Course and Title
MATH 2413: Calculus I
Discipline/Program
Mathematics
Program/Discipline
Goals: If Applicable
This course provides the background in mathematics for sciences or further study in
mathematics and its applications.
Prefix
MATH - Mathematics
Course Level
Sophomore
Course Title
Calculus I
Course Rubric and
Number (e.g. HIST 1301)
Semester with Course
Reference Number
(CRN)
Course Location/Times
MATH 2413
Course Semester Credit
Hours (SCH) (lecture,
lab) If applicable
4 credit (4 lecture).
Course Contact Hours –
specify total numbers
64
Audience
This course is a freshman level mathematics course which requires a background consisting of
Math 2412.
Course Continuing
Education Units (CEU): If
applicable
Course Length (number
of weeks)
Type of Instruction:
Instructor contact
information (phone
number and email
address)
Office location and
hours
Course Description:
ACGM or WECM
Course Description: HCC
Catalog Description
Calculus I. An integrated study of differential calculus with analytic geometry including the study
of functions, limits, continuity, differentiation, and an introduction to integration.
Course Prerequisite(s)
MATH 2412 or consent of the Department Chair
Course Goal
This course provides the background in mathematics for sciences or further study in
mathematics and its applications
1. Demonstrate efficiency in algebraic manipulation of elementary and trigonometric functions.
2. Show an understanding of limits and their relationship to the concept of continuity.
3. Differentiate elementary and trigonometric functions and apply the derivatives to sketches of
curves.
4. Calculate integrals, both approximate and exact, of algebraic and exponential functions,
compute the average value of a function over an interval, and apply integrals to solve applied
problems, including finding areas of defined regions.
Course Student Learning
Outcomes (SLO): 4 to 7
SLO Assessment(s)
Learning
Objectives(Numbering
system should be linked
to SLO – e.g., 1.1, 1.2,
1.3, etc.)
SCANS or Core
Curriculum
Competencies: If
Applicable
Course Calendar
1.1 Describe the basic concepts of mathematical functions and the various types of functions,
which exist.2.1 Demonstrate knowledge of the concept of the limit of a function at a point and
the properties such limits possess.2.2 Demonstrate knowledge of the idea of continuity of a
function2.3 Recognize the discontinuity points of certain types of elementary functions.3.1
Differentiate various types of mathematical functions and know the meaning of the various
orders of the derivatives including applications.3.2 Differentiate the trigonometric functions
with applications. 3.3 Use calculus to sketch the curves of certain types of elementary
functions4.1 Demonstrate the ability to find antiderivatives involving polynomial and
trigonometric functions.4.2 Demonstrate the ability to evaluate a definite integral using
Riemann sums.4.3 Solve applied problems using definite integrals.4.4 Find indefinite integrals
with a change of variable.4.5 Find the area of regions under curves using methods which include
the Trapezoidal Rule and Simpson’s Rule.4.6 Demonstrate the ability to compute the average
value of a function over an interval.4.7 Demonstrate an understanding of the Fundamental
Theorem of Calculus.
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.
Prerequisites - Precalculus Review and Functions Sections: P.1, P.2, P.3
(Optional - no more than 4 hours)
These chapters provide an optional precalculus review including real numbers, the Cartesian
coordinate palen, functions, graphing, modeling, and trigonometry. The instructor may choose
to review any or all of this material before beginning chapter 1. All of this material may be
omitted if desired.
Unit I - Limits and Their Properties Sections: 1.1, 1.2, 1.3,
(10 Hours)
1.4, 1.5
This unit presents the concept of limits and how it relates to Calculus. The instructor should
present the formal definitions of the limit and continuity and discuss the characteristics of a
continuous function. Graphical and analytical methods of evaluating limits, including one-sided
limits and limits at infinity should be emphasized as well.
Unit 2 - Differentiation
Sections: 2.1, 2.2, 2.3,
(12 Hours)
2.4, 2.5, 2.6
This unit presents an introduction to differentiation. The instructor should emphasize the
derivative and the tangent line problem, basic differentiation rules and rates of change, the
product and quotient rules, higher-order derivatives, and the chain rule. This unit concludes
with implicit differentiation and related rates.
