COURSE OUTLINE

MATH 140

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 learn about continuous and discontinuous functions.  They will be able to find derivatives and integrals of both polynomial, rational, radical, trigonometric, exponential, and logarithmic functions.  This include the chain rule, the rules dealing with operations, u-substitution and both definite and indefinite integrals.  Applications dealing with maximum, minimum, velocity and acceleration will be presented.  Graphing (asymptotes, increasing, decreasing, concavity, maximum, minimum) will also be discussed.  Theorems used in the class will include the mean-value theorem for derivatives and integrals, and the fundamental theorems of calculus.  Implicit differentiation, differentials and summations of area will be used when appropriate.  Students will use the computer algebra system, DERIVE, to complete labs. A graphing calculator is recommended.  The use of a computer algebra system will be an integral part of the course. Prerequisite:  MATH 135 or MATH 133 or equivalent.  (4 hours weekly)

 

 

Overall Course Objectives

 

Upon completion of this course, the student will be able to:

 

 1.            Calculate limits of elementary functions at a point.

 2.        Use e-d notation in the proofs of limits.

 3.            Calculate derivatives of functions given either implicitly or explicitly.

 4.            Calculate integrals of functions.

 5.        Apply the theory of derivatives to the graphing of curves, related rate problems, and maximum-minimum problems.

 6.        Apply the theorems of calculus to given functions.

 7.        Solve problems in a neat, organized and easy-to-follow way while using correct mathematical notation.

 8.        Solve various application problems using differential and/or integral calculus.

 9.            Calculate limits of logarithmic and exponential functions at a point.

10.            Calculate derivatives and integrals of logarithmic and exponential functions.         

11.       Use the computer algebra system, DERIVE, as a means of discovery, to reinforce concepts, and as an efficient problem solving tool.

 

 

 

Major Topics

            I.            Limits and Their Properties

                        A.            An Introduction to Limits

                        B.            Properties of Limits

                        C.            Techniques for Evaluating Limits

                        D.            Continuity and One-Sided Limits

                        E.            Infinite Limits

 

            II.            Differentiation

                        A.            The Derivative and the Tangent Lines Problem

                        B.            Basic Differentiation Rules and Rates of Change

                        C.            The Product and Quotient Rules and Higher-Order Derivatives

                        D.            The Chain Rule

                        E.            Implicit Differentiation

                        F.            Related Rates

                       

            III.            Applications of Differentiation

                        A.            Extrema on an Interval

                        B.            Rolle's Theorem and the Mean Value Theorem

                        C.            Increasing and Decreasing Functions and the First Derivative Test

                        D.            Concavity and the Second Derivative Test

                        E.            Limits at Infinity

                        F.            A Summary of Curve Sketching

                        G.            Optimization Problems

                        H.            Differentials

                                          

 

            IV.            Integration

                        A.            Antiderivatives and Indefinite Integration

                        B.            Area

                        C.            Definite Integrals

                        D.            The Fundamental Theorem of Calculus

                        E.            Integration by Substitutions

 

            V.            Logarithms and Exponential Functions

                        A.            The Natural Logarithmic Function and Differentiation

                        B.            The Natural Logarithmic Function and Integration

                        C.            Exponential Functions: Differentiation and Integration

                        D.            Bases Other than e and Applications

                       

 

Other Course Information

            This course may be used as a Mathematics core course or as a Mathematics elective and will transfer to a four-year university.

 

            Academic honesty, as defined in the Student Handbook, is required of all students.

Calculator:            It is recommended that students purchase a programmable, graphing, scientific pocket calculator for computations in this class.  A graphing calculator such as a TI83+ is required.

 

Class                Although attendance is not required, it will be taken and it should be noted that successful Attendance:                  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 which has been recently covered.  The mean of the quiz scores will be added to the next test score.

 

                        There will be a number of DERIVE Labs given during the semester.  The total points earned during the semester will be equivalent to one test grade (100 points).

 

                        Special projects may also be given during the semester.  Both the quizzes and special             projects can add to your point total.

 

                        A comprehensive last exam worth 200 points will be given during the final exam period.

 

                        You will be able to take one make-up exam for each test (except the final exam) to improve your score to a maximum of 80.  The make-up exams will be available in the Test Center.  Each student who wants to take a make-up exam must schedule an appointment with the instructor so that problem areas can be discussed.  You must take the regularly scheduled exam (or have a written, valid, verifiable reason for missing it) in order to take the make-up exam.  Note that there will be no make-up for the make-up exam.  If you take the make-up exam, the score on the make-up exam will replace the original test score.

 

                        Your final grade will be an:

                        A             if you receive 90% of the total points.            (630-700 points)

                        B             if you receive 80% of the total points.            (560-629 points)

                        C             if you receive 70% of the total points.            (490-559 points)

                        D             if you receive 60% of the total points.            (420-489 points)

                        I             if you have completed 90% of the work and the missed 10% resulted because of an                                       emergency