COURSE OUTLINE

MAT 271

CALCULUS I

 

 

 

 

 

 

 

Developed by

Mathematics Instructional Faculty

 

 

 

Cape Fear Community College

411 North Front Street

Wilmington, N. C.   28401-3910

 

December 2005

 

 

Reviewed  By __Jody Hinson   ___________         Date__Decemeber 9, 2005 _______

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MAT  271

 

CALCULUS  I

 

 

 

                I.              COURSE DESCRIPTION :

                               

This course covers in depth the differential portion of a three-course calculus sequence.  Topics include limits, continuity, derivatives, and integrals of algebraic and transcendental functions of one variable, with applications.

 

 

 

                II.            OJECTIVES:

 

Upon completion, students should be able to:

1)       Apply the ε-δ definition of a limit

2)       Take limits of functions

3)       Analyze continuity and discontinuity of functions

4)       Use the limit definition of a derivative

5)       Analyze differentiability of functions

6)       Take derivatives of functions (explicitly, implicitly, and logarithmically)

7)       Use derivatives to find slopes and tangent lines to equations and functions

8)       Use derivatives to verify solutions to differential equations

9)       Use derivatives to find relative and absolute extrema, and points of inflection

10)    Use derivatives and limits to analyze graphs of functions

11)    Use derivatives in problems involving related rates, optimization, and differentials

12)    Evaluate indefinite and definite integrals

13)    Use derivatives and/or integrals to discuss position, velocity, and acceleration

14)    Use summations to find the area under a curve

15)    Use definite integrals to find the area under a curve

16)    Use numerical methods to approximate integrals

 

 

 

III.           OUTLINE OF INSTRUCTION:

               

                A.  Functions

1.        Cartesian Coordinate System

2.        Definitions

3.        Graphs

a.        Basic Graphs

b.       Transformations

 

B.  Limits

1.        ε-δ Definition

2.        Theorems and Properties

3.        Continuity

a.        Definition

b.       Properties

c.        Intermediate Value Theorem

 

C.  Derivatives

1.        Slope and Tangent Lines

2.        Limit Definition

3.        Rules

a.        Power Rule

b.       Constant Multiple Rule

c.        Sum and Difference Rule

d.       Product

e.        Quotient Rule

f.         Chain Rule

4.        Implicit Differentiation

5.        Transcendental Functions

a.        Trigonometric Functions

b.       Exponential Functions

c.        Logarithmic Functions

d.       Hyperbolic Functions

e.        Applications

6.        Logarithmic Differentiation

7.        Rates of Change

a.        Average Rate of Change

b.       Instantaneous Rate of Change

c.        Velocity and Acceleration

d.       Differentials

8.        Newton’s Method

9.        Graphing

a.        First Derivative

                                                                                                                           i.      Increasing, Decreasing, and Constant

                                                                                                                          ii.      Critical Values

                                                                                                                        iii.      First Derivative Test

                                                                                                                        iv.      Extrema

b.       Second Derivative

                                                                                                                           i.      Concavity

                                                                                                                          ii.      Second Derivative Test

                                                                                                                        iii.      Points of Inflection

c.        Asymptotes

10.     Applications

a.        Related Rates

b.       Optimization

c.        Rolle’s Theorem

d.       Mean Value Theorem

 

D.  Integrals

1.        Antiderivatives

a.        Power Rule

b.       Constant Multiple Rule

c.        Sum and Difference

d.       Trigonometric Functions

e.        Integration by Substitution

f.         Exponential Functions

g.       Logarithmic Functions

2.        Definite Integrals

a.        Area

                                                                                                                           i.      Area as a Sum

                                                                                                                          ii.      Area as an Integral

b.       Riemann Sums

c.        Fundamental Theorems

d.       Mean Value Theorem

e.        Average Value

3.        Numerical Approximation

a.        Trapezoid Rule

b.       Simpson’s Rule

c.        Error Analysis

 

IV.           HOURS, CREDITS, PREREQUISITES:

 

                Course Hours Per Week:                    5

                                Semester Hours Credit:                       4

                                Prerequisite:                                          MAT 171 and MAT 172 or MAT 175

                                Co-requisite:                                         None

 

                V.             EVALUATION:

                               

Evaluation is based on performance on instructor prepared tests and a cumulative final exam.  The final exam will weigh a minimum of 20% of the student’s course grade.  Individual instructors may also incorporate student’s class participation, homework, quizzes, Maple lab grades, and/or calculator lab grades as they see fit.

 

                VI.           SUGGESTED TEXT:

               

                                Calculus, 6th ed. By Larson, Hostetler, and Edwards

 

                VII.          SUGGESTED REFERENCES:

 

The instructor should select material that supplements the student’s course of study.  Options include but are not limited to: graphic calculator exercises, application sessions, and/or exercises utilizing Maple software.

 

                VIII.        ADDITIONAL MATERIALS:

                               

A syllabus is required to be given to each student on the first day of class explaining attendance and grading policies.  The syllabus should also include instructor contact information, course description, student learning outcomes, and any prerequisite or co-requisite requirements.