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                                                                            MAT 140 – Analytical Geometry and Calculus I

                                                                    Mathematics Department

 

Semester: Fall 2008

 

Catalog Course Description: This course includes the following topics: derivatives and integrals of polynomial, rational, logarithmic, exponential, trigonometric and inverse trigonometric functions; curve sketching; maxima and minima of functions; related rates; work; and analytic geometry.

 

 

Prerequisite(s):                      MAT 111

Credit Hours:                         4.0 Credit Hours

 

Departmental Website:         http://midlandstech.edu/mathdepartment

 

Instructor:                              Jason Wetzel

Office:                                     Airport Campus     RO 203 

Telephone:                             (803) 822-3074

E-mail:                                   WetzelJ@midlandstech.edu

Campus Mailbox:                  Airport Campus   RO 105

Personal Website:                  http://www.midlandstech.edu/math/wetzel

 

Departmental Assistant:       Mitzi Trigg – TriggM@MidlandsTech.edu – 738-7689

Department Chair:                 Rick Bailey – BaileyR@MidlandsTech.edu – 738-7618

Program Coordinator:            Rose Jenkins – JenkinsR@MidlandsTech.edu – 822-3351       

 

Class Schedule[s]:                 A01:        MW        8:00-10:00               CO128

 

Office Hours:                         Please see my website

 

Textbook(s):                           Calculus, Eighth Edition by Roland E. Larson, Robert P. Hostetler, and Bruce H. Edwards, Houghton Mifflin, 2006

 

Equipment:                             Graphing Calculator, TI-84 or TI-84+

 

General Education Core Competency Statement:  Programs may use this course to meet the general education core competency of mathematics.

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

1.        Calculate limits by using direct substitution, a graph, a table of values, and algebra.

2.        Test functions for continuity.

3.        Calculate derivatives and use the numerical derivative to approximate derivatives.

4.        Use the first and second derivatives as an aide in graphing algebraic functions.

5.        Use numerical methods to evaluate definite integrals.

6.        Find areas between curves, volumes and surface areas of solids, lengths of curves, and amount of work using integrals.

7.        Calculate derivatives and integrals involving exponential and logarithmic functions.                   

Course Outcomes and Competencies:

Intended Course Outcome: Students should be able to understand and apply computational skills, quantitative reasoning and symbolic reasoning to evaluate and solve problems systematically.

            Course Competency: Students should be able to solve mathematical problems by identifying what information is available and relevant to the problem; by selecting or developing appropriate procedures and relationships; by correctly applying the methods selected to the information available; and by verifying the validity and appropriateness of the solution.

            Performance Measurement Instrument: Students will be given four applied mathematical problems to solve selected by the Mathematics Department to measure successful attainment of the competency.  These problems will be embedded within student quizzes and tests.  A student correctly solving 3 out of 4 of the problems will be considered to have successfully attained the competency.  The goal is for 75% of the students completing the assessment to successfully attain the competency.

 

Course Attendance:  

ABSENCE -          Failure to be present for a scheduled meeting of the class or arriving for the class more than ten minutes after the scheduled time for the class to begin.

TARDY ---             Arrival to class after the instructor has called the roll and before ten minutes past the time scheduled for the class to begin.

I.                     Absences are counted from the first day of classes.

II.                   Three  absences are allowed for a class that meets two times per week.

III.                 Three tardies are considered as one absence.  The student must meet with the instructor at the end of the class to which he has been late to have the absence changed to a tardy.

IV.                 There are no "excused" absences; all absences are counted, regardless of the reason for the absence.

V.                   A student missing class time by leaving early will also be counted absent.

 

 Please note the following: You are responsible for all material and announcements presented, whether you are present or absent. 

 

Withdrawal:  Should the maximum allowable absences be exceeded prior to midterm, a "W" will be submitted to the registrar to be recorded on the student's transcript.  Should the maximum allowable absences be exceeded after midterm, a "W" will be submitted to the registrar if the student was passing the course at the time of withdrawal OR a "WF" will be submitted if the student was failing the course at the time of withdrawal.

 

Course Requirements:  For each section we cover in the book, there will be a corresponding homework assignment.   Homework will never be checked.  It will not count toward your grade.  Homework assignments are problems I suggest you do in order to be prepared for the test.  I will answer any questions from homework the first 10 minutes of class.  Pop quizzes will be given occasionally and will count toward the following unit test. 

                                                       

                                          There will be NO make-ups!  If you are absent for a unit test, your final exam grade will also count for the missed test grade.  If you take all five unit tests, your final exam grade will replace your lowest unit test if your final exam grade is higher.

 

Course Grading:        There will be five unit tests and a final exam each worth 100 points.  Your final course grade will be the average of these six grades for a total of 600 possible points.

 

Grading Scale:                       90-100                     A                             Superior Work

                                                                  80-89                     B                             Good Work

                                                                  70-79                     C                             Average Work

                                                  60-69                     D                             Below Average Work

                                                                   0- 59                     F                              Unsatisfactory Work

 

Special Procedures:      Extra Credit:  An electronic course evaluation will become available to you through MTC Online.  It is important for MTC to get your feedback from this course.  At the end of the semester, the class with the highest response rate will earn 3 bonus points on the final exam.

 

 

 

 

Course Topic Outline/Course Calendar with Assignments:

 

WEEK

 

TOPIC

TEXT REF.

1

Limits and Their Properties

 

 

A Preview of Calculus

1.1

 

Finding Limits Graphically and Numerically

1.2

 

Evaluating Limits Analytically

1.3

2

Continuity and One-Sided Limits

1.4

 

Infinite Limits

1.5

 

TEST 1

 

 

 

 

 

 

 

 

 

 

 

 

 

3

The Derivative and the Tangent Line Problem

2.1

 

Basic Differentiation Rules and Rates of Change

2.2

 

The Product and Quotient Rules and Higher-Order Derivatives

2.3

4

The Chain Rule

2.4

 

Implicit Differentiation

2.5

 

Related Rates

2.6

5

TEST 2

 

 

 

 

 

Applications of Differentiation

 

 

Extrema on an Interval

3.1

 

Rolle’s Theorem and the Mean Value Theorem

3.2

6

Increasing and Decreasing Functions and the First Derivative Test

3.3

 

Concavity and the Second Derivative Test

3.4

 

Limits at Infinity

3.5

7

A Summary of Curve Sketching

3.6

 

Optimization Problems

3.7

 

Differentials

3.9

8

TEST 3

 

 

 

 

 

Integration

 

 

Antiderivatives and Indefinite Integration

4.1

 

Area

4.2

9

Riemann Sums and Definite Integrals

4.3

 

The Fundamental Theorem of Calculus

4.4

 

Integration by Substitution

4.5

10

Numerical Integration

4.6

 

TEST 4

 

 

 

 

 

Logarithmic, Exponential, and Other Transcendental Functions

 

 

The Natural Logarithmic Function: Differentiation

5.1

11

The Natural Logarithmic Function: Integration

5.2

 

Inverse Functions

5.3

 

Exponential Functions: Differentiation and Integration

5.4

12

Bases Other Than e and Applications

5.5

 

TEST 5

 

 

 

 

 

Applications of Integration

 

 

Area of a Region Between Two Curves

7.1

13

Volume: The Disc Method

7.2

 

Volume: The Shell Method

7.3

 

Arc Length and Surfaces of Revolution

7.4

14

Work

7.5

 

Comprehensive Final Examination