Course Syllabus
Calculus II
MATHEMATICS DEPARTMENT
Houston Community College-Southeast
Chuen Huang, Ph.D.
Phone 713.718.7150
E-mail: chuen.huang@hccs.edu
Math 2414 Calculus II
CRN61994
Course Syllabus and Outline
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. Prerequisite: MATH 2413. 4 credit (4 lecture).
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 met.
Course Objectives: Upon completion of this course, a student should be able to:
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Define and use transcendental functions including logarithmic and exponential functions.
Compute derivatives and antiderivatives involving transcendental functions.
Apply integration to various applications.
Show various integration techniques
Show correct usage of L’Hopital’s rule.
Describe and solve improper integrals.
Recognize and use infinite series.
Recognize and apply Taylor series to various problems
Demonstrate knowledge of plane curves and polar coordinates.
Math 2414
Textbook: Calculus With Analytic Geometry, by Larson, , and Edwards, Ninth Edition. 2010,2006
Brooks/Cole, Cengage Learning..
Supplemental materials: videotape series is available in the library.
Advising time: M, W 8-9 am, 1:00-1:30 pm, TR 8-9 am Esid 1026
Course Outline: Instructors may find it preferable to cover the course topics in the order listed below.
However, the instructor may choose to organize topics in any order, but all material must 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’Hopital’s Rule,
and Improper Integrals
(14 Hours)
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
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Math 2414
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.
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Math 2414
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.
Departmental Policies:
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Each instructor must cover all course topics by the end of the semester. The final exam is
comprehensive and questions on it can deal with any of the course objectives.
Each student should receive a copy of the instructor’s student syllabus for the course during the first
week of class.
A minimum of three in class tests and a comprehensive final departmental examination must be given.
The final examination must be taken by all students.
All major tests should be announced at least one week or the equivalent in advance.
The final exam must count for at least 25 to 40 percent of the final grade.
The final course average will be used in the usual manner (90-100 ”A”; 80-89 “B”; 70-79 “C”;
60-69 “D”; Below 60 “F”).
Either an open book or a take home major test may be given at the discretion of the instructor.
Any review sheet should be comprehensive and the student should not feel that classroom notes,
homework, and tests may be ignored in favor of the review sheet for any examination.
Resource Materials: Any student enrolled in Math 2414 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.
Suggested Methods: It is helpful to begin each class with questions concerning the material discussed and
the assigned homework problems. In presenting new material, it is suggested that an explanation be
followed by students working examples in class. Students should be encouraged to work the review
exercises at the end of each chapter. Also, they should be encouraged to visit the Academic Support Center
at their respective colleges.
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
Week
1 - 4
Topics
Unit I - Logarithmic, Exponential,
and Other Transcendental Functions
Test 1
4
Math 2414
5- 7
Unit II - Applications of Integration
Test 2
Unit III - Integration Techniques, L’Hopital’s Rule,
8 - 12
13 - 15
Unit IV - Infinite Series
Test 3
Final Exam : Thursday, May 12,2011, 12:30 pm.
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