Identification
Subject
Calculus-2
Department
Mathematics
Program
Undergraduate
Term
Fall, 2013
Instructor
Aslanova Nigar
E-mail
nigar.aslanova@yahoo.com
Phone
421-10-93
Classroom
Room 403N,
Office hours
Tuesday13:40-15:00, 15:10-18:00, Thursday 15:10-16:30
Prerequisites
Consent of instructor
Language
English
Compulsory/Elective
Required
Required textbooks
and course materials
1. Anton Howard, Calculus with Analytic Geometry, IV edition, 1992
2. Richard A. Hunt, Calculus, II edition,1994
3. Winney Tomas, Calculus with Analytic Geometry, 1998
Course website
www.calculus.com
Course outline
The course concerns the study of ant derivatives, integration methods, definite
integrals and their applications to evaluation areas, volumes, arc length It
includes also study of series, repeated and double integrals
Course objectives
The concepts of indefinite and definite integrals. Application of definite
integrals to area and volume problems . Expansion of functions into power and
trigonometric series. Limit and continuity of function of two variables, partial
derivatives, direction derivatives, gradient, maxima and minima problemsare
included.
Learning outcomes
By the end of the course the students should be able:
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Teaching methods
Find indefinite and definite integrals of functions
Find area between different simple curves
Formulate and solve simple optimization problems using calculus of
two or more variablesrank of matrix and apply it to existence problems
of solutions
Evaluate the sum of series using appropriate technics.
Find double integrals, surface area and line integralstransition matrix
from one basis to another basis
lecture
Seminars
Group discussions
Evaluation
Policy
Methods
Percentage
Midterm exam
30
Class participation
10
Quizzes
15
Final exam
45
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Preparation for class
The structure of this courses makes your individual study and
preparation outside the class extremely important. The lecture material
will focus on the major points introduced in the text. Reading the
assigned chapters and having some familiarity with them will assist
your understanding of the lecture. After lecture , you should study
your notes and work relevant problems and cases from the end of the
chapter and sample exam questions.
Withdrawal (pass, fail)
This course strictly follows grading policy of the University. Thus, a
student is normally expected to achieve a mark of a least60% to pass.
In case of failure he/she will be referred orrequired to repeat the
course the following term or year.
Cheating/ plagiarism
Cheating or other plagiarism during the Quizzes, Mid-term andFinal
Examinations will be lead to paper cancellation. In thiscase, the
student will automatically get zero (0), without anyconsiderations.
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Professional behavior guidelines
The students shall behave in the way to create favorable
academic and
professional environment during the class. Unauthorized discussions unethical
behaviors are strictly prohibited. For successful completion of the course, the
students should take an active part during the class time; ask questions and
involving other to discussions.
Tentative Schedule
Week
Topics
Textbook
1
Antiderivative and the indefinite integrals. Table of integrals.Integration by parts.
Integration by substitution.
[1]
2
Trigonometric integrals, reduction formulas, integration of rational functions.
[1]
3
Integration of some irrational functions
[1]
4
The definite integral. Riemann sums.Newton-Leibiniz formula. The fundamental
theorem of calculus.
[1]
5
Application of the definite integral.Area of the region in the plane. Volumes by
slicing. Arc length.
[1]
6
Improper integrals.
[1]
7
Mid-term exam
[1]
8
Infinite series. Comparison test. The integral test. Ratio and root tests.
[1]
9
Alternating series. Absolute and conditional convergence.Convergence sets of
power ser. Taylor series.
[1]
10
Functional series. Majorised series. Inegration and differentiation of series.
[1]
11
Expansion of function in Fourier ser. Fourier ser. For even and odd functions.
[1]
12
Function of 2 variables. Limits and countinuity. Partial derivatives.
[1]
13
Differentiability and gradient. The chain rule.
[1]
14
Maxima and minima for a function of two variables.
[1]
15
Double integral. Double integrals in polar coordinates. Surface area
[1]
16
Final exam