Revised 08-24-12
SOUTHWEST COLLEGE
Department of Mathematics
COURSE SYLLABUS
MATH 2414: Calculus II CRN: 26228
Fall 2012: Tues-Thurs: 9:30AM – 10:30AM SW Hub:
INSTRUCTOR:
Ernest Nwachukwu
CONTACT INFORMATION:
Ernest.Nwachukwu@hccs.edu
OFICE HOUR: Tues, Thurs 3:00pm-4:00pm
Attendance policy:
Students are expected to attend classes regularly. If some special situation arises, which calls for
your missing classes, then please keep me informed. If I am not notified and your absences exceed
12.5% of the number of classes, you will be administratively withdrawn immediately.
Tardiness (lateness to class) policy:
Every student is expected to be in class on time. If a student is late on the examination day, the
student will not be given extra time.
Withdrawal policy:
Any student who is contemplating withdrawing from the class is encouraged to do so on or before
the final day for withdrawal as specified in the class schedule. If a student withdraws after the final
day for withdrawal from the class, the student will get “F”.
Home Work policy:
Home work assignment will be given every week. For a student to get the best out of this class, it is very
important that the student solves problems in the textbook.
Exam Policy:
Cheating is not allowed in the examination. If a student is caught cheating in an examination, the student will
lose all the marks for that examination. College policies on cheating will be enforced. These are clearly
outlined in the HCCS Student Handbook.
Make-up policy:
There will be no make-up of any test. An exception to this can be allowed if there is a case of medical
emergency and with a valid proof. There will be no make-up of the final examination.
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Grading policy:
Each of the first four examinations is worth 20%; and the final examination is worth 40% of the final course
grade. The final course grade (call it FCG) will be calculated using the formula:FCG = Average of the best five grades (final counting double).
Letter grade will be assigned to the FCG.
Grade legend: 90% - 100% - A, 80% - 89% - B, 70% - 79% - C, 60% - 69% - D, below 60% - F.
Final Examination:
The final examination consists of 33 multiple-choice problems. The problems cover only the
material required in this course.
Americans With Disabilities Act (ADA): Students with Disabilities: Any student with a documented
disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the Disability Services Office at the respective college at the
beginning of each semester.
BEGINNING OF SEMESTER ADVISEMENT
Students are advised about the pre-requisites for the above class and how they are related to their
major and the next class to take in mathematics.
“Students who repeat a course for a third time or more may soon face significant tuition/fee
increases at HCC and other Texas public colleges and universities. Please ask your
instructor/counselor about opportunities for tutoring or other assistance prior to considering course
withdrawal or if you are not receiving passing grades."
END OF SEMESTER ADVISEMENT
Students are advised on the future courses in mathematics and how they are related to their
majors. All questions were answered.
Catalog Description: Calculus II. Integral calculus including discussions of transcendental
functions, applications of integration, integration techniques and improper integrals, infinite series,
Taylor series, plane curves, and polar coordinates.
Prerequisites: Math 2413: Pass with a “C” or better
Course Intent: This course provides a detailed study of the logarithmic, exponential, and other
transcendental functions, integration techniques with applications, L’Hopital’s rule, an introduction
to infinite series and power series, as well as Taylor polynomials and approximations, plane curves,
parametric equations, and polar coordinates.
Audience: This course is intended basically for students who are pursuing degrees in mathematical
sciences and engineering and who are required by the nature of their respective curricula to enroll in
the 3 -semester calculus series. Students enrolled in other areas not requiring calculus may wish to
take this course as an elective to broaden their mathematical background provided the necessary
prerequisites have been made.
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Course Objectives: Upon completion of this course, a student should be able to:
1. Describe the basic concepts of mathematical functions and the various types of functions, which
exist.
2. Demonstrate knowledge of the concept of the limit of a function at a point and the properties
such limits possess.
3. Demonstrate knowledge of the idea of continuity of a function
4. Differentiate various types of mathematical functions and know the meaning of the various
orders of the derivatives including applications.
