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Math 545: Introductory Mathematical Analysis
Fall 2018 Graduate 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: Rigorous treatment of the calculus of real-valued functions of one real variable: the real number system, epsilon-delta theory of limit, continuity, derivative, and the Riemann integral. The fundamental theory of calculus. Series and sequences including Taylor series and uniform convergence. The inverse and implicit function theorems.

Number of Credits: 3

Prerequisites: MATH 211 or MATH 213, and departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 545-001 Professor B. Hamfeldt

Office Hours for All Math Instructors: Fall 2018 Office Hours and Emails

Required Textbooks:

Title Introduction to Real Analysis
Author W. Trench
Edition Digital Version
Publisher Digital Commons@Trinity
ISBN # ---
Notes SEARCH trench introduction to real analysis for a pdf file)

Course Assessment Criteria: Outcomes are assessed through class participation, homework assignments, two midterm exams, and a comprehensive final exam.

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 12, 2018. It will be strictly enforced.


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:

Participation 5%
Homework 20%
Midterm Exams (2) 40%
Final Exam 35%

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

A 90 - 100 C+ 76 - 79
B+ 86 - 89 C 70 - 75
B 80 - 85 F 0 - 69

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: Homework assignments will be given frequently. Assignments will be posted on Moodle.  Each assignment must be handed in at the beginning of class on the due date. Late assignments are NOT accepted.  Solutions will be graded for correctness, completeness, and clarity.

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

Midterm Exam I October 9, 2018
Midterm Exam II November 13, 2018
Final Exam Period December 15 - 21, 2018

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

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 2018 Academic Calendar, Registrar)

Date Day Event
September 4, 2018 T First Day of Classes
September 10, 2018 M Last Day to Add/Drop Classes
November 12, 2018 M Last Day to Withdraw
November 20, 2018 T Thursday Classes Meet
November 21, 2018 W Friday Classes Meet
November 22 - 25, 2018 R - Su Thanksgiving Recess
December 12, 2018 W Last Day of Classes
December 13 & 14, 2018 R & F Reading Days
December 15 - 21, 2018 Sa - F Final Exam Period

Course Outline

Week Date Topic
1 9/4 & 9/6 1.1-1.2: Real numbers & mathematical induction
2 9/11 & 9/13 1.3-2.1: Real numbers and limits
3 9/18 & 9/20 2.1-2.2: Limits and continuity
4 9/25 & 9/27 2.3: Mean Value Theorem
5 10/2 & 10/4 2.4: L’Hospital’s Rule and review
6 10/9 & 10/13 Midterm (October 10) and 2.5: Taylor’s Theorem
7 10/16 & 10/20 3.1: Integrals
8 10/23 & 10/25 3.2-3.3: Properties of the integral
9 10/30 & 11/1 3.4-4.1: Improper integrals and sequences
10 11/6 & 11/8 4.1: Sequences and review
11 11/13 & 11/15 Midterm (November 14) and 4.2: Sequences
12 11/20 (no class 11/22) 4.3: Infinite series
13 11/27 & 11/29 4.3-4.4: Sequences and series of functions
14 12/4 & 12/6 4.4-4.5: Power series
15 12/11 Review

Updated by Professor B. Hamfeldt - 9/1/2018
Department of Mathematical Sciences Course Syllabus, Fall 2018