COURSE DESCRIPTION: This course includes the following topics: differentiation and integration of polynomial, rational, logarithmic and exponential functions; and interpretation and application of these processes.
TEXT: Brief Calculus, An Applied Approach, 7th edition by Ron Larson and Bruce Edwards Houghton Mifflin Company, 2006
PREREQUISITE: MAT 110
EQUIPMENT: Graphing calculator required; TI-83 or TI-83+ recommended
Departmental Eduspace Course Codes: JENKI-17B6EA47FD590C (optional)
GRADING SCALE:
A 90 - 100 B 80 - 89 C 70 - 79 D 60 - 69 F below 60
MATHEMATICS DEPARTMENT AiRport: 822-3357 Beltline: 738-7689 Revised: 3/08/2007
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
MAT 130 ELEMENTARY CALCULUS COURSE OBJECTIVES
Students should be able to:
1. Evaluate limits for algebraic functions.
2. Evaluate derivatives of algebraic functions
3. Solve problems in which the derivaive is interpreted as a slope, rate of change, velocity, acceleration, etc.
4. Use properties of the first and second derivative as an aid in curve sketching.
5. Solve maximum - minimum problems.
6. Differentiate logarithmic and exponential functions and apply this to solve growth and decay problems.
7. Integrate using basic formulas and the techniques of substitution and integration by parts.
8. Integrate to find areas under a curve and between two curves.
9. Solve problems by identifying what information is available and relevant to the problem.
10. Solve problems by selecting or developing appropriate procedures and relationships.
11. Solve problems by correctly applying the methods selected to the information available.
12. Solve problems by verifying the validity and appropriateness of the solution.
Note: This outline is given for the regular Fall/Spring fourteen week semesters. The same material is covered in the summer term and the sessions classes, but in the appropriate fewer number of weeks: ten weeks for summer term, seven weeks for fall and spring sessions classes, and five weeks for summer session classes.
| WEEK | TOPIC | SECTION |
| 1 | Functions, Graphs, and Limits | |
| Limits | 1.5 | |
| Continuity | 1.6 | |
| Differentiation | ||
| The Derivative and the Slope of a Line | 2.1 | |
| 2 | Some Rules for Differentiation | 2.2 |
| Rates of Change: Velocity and Marginals | 2.3 | |
| The Product and Quotient Rules | 2.4 | |
| 3 | The Chain Rule | 2.5 |
| Higher Order Derivatives | 2.6 | |
| Implicit Differentiation | 2.7 | |
| 4 | Related Rates | 2.8 |
| TEST 1 | ||
| 5 | Applications of the Derivative | |
| Increasing and Decreasing Functions | 3.1 | |
| Extrema and the First-Derivative Test | 3.2 | |
| Concavity and the Second-Derivative Test | 3.3 | |
| 6 | Optimization Problems | 3.4 |
| Business and Economics Applications | 3.5 | |
| 7 | Asymptotes | 3.5 |
| Curve Sketching: A Summary | 3.7 | |
| Differentials and Marginal Analysis | 3.8 | |
| 8 | TEST 2 | |
| Exponential and Logarithmic Functions | ||
| Exponential Functions | 4.1 | |
| Natural Exponential Functions | 4.2 | |
| Derivatives of Exponential Functions | 4.3 | |
| 9 | Logarithmic Functions | 4.4 |
| Derivatives of Logarithmic Functions | 4.5 | |
| Exponential Growth and Decay | 4.6 | |
| 10 | TEST 3 | |
| Integration and Its Applications | ||
| Antiderivatives and Indefinite Integrals | 5.1 | |
| The General Power Rule | 5.2 | |
| 11 | Exponential and Logarithmic Integrals | 5.3 |
| Area and the Fundamental Theorem of Calculus | 5.4 | |
| The Area of a Region Bounded by Two Graphs | 5.5 | |
| 12 | The Definite Integral as the Limit of a Sum (optional) | 5.6 |
| Volumes of Solids of Revolution (optional) | 5.7 | |
| 13 | Techniques of Integration | |
| Integration by Substitution | 6.1 | |
| Integration by Parts and Present Value | 6.2 | |
| 14 | Integration Tables and Completing the Square | 6.4 |
| TEST 4 | ||
| Comprehensive Final Exam |