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.

# Mathematics 480-001:

## INTRODUCTORY MathEMATICAL ANALYSIS

### FALL 2008

Instructor:

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:

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 .

 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 27-28, 2008 R-F 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 epsilon-delta theory of the limit, structure of epsilon-delta proofs, methods for finding delta, negation and non-limits 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 Epsilon-Delta 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 15-19, 2008

Prepared By:  Prof. Amit Bose

Last revised:  July 10, 2008

 Calendar of Weeks for Fall 2008 1 9/2 - 9/5 5 9/29 – 10/3 9 10/27 – 10/31 13 11/24 – 11/28 2 9/8 – 9/12 6 10/6 -10/10 10 11/3 - 11/7 14 12/1 – 12/5 3 9/15 – 9/19 7 10/13 –10/17 11 11/10 – 11/14 15 12/8 – 12/10 4 9/22 – 9/26 8 10/20 – 10/24 12 11/17 – 11/21 Finals 12/15 – 12/19