COURSE OUTLINE
MATH 181 Calculus I
4 Semester Hours
Andrew Bulleri
HOWARD COMMUNITY COLLEGE
Description
In this course, students will develop skills in the initial content of both differential and integral calculus. Students will be able to find limits of functions, be exposed to the epsilon-delta process, and study continuity. They will be able to find derivatives and integrals of polynomial, rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic functions. This includes the chain rule, inverse functions, and integration by substitution. Applications dealing with optimization, related rates, Newton's method, L'Hopital's rule, and motion problems will be presented. Properties of the graphs of functions will also be analyzed. Theorems used in the class will include the mean-value theorem for derivatives and integrals, the squeeze theorem and the fundamental theorems of calculus. Implicit differentiation, differentials and summations of area will be used when appropriate. A graphing calculator is required. Credit will only be granted for one of the following: MATH 140, MATH 145 or MATH 181. Prerequisite: MATH 153 or MATH 155 or appropriate score on the mathematics placement test. A grade of C or higher in the Precalculus sequence is strongly recommended. (4 hours weekly)
Statement on General Education and Liberal Learning
A liberal education prepares students to lead ethical, productive, and creative lives and to
understand how the pursuit of lifelong learning and critical thinking fosters good citizenship.
General education courses form the core of a liberal education within the higher education
curriculum and provide a coherent intellectual experience for all students by introducing the
fundamental concepts and methods of inquiry in the areas of mathematics, the physical and
natural sciences, the social sciences, the arts and the humanities, and composition. This course is
part of the general education core experience at Howard Community College.
Overall Course Objectives
Upon completion of this course, the student will be able to:
1. Calculate limits of elementary functions.
2. Apply the derivative to determine instantaneous rate of change and local linear approximation.
3. Determine derivatives of functions which are given either implicitly or explicitly.
4. Apply the theory of derivatives to graph curves, approximate function values using Newton’s method, and solve a variety of problems, such as related rates, optimization, and differentials.
5. Apply the Intermediate and Mean Value Theorems.
6. Apply the definite integral both as a limit of Riemann sums and as the net accumulation of change.
7. Apply the Fundamental Theorems of Calculus.
8. Determine an antiderivative of a function and calculate definite integrals of functions.
9. Communicate solutions to problems in a neat, organized and easy-to-follow way while using correct mathematical notation.
10. Use technology as a means of discovery, to reinforce concepts, and as an efficient problem solving tool.
11. Demonstrate an appreciation of the historic development of calculus in its multicultural context as well as through contributions of Newton and Leibnitz.
Major Topics
I. Limits
A. Informal Definition of a Limit
B. Properties of Limits
C. Techniques for Computing Limits
D. Continuity and One-Sided Limits
E. The Squeeze Theorem
F. Infinite Limits and Limits at Infinity
G. Intermediate Value Theorem
H. Precise Definition (e-d) of a Limit
II. Differentiation
A. Rates of Change and the Tangent Line
B. Formal Definition of Derivative
C. Basic Differentiation Rules
D. Higher Order Derivatives
E. The Product and Quotient Rules
F. Derivatives of Trigonometric Functions
G. Derivatives as Rates of Change
H. The Chain Rule
I. Implicit Differentiation
J. Derivatives of Logarithmic and Exponential Functions
K. Derivatives of Inverse Trigonometric Functions
L. Related Rates
III. Applications of Differentiation
A. Maxima and Minima
B. Increasing and Decreasing Functions and the First Derivative Test
C. Concavity and the Second Derivative Test
D. Graphing Functions
E. Optimization Problems
F. Linear Approximation and Differentials
G. Mean Value Theorem
H. L’Hopital’s Rule
I. Antiderivatives
J. Newton’s Method
IV. Integration
A. Approximating Areas under Curves: Riemann Sums
B. Definite Integrals
C. The Fundamental Theorem of Calculus
D. Average Value of a Function
E. Mean Value Theorem for Integrals
F. Integration by Substitution
G. Velocity and Net Change
Course Requirements
Grading/Exams: Grading procedures will be determined by the individual faculty member within the guidelines of the Mathematics Division and will include several unit exams, projects and a comprehensive departmental final exam.
Required Text: Calculus: Early Transcendentals, 1st edition, by Briggs & Cochran
Required Calculator: Programmable Graphing Calculator (TI-83+/84 recommended)
Other Course Information
This course may be used as a Mathematics core course or as an Arts and Science elective. Check with your transfer institution concerning transferability for your program.
Class Attendance:
Although attendance is not required, it will be taken and it should be noted that successful completion of the course objectives will be extremely difficult without regular attendance. If it is necessary to miss a class, it is the student's responsibility to find out what happened in class that day and to come to the next class prepared to actively participate.
Homework:
Homework assignments will be given daily. Problem areas will be discussed during the class period following their assignment. A homework package will be collected on Exam day. It will include all the individual assignments plus any special handouts. It must be clipped together in the order given on the assignment sheet with the page numbers highlighted in some manner. In order to receive credit for an individual homework assignment, 3/4 or more of it must be completed. All work must be shown, answers are not enough. In "borderline" cases, homework will be used to increase your final grade, if at least 3/4 of it is completed. The maximum adjustment will be the percent of homework completed multiplied by 20 points.
Class Time:
This course meets four hours each week. Each class will be devoted to lecture/discussion presentations, which will cover the material necessary to satisfy the objectives of the course.
Grading:
There will be 4 exams scheduled during the semester, each worth 100 points. Quizzes may be
given throughout the semester during the first five minutes of class time. The quizzes will be
based on material that has been recently covered. The mean of the quiz scores will be added
to the next test score.
There will be 4 Projects given during the semester. The total possible points earned
during the semester will be 80 points.
Online Quizzes will be worth 80 points and Online Homework will be worth 40 points.
A comprehensive Final exam worth 200 points will be given during the Final Exam period.
Your final grade will be an:
A if you receive 90% of the total points. (720-800 points)
B if you receive 80% of the total points. (640-719 points)
C if you receive 70% of the total points. (560-639 points)
D if you receive 60% of the total points. (480-559 points)
I if you have completed 90% of the work and the missed 10% resulted because of an emergency.
Weather related cancellations
Weather-related class cancellations due to weather emergencies will be published on the HCC website. Cancellations will also be aired on local radio and television stations affiliated with the three major networks between 6:00 a.m. and 9:00 a.m. When Howard County public schools are closed because of weather emergencies, the HCC classes held at these schools are automatically canceled. Special attention should be paid to confirm whether closing decisions apply to the county school system or HCC, credit, non-credit, day and/or evening courses. If classes are cancelled any time after school opens, announcements will be made in the same manner. A recorded message will be played on the college’s main telephone number, 443-518-1000.
Late Opening Policy
If the college has a late opening and there is more than 30 minutes of time left in a scheduled class at the late opening time, that particular class with meet for the remainder of the class time.
Early Closing Policy
If the college will be closing early and there will be more than 30 minutes of time available for a scheduled class before the college closes, that particular class will meet during the available time.
Disability accommodation
Any student who may need an accommodation due to a disability must contact the HCC office of Disability Support Services in RCF302. A memo from this office listing your accommodation will be needed in order to provide the modification to normal course procedures.