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Math 213: Calculus III B
Fall 2017 Course Syllabus

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.

Course Information

Course Description: Topics include vectors, curvature, partial derivatives, multiple integrals, line integrals, and Green's, divergence, and Stokes' theorems. Effective From: Fall 2012.

Number of Credits: 4

Prerequisites: Math 112 with a grade of C or better or Math 133 with a grade of C or better.

Course-Section and Instructors

Course-Section Instructor
Math 213-003 Professor P.G. Petropoulos
Math 213-009 Professor P.G. Petropoulos

Office Hours for All Math Instructors: Fall 2017 Office Hours and Emails

Required Textbook:

Title Thomas' Calculus: Early Transcendentals
Author Thomas
Edition 13th
Publisher Pearson
ISBN # 978-0321981677
Notes w/ MyMathLab

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 6, 2017. It will be strictly enforced.

Course Goals

Course Objectives

Course Outcomes


DMS Course Policies: 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.

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

Homework and Quizzes 20%
Common Midterm Exam I 17%
Common Midterm Exam II 17%
Common Midterm Exam III 17%
Final Exam 29%

Your final letter grade will be based on the following tentative curve.

A 88 - 100 C 65 - 71
B+ 83 - 87 D 60 - 64
B 77 - 82 F 0 - 59
C+ 72 - 76

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Homework Policy: The homework assignments are online. In order to do the assignments you need to have a student access code. You can get an access code with a new book purchase that is bundled with My MathLab or by buying the code separately at the campus bookstore. If you buy a new book from another source make sure it is bundled with My MathLab. On the first day of class your course instructor will give you an additional code needed to access the homework assignments. In addition, there will be a small number of hand-in homework assignments to be graded.

Quiz Policy: At least two quizzes based on the homework problems will be given each week in class. All of the quizzes will be graded. The homework and quizzes are intended to develop your problem-solving skills and to prepare you for the exams. The quiz and homework grades will be a significant component of your course grade.

How to Get Started with MyMathLab:

MATLAB: MATLAB is a mathematical software program that is used throughout the science and engineering curricula. Several MATLAB assignments will be given out. These assignments have been designed to help you learn how to use this software in order to visualize many of the concepts taught in class. Each MATLAB assignment will be graded and will be counted as a weekly quiz grade.

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

Common Midterm Exam I September 27, 2017
Common Midterm Exam II October 25, 2017
Common Midterm Exam III November 29, 2017
Final Exam Period December 15 - 21, 2017

The time of the midterm exams is 4:15-5:40 pm for daytime students and 5:45-7:10 pm for evening students. The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

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

Additional Resources

Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Fall 2017 Hours)

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Fall 2017 Academic Calendar, Registrar)

Date Day Event
September 5, 2017 T First Day of Classes
September 11, 2017 M Last Day to Add/Drop Classes
November 6, 2017 M Last Day to Withdraw
November 21, 2017 T Thursday Classes Meet
November 22, 2017 W Friday Classes Meet
November 23 - 26, 2017 R - Su Thanksgiving Break - University Closed
December 13, 2017 W Last Day of Classes
December 14, 2017 R Reading Day
December 15 - 21, 2017 F - R Final Exam Period

Course Outline

Lecture Sections Topic
1 12.1-12.2 Three-Dimensional Coordinate Systems, Vectors
2 12.3-12.4 The Dot Product, the Cross Product
3 12.4-12.5 The Cross Product, Lines and Planes in Space
4 12.5-12.6 Lines and Planes in Space, Cylinders and Quadric Surfaces
5 12.6 Cylinders and Quadric Surfaces
6 13.1 Curves in Space and Their Tangents
7 13.2 Integrals of Vector Functions; Projectile Motion
8 13.3 Arc Length in Space
9 13.4-13.5 Curvature and Normal Vectors, Tangential and Normal Components of Acceleration
10 14.1 Functions of Several Variables
Common Exam 1: Wednesday, September 27, 2017
11 14.2-14.3 Limits and Continuity in higher Dimensions, Partial Derivatives
12 14.3 Partial Derivatives
13 14.4-14.5 The Chain Rule, Directional Derivatives and Gradient Vectors
14 14.5-14.6 Directional Derivative and Gradient Vectors, Tangent Planes and Differentials
15 14.7 Extreme Values and Saddle Points
16 14.8 Lagrange Multipliers
17 14.8-14.9 Lagrange Multipliers,
Taylor's Formula in Two Variables
18 15.1 Double and Iterated Integrals over Rectangles
19 15.2 Double Integrals over General Regions
20 15.3 Area by Double Integration
21 15.4 Double Integrals in Polar Form
22 15.5 Triple Integrals in Rectangular Coordinates
Common Exam 2: Wednesday, October 25, 2017
23 15.7 Triple Integrals in Cylindrical and Spherical Coordinates
24 15.8 Substitutions in Multiple Integrals
25 15.8 Substitutions in Multiple Integrals
26 16.1 Line Integrals
27 16.1-16.2 Line Integrals, Vector Fields and Line Integrals: Work, Circulation, and Flux
28 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
29 16.3 Path Independence, Conservative Fields, and Potential Functions
30 16.3 Path Independence, Conservative Fields, and Potential Functions
31 16.4 Greens Theorem in the Plane
32 16.4 Greens Theorem in the Plane
33 16.5 Surfaces and Area
34 16.5 Surfaces and Area
Common Exam 3: Wednesday, November 29, 2017
35 16.6 Surface Integrals
36 16.6 Surface Integrals
37 16.7 Stokes Theorem
38 16.7 Stokes Theorem
39 16.8 The Divergence Theorem
40 16.8 The Divergence Theorem
41 Applications of the Stokes Theorem and the Divergence Theorem

Updated by Professor P.G. Petropoulos 8/30/2017
Department of Mathematical Sciences Course Syllabus, Fall 2017