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Math 481: Advanced Calculus
Spring 2018 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: 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.

Number of Credits: 3

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

Course-Section and Instructors

Course-Section Instructor
Math 481-002 Professor B. Hamfeldt

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

Required Textbook:

Title Advanced Calculus
Author P. M. Fitzpatrick
Edition 2nd
Publisher AMS
ISBN # 978-0821847916
Extra Materials W. Trench, Introduction to Real Analysis, Digital Commons@Trinity. Provided by instructor (or search trench introduction to real analysis for a pdf file)

University-wide Withdrawal Date: The last day to withdraw with a W is Monday, April 2, 2018. It will be strictly enforced.

Course Assessment

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

Policies

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 20%
Midterm Exams 40%
Final Exam 40%

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

A 90 - 100 C 70 - 75
B+ 86 - 89 D 60 - 69
B 80 - 85 F 0 - 59
C+ 76 - 79

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 February 20, 2018
Midterm Exam II April 3, 2018
Final Exam May 4 - 10, 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: There will be No make-up QUIZZES OR EXAMS during the semester. In the event an exam is not taken under rare circumstances where the student has a legitimate reason for missing the exam, the student should contact the Dean of Students office and present written verifiable proof of the reason for missing the exam, e.g., a doctor’s note, police report, court notice, etc. clearly stating the date AND time of the mitigating problem. The student must also notify the Math Department Office/Instructor that the exam will be missed.

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: Spring 2018 Hours)*

Further Assistance: For further questions, students should contact their instructor. All instructors have regular office hours during the week. These office hours are listed on the Math Department's webpage for Instructor Office Hours and Emails.

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

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 lyles@njit.edu. 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: Spring 2018 Academic Calendar, Registrar)

Date Day Event
January 16, 2018 T First Day of Classes
January 22, 2018 M Last Day to Add/Drop Classes
March 11 - 18, 2018 Su - Su Spring Recess - No Classes/ University Closed
March 30, 2018 F Good Friday - No Classes/ University Closed
April 2, 2018 M Last Day to Withdraw
May 1, 2018 T Friday Classes Meet - Last Day of Classes
May 2 - 3, 2018 W - R Reading Days
May 4 - 10, 2018 F - R Final Exam Period

Course Outline

Week Dates Topic
1 1/16 & 1/18 5.1: Structure of Rn
2 1/23 & 1/25 5.2-5.3: Continuity and partial derivatives
3 1/30 & 2/1 5.4: Chain rule and Taylor’s Theorem
4 2/6  & 2/8 6.1-6.2: Continuity and differentiability of transformations
5 2/13 & 2/15 6.3: Inverse Function Theorem and review
6 2/20 & 2/22 Midterm (February 20) and 6.3: Inverse Function Theorem
7 2/27 & 3/1 6.4: Implicit Function Theorem
8 3/6 & 3/8 7.1-7.2: Multiple integrals
9 3/13 & 3/15 Spring Break – No Class
10 3/20 & 3/22 7.3: Change of variables in multiple integrals
11 3/27 & 3/29 8.1: Metric spaces and review
12 4/3 & 4/5 Midterm (April 3) and 8.1: Metric spaces
13 4/10 & 4/12 8.2: Compact sets in metric spaces
14 4/17 & 4/19 8.3: Continuous functions on metric spaces
15 4/24 & 4/26 Extra/review
16 5/1 (No class) Friday Schedule – No class

Updated by Professor B. Froese - 1/18/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018