COURSE OUTLINE

MIDLANDS TECHNICAL COLLEGE

MAT 140 ANALYTICAL GEOMETRY AND CALCULUS I

4.0 Credit Hours

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.

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

PREREQUISITE: MAT 110 and MAT 111

EQUIPMENT: Graphing Calculator, preferably TI-83 or TI-83+

GRADING SCALE:

A 90 - 100        B 80 - 89        C 70 - 79        D 60 -69        F Below 60

MATHEMATICS DEPARTMENT ATTENDANCE REQUIREMENTS

DEFINITIONS:

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. Five absences are allowed for a class that meets three times per week, and 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: You are responsible for all material and announcements presented, whether you are present or absent.

Mathematics Department                                                        Airport: 822-3357                                                                    Beltline: 738-7689                                                                     Revised 2/27/2007

MAT 140 COURSE OBJECTIVES

Students should 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.

8. Solve problems by identifying what information is available and relevant to the problem.

9. Solve problems by selecting or developing appropriate procedures and relationships.

10. Solve problems by correctly applying the methods selected to the information available.

11. Solve problems by verifying the validity and appropriateness of the solution.

 

MAT 140 ANALYTICAL GEOMETRY AND CALCULUS I


WEEK TOPIC SECTION
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 he Second Derivative Test 3.4
      Limits at Infinity 3.5
     
7     A Summary of Curve Sketching 3.6
      Optimization 3.7
      Differentials 3.8
     
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 Integrations  
      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