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: Builds on principles taught in basic calculus courses. Topics discussed include continuity, differentiation, integration, and the limit process of sequences and series.
Textbook: Elementary Classical Analysis (2nd Ed.), Mardsen and Hoffman. ISBN-13: 978-0-7167-2105-5.
Instructor: (for specific course-related information, follow the link below)
Math 480-101 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework: |
15% |
▪ Midterm Exam I: |
25% |
▪ Midterm Exam II: |
25% |
▪ Final Exam: |
35% |
Your final letter grade will be based on
the following tentative curve. This curve may be adjusted slightly
at the end of the semester.
NOTE: This course needs to be passed with a grade of C or better in order
to proceed to
Math 481
or
Math 546.
A |
90-100 |
C |
60-69 |
B+ |
85-89 |
D |
50-59 |
B |
75-84 |
F |
0-49 |
C+ |
70-74 |
|
|
Drop Date: Please note that the University Drop Date November 6, 2012 deadline will be strictly enforced.
Homework Policy: It is vital that you complete all of the homework assignments by the specified dates.
MATLAB: MATLAB is a mathematical software program that is used throughout the science and engineering curricula.
Attendance: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Department’s Attendance Policy. This policy will be strictly enforced.
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: |
October 12, 2012 |
Midterm Exam 2: |
November 16, 2012 |
Final Exam Week: |
December 14-20, 2012 |
Makeup Exam Policy: There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
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.
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.
M |
Labor Day ~ No classes |
|
T |
Last Day to Withdraw from this course |
|
T |
Classes follow a Thursday Schedule |
|
W |
Classes follow a Friday Schedule |
|
R-Su |
Thanksgiving Recess |
|
R |
Reading Day |
|
F- R |
Final Exams |
Course Outline:
Week |
Section
& Topic |
Lecture |
Homework Assignments |
|
|
||||
Week 1
9/4 – 9/7
Week 2
9/10-9/14 |
Introduction: Sets and Functions |
1 |
|
|
1.1-1.2 |
Ordered
Fields and the Number System
Completeness
and the Real Number System |
|
||
1.3-1.4 |
Least Upper
Bounds and Cauchy Sequences |
2 |
|
|
1.5-1.6 |
Cluster
Points: lim inf and lim sup. and
Euclidean Space. |
|
||
Week 3 |
1.7-1.8 |
Norms, Inner
products, and Metrics.
The Complex
Numbers |
3 |
|
2.1-2.3
|
Open Sets,
Interior of a Set, and Closed Sets |
|
||
Week 4 |
2.4-2.6 |
Accumulation
Points, Closure of a Set, and Boundary of a Set. |
4 |
|
2.7-2.10 |
Sequences,
Completeness, and Series of Real Numbers and Vectors. |
|
||
Week 5 |
3.1-3.2 |
Compactness,
The Heine-Borel Theorem |
5 |
|
3.4-3.5 |
Path-Connected Sets and Connected Sets |
|
||
Week 6 |
REVIEW FOR EXAM #1 |
6 |
└► STUDY FOR EXAM #1 |
|
MIDTERM EXAM I: FRIDAY ~
October 12, 2012 |
||||
Week 7 |
4.1-4.3 |
Continuity,
Images of Compact and Connected Sets and Operations on
Continuous mappings |
7 |
|
4.4-4.6 |
The
Boundedness of Continuous Functions on Compact Sets, The
Intermediate value Theorem, and Uniform Continuity. |
|
||
Week 8 |
4.7-4.8 |
Differentiation of Function of One variable and
Integration of Function of One Variable |
8 |
|
5.1-5.3 |
Pointwise
and Uniform Convergence, The Weierstrass M test and
Integration and Differentiation of Series |
|
||
Week 9 |
5.4-5.5 |
The
Elementary Functions and the Space of Continuous
Functions |
9 |
|
5.7-5.8 |
The
Contraction Mapping and its applications and
Stone-Weierstrass Theorem |
|
||
Week 10 |
Last Day to
Withdraw from this course |
|
||
5.9-5.10 |
The
Direchlet and Abel Tests, Power Series and Cesaro and
Abel Summability |
10 |
|
|
6.1-6.3 |
Definition
of Derivative and Matrix Representation, and Continuity
of Differentiable Mappings. |
|
||
Week 11 |
REVIEW FOR EXAM #2 |
11 |
└►
STUDY FOR EXAM #2 |
|
MIDTERM EXAM II: FRIDAY ~
November 16, 2012 |
||||
Week 12 |
6.4-6.6 |
.Conditions
for Differentiability, the Chain Rule, and Product Rule
and Gradients.. |
12 |
|
6.7-6.8 |
The mean
value Theorem and Taylor’s Theorem and Higher
Derivatives |
|
||
Week 13 |
6.9, 8.1 |
Maxima and
Minima and integrable Functions |
13 |
|
Week 14 |
8.2-8.3 |
Volume and
Sets of Measure Zero and Lebesgue’s Theorem |
14 |
|
|
||||
Week 15 |
REVIEW FOR FINAL EXAM |
15 |
└►
STUDY FOR FINAL EXAM |
|
|
|
|||
|
||||
Week 16 |
Final EXAM WEEK: December
14-20, 2012 |
Prepared By: Prof. Jey Ratnaswamy
Last revised: May 2, 2012