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Syllabus
MAT 104: Calculus 2
AUBG, Math & Sci Dept, Spring 2010
MAT 104: Calculus 2
required for Math Major & Minor; GenEd in quantitative reasoning
Tatiana Gateva-Ivanova
[email protected]
office 317 NAB, phone: 491,
Problem solving sessions given by the instructor and Office hours : We 19:15 - 20:30 R202 NAB
Tutorials given by experience tutors: Mo 19:15-20:30 R 201 NAB
Course description:
The course aims to further develop and extend the methods and technique of Calculus I.
Expected Outcomes:
At the end of the course the student should:
 Become familiar with some applications of integration
 Become familiar with the general concept of inverse functions, exponential and logarithmic functions,
inverse trigonometric functions, l’Hospital’s rule.
 Develop skills in standard techniques of integration
 Become familiar with parametric and polar curves
 Develop skills in dealing with infinite sequences and series, power series and representing functions as
sums of power series.
The above is a list of technical math skills we want to develop but what is more important
We want to learn to think creatively, be able to attack a problem you have not seen before, develop tools for that,
develop a mathematical model for a given “real life” situation.
Prerequisites: MAT 103 (Calculus I) or equivalent
(limits and continuity, derivatives and curve sketching, integrals and applications to evaluating areas and volumes)
Textbook: J. Stewart, Calculus, fifth edition,
(Brooks/Cole Publishing Company, Pacific Grove, 2003)
Expanded Description: (sections from the textbook we will cover)
Content
No of Lectures
1. Inverse Functions (Chapter 7)
Inverse Functions
The Natural Logarithmic Function
The Natural Exponential Function
General Logarithmic and Exponential Functions
Inverse Trigonometric Functions
Indeterminate Forms and L’Hospital’s Rule
6
2. Techniques of Integration (Chapter 8)
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Rationalizing Substitutions
Strategy for Integration
Improper Integrals
6
3. Applications of Integration (Chapter 9)
2
*Differential Equations
Arc Length
Area of a Surface of a Revolution
4. Parametric Equations and Polar Coordinates (Chapter 11)
Curves Defined by Parametric Equations
Tangents and Areas
Arc Length and Surface Area
Polar Coordinates
Areas and Lengths in Polar Coordinates
*Conic Sections
*Conic Sections in Polar Coordinates
3
5. Infinite Sequences and Series (Chapter 12)
Sequences
Series
The Integral Test and Estimates of Sums
The Comparison Test
Alternating Series
Absolute Convergence and the Ratio and Root Tests
Strategy for Testing Series
Power Series
Representations of Functions as Power Series
Taylor and Maclaurin Series
*The Binomial Series
*Applications of Taylor Polynomials
8
Total
25 lectures
Assessment: Your grade will be formed by
two quizzes (midterms)
each giving 25% of the final grade (each gives a maximum of 100
points)
final exam
40 % of the final grade ( maximum of 100 points)
popquizzes, home assignments, participation in class 10%
Assessment: Your grade will be formed by
final exam 40 % of the final grade ( maximum of 100 points)
two quizzes (midterms) each giving 25% of the final grade (each gives a maximum of 100 points)
popquizzes (4) , home assignments, participation in class 10% of the final grade
Total : = 10%P +25%M1+ 25%M2 +40%F
Max total
100
Points/Grade Map:
A 100
A- 93-99
B+ 86-92
B 79-85
B- 71-77
C+ 66-70
C 60-65
C- 54-59
D+ 49-54
D 40-48.
Every class session I will ask the students to participate actively in the solutions of the problems.
Problems from the home assignments will be often discussed in class and in the problem solving sessions.
Solving them is a good preparation for popquizzes, quizzes and final.
• The popquizzes will be scheduled sporadically (typically at the end of the class) and will last 15-20 minutes.
(There will be two popquizzes in the period 27.01- 8.02 ). Each popquiz will contain 2-3 routine problems and will
give in total 3-5 points. The grade for the popquizzes is cumulative, based on the total number of points received
for (all) popquizzes. The maximal total number is 16, but only 10 points participate in the final grade. The
problems are designed so, that computation should not create difficulties, and only solutions which are with no error
will bring points. There is no make up for popquizzes.
• Each quiz will hold 70 min and will consist of 5 or more problems. Some will be routine (up to 90 points). Do
expect also one or two nontrivial problems (given as bonus problems). Each exam (quizzes and final) is designed
for 130 points max, (30 are bonus) but only 100 points participate in the final grade. There will a be make up for
each quiz on a date and time fixed by the professor. make up will take place simultaneously in December.
• The final will be comprehensive, i.e., over all the material covered by the course.
Attendance and participation in class:
Student will be expected to participate actively in class. Attendance will be checked regularly, starting from the
first week of the semester.
An excuse should be asked from the professor before the class.
In case of absences due to medical reasons, the student is kindly requested to inform the professor via e-mail
(before the class).
I expect you to come to class prepared (with written home work, and having read the assigned text if there is such)
and to participate actively during the class.
Important dates:
• Midterm 1: February 22, Mo, 7:30-9 pm, Auditorium, Main Building
• Make up M1: March 22, Mo, 7:15-8:45 pm, Auditorium, Main Building
• Midterm 2: April 14, 7:30-9 pm, Auditorium, Main Building
• Make up M 2 April 26
• Popquizzes (4-5) will be scheduled sporadically and will last 20 minutes. There is no make up for popquizzes.
Academic Honesty Policy. Students are expected to adhere to the Academic Honesty Policy stated in the Catalog
and the Student Handbook. Consequences for violations are included in the Catalog and the Student Handbook.
Exam policies. During quizzes, exams and the final all that you will need and will be allowed to use is a pen/pencil
and the sheets of paper I give you. (no textbooks, notes, calculators, please, no sheets of paper flying around the
room, etc.). You should work strictly by yourself – you should not communicate in any way with your classmates –
violation of this will be considered cheating with all the ensuing consequences (see the AUBG documentation for
the consequences of cheating). Cheating is not only talking to the person next to you (talking about anything: math,
the problems, the weather, last nights party…) but also intentionally making your work available to others during
the exam.
Assignments: Often I will assign sections from the textbook for you to read ahead and from time to time I will
make reading quizzes to check if you have read the assigned part. I will also expect that on the average you spend
5 hours per week (at least) on top of the regular Calculus II classes working on problems from the book, or
additional problems given in class. I will regularly give a list of problems as optional homework, i.e., I will not
collect these optional homeworks but you are strongly encouraged to do as many as possible.
Office hours: - during the problem solving sessions. If the “official” office hours above are not convenient for you
please contact me to arrange some other time. Don’t be shy to ask. There are no stupid questions.
Disclaimer: This syllabus is subject to modification. The instructor will communicate with students on any
changes. The above distribution of weeks per chapter is only approximate.