Dr. Abdul Hassen
Office: Robinson Hall, Mathematics Department, Room 229E
Phone (856) 256-4500 ext 3888. e-mail: hassen@rowan.edu
Office Hours: T 11:00 a.m. - 12:00 noon. R 12:15 - 2:00pm. F 11:00 a.m. – 12 noon by appointment
Prerequisite: Calculus I
Text: Calculus: Early Transcendental by Ron Rogawski published by W. H. Freeman and Co.
Course Description: This course begins with the applications of integration to area volume and arc length. Then techniques for differentiating and integrating the hyperbolic functions and the inverse trigonometric functions and improper integrals will be discussed. Integration by parts, partial fractions and other more advanced integration techniques are introduced, along with a discussion of numerical integration, sequences and infinite series.
Course Objectives: Theory and application of infinite series and improper integrals will be considered. In particular we will examines Euler’s approach to divergent infinite series and develop the theory of various ways of summing infinite series. We will also study functions defined by integrals, their analysis and applications. As an example of functions defined by integrals, we will develop the theory of trigonometric functions and consider their roles in integration techniques. Motivation for class discussions and student essays will stem from the historical development of infinite series and the struggle by early mathematicians to establish it on a firmer foundation. In addition, students will demonstrate the ability to:
(i) perform integration by parts, partial fractions and various substitutions as well as selected numerical techniques;
(ii) recognize and evaluate indeterminate forms and improper integrals;
(iii) determine convergence and divergence of infinite series and find Taylor Series and their interval of convergence.
Calculator: A graphic calculator is required. I will be using TI-89. You can use any graphing calculator but I highly recommend that you use TI-89. We will also use Mathematica. A short manual on the use of IT 89 will be posted on Bb-CE.
Content:
CHAPTER 6 Applications of Integration
All sections
CHAPTER 7 Techniques of Integration
All section will be covered.
CHAPTER 8 Further Applications of Integration
All section will be covered.
CHAPTER 10 Infinite Sequences and Series
All section will be covered.
CHAPTER 11 Parametric Equations, Polar Coordinates and Conic Sections
All section will be covered.
Note: As with Honors Calculus I, this course will take a more rigorous approach towards the study of calculus by encouraging students to critically examine the ideas of a mathematical limit, integral, and infinite series. Motivation for class discussions will stem from the historical development of calculus occurring around and after Newton’s lifetime and the philosophical debate/struggle of earlier mathematicians to establish calculus and the notion of a function on a firmer foundation. This includes the achievements of Leonard Euler and his contemporaries in the 18th-century connecting infinite series with integration. Rigorous techniques such as Cauchy’s epsilon-N argument and mathematical induction will be extensively used.
Grading Policy: Your final grades will be determined by your results on three tests, Mathematica projects, home work assignments, essays, and class participation. Thus attendance will be very important. The dates for each test will be announced in class two weeks before the test date. The materials covered in the four tests will be as follows:
Test 1 (20% of the total grade) Covers chapter 6 and 7.
Test 2 (20% of the total grade) Covers chapter 8 and part of chapter 10.
Test 3 (20% of the total grade) Covers part of chapter 10 and all of chapter 11.
10% of your grade will be from home work assignments 20% will be on essays and 10% will be from Mathematica projects. The letter grade assignment will be as follows:
A(A-) = 90 to 100 B(-,+) = 80 to 89 C(-,+) = 70 to 79 D(-,+) = 55 to 69 F = 0 to 54
Homework: The homework problems can be on Bb-CE.
Projects: Project problems will be posted on Blackboard-CE. Please note there will be three projects that can be done in groups of two or three. These projects are not optional.
Essays: Students will also be asked to write essays or project reports on the following topics:
1.
Infinite and limiting processes used to define quantities such as
.
2. Infinite sums, infinite products, continued fractions
3. Circular functions and hyperbolic functions
4. The notion of a function.
5. Defining functions using infinite series and integrals.
Attendance Policy:
Attendance is mandatory. An attendance sheet will be passed around at the beginning of each class period. Please write your signature next to your printed name on the list. If you are absent/tardy from a class, you must submit a note requesting that the absence/tardiness be excused by the next class meeting. Each student is allowed a total of three unexcused absences/tardies (combined). If you miss a class, it is your responsibility to study the section(s) covered and do the homework.
If you are absent the day of a regularly scheduled test, a grade of zero is automatically recorded as your test score. You will be permitted to make up this zero only when you can confirm that you were absent for reasons beyond your control. In such cases, you must telephone 256-4500 extension 3888 (or send me an e-mail) and leave a message including your name and telephone number, the reason for your absence and the date you anticipate returning. Students who fail to leave the above information will be assigned the grade of zero for that test.
Academic Honesty: Cheating on a
test or assignment seriously undermines the integrity of the academic system
and will not be tolerated. If I determine that a student has cheated, I
will assign the grade of F for this course and send a letter to this effect to
his advisor. Although a student is not cheating, he or she is expected to
refrain from actions that could be suspicious. Using common sense on your
part should avoid unnecessary embarrassment.
Classroom rules:
· Students will abide by Rowan's student code of conduct and policy on
academic honesty (p. 19 and p. 28 of Rowan 1999-2000 undergraduate catalog,
respectively). Improper behavior will not be tolerated.
· Students are not permitted to leave the classroom during class period except
for emergencies or unless prior arrangements have been made with the
instructor. Please use the restrooms before class begins.
Students with Disabilities and Special Needs: Please speak with me as early in the semester as possible so that we can make appropriate accommodations for you. If necessary, you can also contact the Office of Special Services.
Questions in Class: The best time
to ask questions is during class. Many times students fear that their questions
will seem foolish, while in fact, many others also have the same
question. I urge you to ask your questions during class. If you have
questions that were not answered in class, you may stop by my office during my office
hours.