Unit 3 - Applications of Differentiation Sections: 3.1, 3.2, 3.3,
(18 Hours)
3.4, 3.5, 3.6,3.7, 3.8, 3.9
This unit includes the various applications of differentiation. The instructor should emphasize
extrema on an interval, Rolle’s Theorem and the Mean Value Theorem, increasing and
decreasing functions, and the first derivative test, concavity and the second derivative test,
limits at infinity, a summary of curve sketching, optimization problems, and Newton’s Method.
This unit concludes with differentials and linear approximations.
Unit 4 - Integration
Sections: 4.1, 4.2, 4.3,
(16 Hours)
4.4, 4.5, 4.6
This unit includes the basic concepts of integration. The instructor should emphasize
antiderivatives and indefinite integration, area, Riemann Sums and definite integrals, the
fundamental theorems of calculus, and integration by substitution. This unit concludes with
numerical integration methods.
Instructional Methods
Requisites
Student Assignments
Student Assessment(s)
Instructional Materials
HCC Policy Statement:
ADA
Calculus, by Larson, Hostetler, and Edwards, Eighth Edition.
Houghton Mifflin Company, 2006.
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 his or her respective college at the beginning of each semester. Faculty members are
authorized to provide only the accommodations requested by the Disability support Services
Office. Persons needing accommodations due to a documented disability should contact the
ADA counselor for their college as soon as possible. Also, interested students may wish to
consult the Disability Support Services Student Handbook which may be found online.
HCC Policy Statement:
Academic Honesty
At Houston Community College, academic integrity is expected of all its members and
stakeholders. Academic dishonesty includes, but is not limited to, the willful attempt to
misrepresent one’s work, cheat, plagiarize, or impede other students’ scholastic progress.
Scholastic dishonesty is treated with the utmost seriousness by the instructor and the College.
Please refer to the Student Handbook for specific information related to professional conduct
and scholastic dishonesty.
HCC Policy Statement:
Student attendance, 3peaters, withdrawal
deadline
Attendance: The student is expected to be on time at the beginning of each class period. For
complete information regarding Houston Community College’s policies on attendance, please
refer to the Student Handbook.
3-peaters: Effective Fall 2006, HCC charges a higher tuition rate to students registering for the
third or subsequent time for certain courses. Students who enroll for most credit and CEU
classes for a third or more time will be charged an additional $50 per semester credit hour and
$3.00 per contact hour, except for courses exempted by The Texas Higher Education
Coordinating Board.
Withdrawals: It is the responsibility of the student to officially drop or withdraw from a course.
Failure to officially withdraw may result in the student receiving an ‘F’ in the course. A student
who officially withdraws from a course before the Official Date of Record will not receive a grade
and the course will not appear on the student's permanent record. A student withdrawing from
a course after this period and prior to the deadline designated in the HCC calendar will receive a
grade of ‘W’. Students should take care in dropping a course, since the third or future attempt to
retake a course will result in a higher rate of tuition.
Students may only drop online during the drop/add period listed in the registration calendar.
After the first week of class in a regular term, students must complete a withdrawal form and
meet with a counselor to complete the withdrawal process.
Instructor’s
Requirements
Program/Discipline
Requirements: If
applicable
Departmental Policies:
HCC Grading Scale
90-100 "A"; 80-89 "B"; 70-79 "C"; 60-69 "D"; Below 60 "F"
Instructor Grading
Criteria
Sample Syllabus
Test Bank
Scoring Rubrics
Sample Assignments
Sample Instructional
Methods/Activities
1. 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.
2. Each student should receive a copy of the instructor’s student syllabus for the course during
the first week of class.
3. A minimum of three tests and a comprehensive final examination must be given. The final
examination must be taken by all students.
4. All major tests should be announced at least one week or the equivalent in advance.
5. The final exam must count for at least 25 to 40 percent of the final grade.
6. 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”).
7. Either an open book or a take home major test may be given at the discretion of the
instructor.
8. 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.