration
01/25/2005
 9.3 - 9.4 Polar Coordinates; Graphing
01/27/2005
 9.5 Computing Area in Polar
02/1/2005 9.6 - 9.7
 Parametric Equations
02/3/2005 9.8
 Arc Length
02/8/2005 Appendix I Complex Numeber System
02/10/2005 Appendix I -same-
02/15/2005 10.1, 10.2 Sequences, Limit of  a Sequence
02/17/2005 10.3 Limits with Proofs
02/22/2005 10.4
 Computing Limits
02/24/2005 Exam I
 Exam I
03/1/2005 10.5 more Proofs
03/3/2005 10.6, 10.7 Indeterminate Forms, Improper Integrals
03/8/2005 10.7 -same-
03/10/2005 11.1 Infinite Series
03/15/2005 Spring
 Break
03/17/2005 Spring
 Break
03/22/2005 11.1, 11.2 Infinite Series, Test for Convergence
03/24/2005 11.2 -same-
03/29/2005 11.3 Proofs of Convergence
03/31/2005 Exam II Exam II
04/5/2005 11.4 Conditional Convergence
04/7/2005 11.5 Taylor Series
04/12/2005 11.6 -same-
04/14/2005 11.7 Power Series
04/19/2005 11.8 -same-
04/21/2005 11.9 -same-
04/26/2005 Appendix II Numerical Methods
04/28/2005 Appendix II -same-

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

Assigned
 Due
 Homework Exercises
01/20/2005 01/25/2005 Section 8.2: 18, 32, 40, 43, 44, 52, 73, 74, 78, 79
Section 8.6: 8, 11, 15, 23, 25, 28, 38, 41
01/27/2005
 02/01/2005
 Section 8.7: 5, 25
Section 9.3: 23, 25, 26, 27, 36, 44, 45, 54, 63
Section 9.4: 23, 24, 29, 35, 40, 45, 48, 49, 54
02/03/2005
 02/08/2005
 Section 9.5: 7, 15, 24, 29, 31, 35, 41, 42
Section 9.6: 12, 23, 24, 31, 33, 34, 35, 42, 43, 55, 57
02/10/2005
 02/15/2005
 Section 9.7: 10, 14, 26, 30, 36, 39, 44
Section 9.8: 16, 20, 24, 27, 28, 37, 39, 42, 48, 51
02/17/2005
 02/22/2005
 Apendix I: 1.5.3, 1.5.4, 1.6.1(a)(b), 1.6.10, 1.7.1(g)(h), 1.7.4, 1.8.1, 1.8.6, 2.3.3(a)(b), 2.3.5, 2.3.6, 2.4.5, 2.4.6, 2.4.9
02/23/2005
 03/01/2005
 Section 10.2: 11, 27, 41, 45, 49, 57, 61, 63
Section 10.3: 27, 30, 35, 36, 39, 40, 46, 56
Solutions
03/03/2005
 03/08/2005
 Section 10.4: 7, 29, 35, 38 (abc), 41 (ab), 43, 44, 45, 47, 49
Section 10.5: 1, 25, 45, 46, 48, 50, 51, 52
Solutions
03/10/2005
 03/22/2005
 Section 10.6: 7, 20, 21, 30, 37, 41, 53, 57, 59 (ab), 62
Section 10.7: 13, 20, 23, 24, 34, 37, 38 (ab), 39, 56, 57 (ab), 60
Solutions
03/24/2005
 03/29/2005
 Section 11.1: 14, 17, 24, 39, 44, 47
Section 11.2: 15, 25, 32, 34, 40, 47, 48, 50, 54
Section 11.3: 19, 27, 28, 30, 37, 38, 45
Solutions
03/30/2005
 04/05/2005
 Section 11.4: 3, 13, 24, 26, 30, 31, 36, 44, 47, 50
Section 11.5: 8, 21, 25, 28, 32, 43, 45, 49, 50, 52, 58, 63
Solutions
04/07/2005
 04/12/2005
 Section 11.6: 1, 5, 9, 12, 26, 28, 32, 34 (abc)
Section 11.7: 1 (abcd), 2(abcd), 7, 11, 25, 31, 39, 41 (abc), 45, 48
Solutions
04/14/2005
 04/19/2005
 Section 11.8: 3, 8, 15, 23, 25, 27, 29, 31, 39, 41, 43, 44, 49, 50
Section 11.9:  3, 11(ab), 14, 17
Solutions