Mathematics
Spring Branch Campus
Math 2413: Calculus I
CRN 11283 – Sum I Sem./2014
Room 215 | 6 – 9:15 pm | MTWT
4 hour lecture course / 64 hours per semester/ 5 weeks
Textbook: Calculus, Tenth Edition, by Ron Larson & Bruce H. Edwards
ISBN-13: 9781285057095
Instructor: Oscar Castro
Instructor Contact Information: oscar.castro@hccs.com | Math Off: 713-718-5511
Office location and hours: None. Meet by appointment only.
Course Description
Math 2413: Calculus I. An integrated study of differential calculus with analytic geometry including the study of
functions, limits, continuity, differentiation, and an introduction to integration.
Prerequisites
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
Course Student Learning Outcomes (SLO):
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.
Learning outcomes
Students will:
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 function
2.3 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 functions
4.1 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.
Instructional Methods: The class will be taught using a combination of power point presentations, lecture, problem
sessions, question and answer sessions, and suggested problems for student consideration. Emphasis will be placed on
the application of methods taught to various career fields. Student(s) should ask questions whenever necessary in order
to resolve problem areas. REMEMBER! I CAN’T HELP YOU IF I DON’T KNOW YOUR PROBLEM.
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
Prerequisites - Precalculus Review and Functions
(Optional - no more than 4 hours)
Sections: P.1, P.2, P.3
These sections provide an optional precalculus review including real numbers, the Cartesian coordinate
plane, 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
(10 Hours)
Sections: 1.1, 1.2, 1.3,
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
(12 Hours)
Sections: 2.1, 2.2, 2.3,
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
(18 Hours)
Sections: 3.1, 3.2, 3.3,
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, 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
(16 Hours)
Sections: 4.1, 4.2, 4.3,
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.
Departmental Policies:
1. The 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 in class tests 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 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”; 6069 “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. 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 2415 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.
Student Assignments
All assignments are shown in the Course Outline including quizzes and tests. REMEMBER!
Quizzes are subjective and all work leading to your final answer must be shown and must be readable.
A correct answer shown without work will not be given full credit. Tests are objective tests and, as such,
your answer is either right or wrong. For the quizzes, a graphing calculator can be used to verify your
answer, but will not be accepted as your method of work for the problem.
Assessments
All quizzes will be subjective in nature. The highest 3 grades of 4 or more quizzes will be
averaged. Also, the high 3 average of 4 major tests will be computed. The quiz average is worth 25% of
your grade, test average is worth 50%, and the final exam is worth 25%.
Americans With Disabilities Act (ADA)
Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who
needs to arrange accommodations must contact the Disability Services Office at their respective college
at the beginning of each semester. Faculty are authorized to provide only the accommodations requested
by the Disability Support Services Office.
Student Conduct
Students will be expected to treat each other and the instructor courteously and with respect. In class, please
greet each other pleasantly, refrain from activities which may be distracting to others, and participate
honestly in group work and exams. If you are dissatisfied with any aspect of the instructor or with other
students, please discuss your concerns with the instructor. If such discussion does not produce a resolution
for your concern, feel free to contact the department chair. Any student who proves to be disruptive to the
learning process of others will be removed from class and dealt with by the administration.
Student Responsibilities
Consider being a student as a part-time or full-time job. It is each student’s job to learn. With this job, the
student has the responsibility to participate in class, ask relevant questions, seek help when needed, and
submit assignments when they are due. Treat each deadline as you would an interview: do not miss a
deadline. Expect to spend a minimum of 2-6 hours per week, in addition to class time, studying
mathematics. If you miss class, it is your responsibility to make up any work assigned, get notes or
handouts, and determine if any pertinent announcement were made during your absence. If you are not
attending, you are not learning. As the information that is discussed in class is important for your career, a
student may be dropped from a course after accumulating absences in excess of six(6) hours of
instruction. The six hours of class time will include any total classes missed or for excessive tardiness or
leaving class early.
Academic Honor
Every student in the class is expected to exhibit a high degree of ethical standards as concerns the work in
this class. Every graded assignment in this course(homework/quiz, library assignment, or test) is to be
entirely your own work unless otherwise stated. Any violation of this policy will result in a minimum
penalty of failure of the assignment and a maximum penalty of expulsion from the college. If you are
uncertain as to whether you may work with another person on an assignment, ask the instructor. It is also
expected that if you see another person cheating in any way, you will report it to the instructor.
