All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly. This means 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 Honor Code, students are obligated to report any such activities to the Instructor.
◘ Instructor: Prof. Bose
◘ Textbook: Calculus by Michael Spivak.
◘ Grading Policy: The final grade in this course will be determined as follows:
Å Homework: 

15% 
Å Midterms: 

50% 
Å Final Exam: 

35% 
Please note that the University Drop Date November 3, 2008 deadline will be strictly enforced.
◘ Exams: Two midterm exams will be given. The dates are October 9, 2008 and November 13, 2008:




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 universitywide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.
September 1, 2008 
M 
Labor Day ~ No Classes Scheduled 
November 3, 2008 
M 
Last Day to Withdraw from Classes 
November 25, 2008 
T 
Classes Follow a Thursday Schedule 
November 26, 2008 
W 
Classes Follow a Friday Schedule 
November 2728, 2008 
RF 
Thanksgiving Recess ~ No Classes Scheduled 
Course Outline:

1.) Properties of Numbers: field axioms, order axioms, PROOF WRITING, mathematicalinduction, rational and irrational numbers 
2.) Functions and Graphs: definition of a function, graphs, rational functions, images of intervals under rational functions 
3.) Inequalities: images of intervals under elementary functions, triangle inequality, absolute values 
4.) Limits: the epsilondelta theory of the limit, structure of epsilondelta proofs, methods for finding delta, negation and nonlimits 
5.) Properties of Limits: uniqueness of the limit, limit of sums, products, quotients and composites 
6.) Completeness and Continuous Functions on Closed Bounded Intervals: least upper bound axiom, boundedness, assumption of extrema, intermediate value theorem, continuity 
7.) The Derivative as an EpsilonDelta Limit: differentiability implies continuity, derivatives of sums, products, quotients and composites, derivative at extreme points, mean value theorems, L'Hopital's rule 
8.) Inverse Functions: monotonicity, inverse functions, continuity and differentiability of inverse functions 
9.) Riemann Integral: upper and lower sums, the Riemann integral, conditions for integrability, Riemann sums 
10.) Fundamental Theorem of Calculus: first and second FTC, differentiation of integrals, integration in elementary terms 
11.) Elementary Functions as Solutions of ODE's: polynomials, logs, exponentials, trig functions and their properties 
12.) Taylor's Theorem, Sequence and Series: Taylor's theorem, convergence of sequences, monotone sequences, Cauchy sequences, infinite series 
13.) Convergence Tests for Series: boundedness criterion, the comparison test, ration test, integral test, absolute convergence, alternating series, rearrangement of series, multiplication of ab 

FINAL EXAM WEEK: December 1519, 2008 
Prepared By: Prof. Amit Bose
Last revised: July 10, 2008
Calendar of Weeks for Fall 2008 





1 
5 
9 
13 
2 
6 
10 
14 
3 
7 
11 
15 
4 
8 
12 
Finals 



