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NJIT Academic Integrity CODE:  All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly.  This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

 

 

 

Number of Credits:  3

 

Course Description:   Systematic development of partial differentiation, multiple and improper integrals, transformations, inverse and implicit function theorems, and integrals over curves and surfaces. Effective From: Spring 2009

Prerequisites:  Math 480 with a grade of C or better.

Textbook:  C. H. Edwards, Jr., Advanced Calculus of Several Variables, Dover Publications (1994)

Instructor:   (for specific course-related information, follow the link below)

 

Math 481-102

Prof. Muratov

 

Grading Policy:  The final grade in this course will be determined as follows: 

▪ Homework:	22%
▪ Midterm Exam I:	22%
▪ Midterm Exam II:	22%
▪ Final Exam:	34%

Drop Date:  Please note that the University Drop Date March 26, 2013 deadline will be strictly enforced.

Homework Policy:  Problem sets will be assigned and collected on a weekly basis. Selected problems will be graded and will constitute a substantial portion of the grade.

Attendance:  Your absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Attendance at all classes will be recorded and is mandatory.

Exams:  There will be two midterm exams and one comprehensive final exam during the semester. Exams are held in class on the following days:

Midterm Exam 1:	February 26, 2013
Midterm Exam 2:	April 2, 2013
Final Exam Week:	May 9-15, 2013

 

Makeup Exam Policy:  Makeup exams will be offered to those students who, for some legitimate reason, cannot take the exam at the regular time. Legitimate reasons may include illness, death in the family, accident, requirement to appear in court, etc. If you have a legitimate reason not to take the exam at the time it is being offered, you may take a makeup exam ONLY if you received the instructor's permission in advance. You must notify the instructor of your problem before the date of the exam. The only exception to this rule is if you had an accident on the day of the exam. In this case, you must present proof, like a doctor's note, police report, etc., clearly stating the date AND time.

Further Assistance:  For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.

Cellular Phones:  All cellular phones and beepers must be switched off during all class times.

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MATH DEPARTMENT CLASS POLICIES LINK 

All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.

January 21, 2013	M	Dr. Martin Luther King, Jr. Day ~ University Closed
March 17-24, 2013	Su-Su	Spring Recess ~ No Classes Scheduled ~ University Open
March 26, 2013	T	Last Day to Withdraw from this course
March 29, 2013	F	Good Friday ~ University Closed
May 7, 2013	T	Classes follow a Friday Schedule, Last Day of Classes
May 8, 2013	W	Reading Day
May 9-15, 2013	T-W	Final Exams

 

Course Outline:

 

Week	Section	Topic	Homework
1	1.1, 1.2	The vector space Rn, subspaces of Rn	1.2, 1.4, 2.2(b,c,d), 2.4
	1.3	Inner products and orthogonality	2.3, 3.1, 3.5, 3.6
2	1.4	Linear mappings and matrices	3.7, 4.2, 4.6
	1.5, 1.6	The kernel and image of a linear mapping, determinants	4.7, 4.8, 5.1, 5.2
3	1.7, 1.8	Limits and continuity, elementary topology in Rn	7.1, 7.2, 7.3, 7.4
	2.1	Curves in Rn	1.2, 1.9,1.10, 1.12
4	2.2	Directional derivatives and the differential	2.1, 2.3, 2.4, 2.6(a)
	2.3	Chain rule	3.1, 3.6, 3.8, 3.11, 3.16
5	2.4	Critical points in two dimensions	4.1, 4.5, 4.14, 4.15
		Review
6		Exam 1 (02/26/13)
	2.5	Manifolds and Lagrange multipliers	5.5, 5.10, 5.11
7	2.7	Taylor formula in several variables	7.3, 7.4, 7.6
	2.8	Classification of critical points	8.2, 8.6
8	3.1	Newton's method and contraction mapping	1.1, 1.8
	3.3	Inverse and implicit mapping theorems	3.1, 3.3, 3.4
9	4.2	Volume and the n-dimensional integral	2.4
		Review
10		Exam 2 (04/02/13)
	4.4	Iterated integrals and Fubini's theorem	4.4, 4.5, 4.7
11	4.5	Change of variables	5.6, 5.7, 5.10, 5.11
	5.1	Pathlength and line integrals	1.10, 1.11, 1.14, 1.18
12	5.2	Green's theorem	2.1, 2.3, 2.4, 2.6
	5.5	Differential forms
13	5.6	Stokes' theorem
	5.7	The classical theorems of vector analysis	7.1, 7.4, 7.6
14	6.1, 6.3	Variational problems
		Review

 

Prepared By:  Prof. Cyrill Muratov

Last revised:  January 22, 2013