Makeup Exams/Quizzes
Makeups are given at the discretion of the instructor and only in the case of verified medical or other
documented emergencies. A makeup is only allowed for major tests(Not for a quiz). Notify your
instructor, if possible, before the test is given. If the event is not an emergency, you must notify the
instructor in advance to request a makeup. REMEMBER: The instructor is not required to
accommodate you.
Final Grade: The final grade will be based on the following method:
E = Exam Average
Q = Daily Average(includes quizzes, daily work, etc.)
F = Final Exam Score
Grade = 0.25Q + 0.50E + 0.25F
By the second week of school, each student will have a calendar to cover all quizzes, exams, and the final
exam. Grades of A, B, C, D, or F will be assigned according to departmental policy. The grade of ‘I’ is
given only in exceptional circumstances. When a student for good reason misses too much work or the
final exam and notifies the instructor promptly, the instructor may give the grade ‘I’(incomplete) and
specify what work should be completed to remove the ‘I’ grade. The ‘I’ will become an ‘F’ if not replaced
after one full semester.(Refer to the student handbook.)
INFORMATION CONCERNING STUDENT DISCIPLINE AND CONDUCT NOT COVERED
CAN BE LOCATED IN THE STUDENT HANDBOOK. ALL MATERIAL CONTAINED
THEREIN WILL APPLY TO THIS CLASS.
Tentative Instructonal Outline: Calculus I Oscar J. Castro
SUMMER I 2014
Week
Number
1
Topic Outline
Assignment Schedule
JUN 2
Responsible for reading
all
secInfo, P.1 – P-3
Class
You are responsible for reviewing all
ections and
sections
andexercise
exerciseproblems.
problems. Work selectively.
JUN 3
JUN 4
JUN 5
(1.1)3,4,5,6.9 (1.2)18,25,26,42,51,66
Secs 1.1 – 1.3
ad Details(1.3)14,24,34,44,60,64
Secs 1.4-1.5 Q1 on 1.1-1.3 (1.4)6,16,44,45,48,58,64 (1.5)6,22,24,38,50,60
(2.1)8,18,30,34,42,58 (2.2)14,30,38,44,56,96
Secs 2.1 – 2.2
2
Secs 2.3 - 2.4 T1 on C1
Sec 2.5 Q2 on 2.1-2.3
Secs 3.1 – 3.2
Sec 3.3 T2 on C2
(2.3)18,38,62,66,76,92 (2.4)28,66,70,82,100,112
Secs 3.4 – 3.5
Sec 3.6
Q3 on 3.1 – 3-4
Secs 3.7 – 3.9
Sec 4.1
T3 on C3
(3.4)18,34,64,68,72,80 (3.5)12,18,26,42,58,86
JUN 23
Secs 4.2 – 4.3
(4.2)10,32,44,50,64,82 (4.3)6,10,20,38,48,72
JUN 24
Quiz on 4.1 – 4.3
Secs 4.4 - 4.5
T4 on C4.
(4.4)12,32,40,62,76,96 (4.5)34,35,46,48,52
JUN 9
JUN 10
JUN 11
JUN 12
(2.5)12,32,42,48,68,78
(3.1)16,22,26,38,44,62 (3.2)6,16,24,40,58,66
(3.3)10,22,30,42,52,78
3
JUN 16
JUN 17
JUN 18
JUN 19
(3.6)18,34,68,72
(3.7)6,12,20,24,42,56 (3.8)18,34,64,68,72,80 (3.9)14,20,28,33,39,42
(4,1)32,39,42,62,70,74
4
JUN 25
JUN 26
5
JUN 30
JUL 1
JUL 2
JUL 4
Make-up Day & Problems
FE Rev
Final Exam -- TBA
Offices Closed
IMPORTANT DATES
JUN 5, 2014
JUN 23, 2014
JUL 11, 2014
Instruction Ends
Comprehensive::6 PM : Scantron Required
Independence Day Holiday
Official Date of Record
Last Day for Admin/Student Withdrawals---4:30 PM
Grade Available to Students