5. Recognize the discontinuity points of certain types of elementary functions.
6. Differentiate the trigonometric functions with applications.
7. Use calculus to sketch the curves of certain types of elementary functions
Textbook: Calculus by Larson and Edwards; ninth Edition.
Calculus 9/e
Larson and Edwards
Brooks/Cole
Student Learning Outcomes
1. Compute derivatives and antiderivatives
of transcendental functions.
Course Objectives
1.1 Define and use transcendental functions
including logarithmic and exponential
functions.
1.2 Compute derivatives and antiderivatives
involving transcendental functions.
2. Identity and apply the appropriate
integration technique, and apply them to
set up and solve various applications.
2.1 Apply integration to various applications.
2.2 Show various integration techniques
3. Demonstrate the correct use of
L’Hospital’s rule and various techniques
for solving improper integrals.
3.1 Show correct usage of L’Hopital’s rule.
3.2 Describe and solve improper integrals.
4. Recognize and use infinite series with
attention to the application of the Taylor
4.1 Recognize and use infinite series.
4.2 Recognize and apply Taylor series to
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series.
5. Demonstrate knowledge of plane curves
and polar coordinates.
various problems
5.1 Demonstrate knowledge of plane curves
and polar coordinates.
Course Outline: The instructor may choose to organize topics in any order, but all material will be
covered.
APPROXIMATE TIME
TEXT REFERENCE
Unit I - Logarithmic, Exponential,
and Other Transcendental Functions
(12 Hours)
Sections: 5.1, 5.2, 5.3,
5.4, 5.5, 5.6,
5.7, 5.8
This unit presents the concept of logarithms. The instructor should emphasize the natural
logarithmic function with respect to differentiation and integration. Inverse functions, exponential
functions with respect to differentiation and integration, bases other than e and applications. Inverse
trigonometric functions should also be presented. This unit concludes with a study of hyperbolic
functions
Unit II - Applications of Integration
(14 Hours)
Sections: 7.1, 7.2, 7.3,
7.4, 7.5, 7.6, 7.7
This unit presents applications of integration. The instructor should emphasize area of a region
between two curves, volume-the disc method, volume-the shell method, arc length and surface of
revolution, work, and fluid pressure and fluid force. This unit concludes with moments, centers of
mass, and centroids.
Unit III - Integration Techniques, L’Hospital’s Rule,
and Improper Integrals
(14 Hours)
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Sections: 8.1, 8.2, 8.3,
8.4, 8.5, 8.6,
8.7, 8.8
This unit includes integration techniques. The instructor should emphasize basic integration rules,
integration by parts, trigonometric integrals and substitution, partial fractions, integration by tables,
other integration techniques, and indeterminate forms and L’Hopital’s Rule. This unit concludes
with improper integrals.
Unit IV- Infinite Series
(14 Hours)
Sections: 9.1, 9.2, 9.3,
9.4, 9.5,9.6
9.7, 9.8, 9.9, 9.10
This unit includes the basic concepts of infinite series. The instructor should emphasize sequences,
series and convergence, the integral test and p-series, comparisons of series, alternating series, ratio
and root tests, Taylor polynomials and approximations, power series, and representation of functions
by power series. This unit concludes with a discussion of Taylor and Maclaurin series.
Unit V - Plane Curves, Parametric Equations,
Polar Coordinates
(10 Hours)
Sections: 10.1(optional) , 10.2,
10.3, 10.4, 10.5, 10.6
This unit includes the basic concepts of Plane Curves, Parametric Equations, and Polar Coordinates.
The instructor should emphasize plane curves and parametric equations, parametric equations and
calculus, polar coordinates and polar graphs, and area and arc length in polar coordinates. This unit
concludes with a discussion of polar equations of conics and Kepler’s laws. Section 1 of this chapter
reviews conics and may be covered optionally but is nor required.
Resource Materials: Any student enrolled in Math 2413 at HCCS has access to the Academic
Support Center where they may get additional help in understanding the theory or in improving their
skills. The Center is staffed with mathematics faculty and student assistants, and offers tutorial help,
video tapes and computer-assisted drills. Also available is a Student’s Solutions Manual which may
be obtained from the Bookstore.
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