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MASTER SYLLABUS |
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MATH 1830 (formerly MTH 1255) |
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| Class Hours: 4.0 | Credit Hours: 4.0 | ||||||||
| Laboratory Hours: 0.0 | Date Revised: Fall 2001 | ||||||||
| Catalog Course Description: | |||||||||
| Topics include differentiation and integration of polynomial, rational, exponential, and logarithmic functions, and methods of numerical integration. Topics from business modeling, such as economic applications and case studies, will be explored with computer simulations, computer labs, or calculators. A graphing calculator is required. | |||||||||
| Entry Level Standards: | |||||||||
| Students must be able to read, write, and speak at college level. | |||||||||
| Prerequisites: | |||||||||
| Two years of high school algebra, precalculus, and satisfactory placement scores; or MATH 1130, MATH 1730, or MATH 1731 (formerly MTH 1010, 1020, 1021) | |||||||||
| Textbook(s) and Other Reference Materials Basic to the Course: | |||||||||
| Textbook:
Armstrong, Bill and Don Davis. Brief Calculus: The Study of Rates of Change, Prentice-Hall, Inc., 2000. References: Bittinger, Marvin L. Calculus and Its Applications, Addison-Wesley, 7th Ed., 2000. Warner, Stefan and Steven R. Costenoble. Applied Calculus, Brooks/Cole, 2nd Ed., 2001. Hughes-Hallett/Gleason/Loch/Flath/Etal. Applied Calculus, John Wiley & Sons, 1999. Personal Equipment: A graphing calculator is required. |
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| I. Week/Unit/Topic Basis: | |||||||||
| Week | Topic | ||||||||
| 1 | Functions. Linear Functions. Average Rate of change. Quadratic Functions. | ||||||||
| 2 | Average Rate of Change on an Interval. Operations on Functions. Rational, Radical, and Power Functions. | ||||||||
| 3 | Exponential Functions. Logarithmic Functions. Regression and Mathematical Models. Test 1 | ||||||||
| 4 | Limits. Asymptotes. Instantaneous Rates of Change. | ||||||||
| 5 | The Derivative. Derivatives of Constants, Powers, and Sums. | ||||||||
| 6 | Derivatives of Products and Quotients. Test 2 | ||||||||
| 7 | Differentials and Linear Approximations. Marginal Analysis. | ||||||||
| 8 | Measuring Rates and Errors. The Chain Rule. | ||||||||
| 9 | Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Test 3 | ||||||||
| 10 | First Derivatives
and Graphs. Second Derivatives and Graphs. Graphical
Analysis. Curve Sketching. |
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| 11 | Optimizing Functions on a Closed Interval. Optimization Problems on an Open Interval. Test 4 | ||||||||
| 12 | The Indefinite Integral. Area. The Definite Integral. | ||||||||
| 13 | Fundamental Theorem
of Calculus. Integrals that Yield Logarithmic and
Exponential Functions. |
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| 14 | Average Value of a Function. The Definite Integral in Finance. | ||||||||
| 15 | Area between Curves. Applications. Numerical Integration. Test 5 | ||||||||
| 16 | Review and Final Exam | ||||||||
| II. Course Objectives*: | |||||||||
| A. | Analyze behavior of functions. VI.1,3 | ||||||||
| B. | Compute derivatives of algebraic, logarithmic, and exponential functions. VI. 1,3,4 | ||||||||
| C. | Calculate integrals of algebraic, logarithmic, and exponential functions. VI.1,3,5 | ||||||||
| D. | Solve problems from business, economics, social and life science. VI.1,3 | ||||||||
| E. | Interpret, communicate, and report business application problems and their solutions in a clear and concise manner. VI.1, 4 | ||||||||
| *Roman numerals after course objectives reference goals of the university parallel program. | |||||||||
| III. Instructional Processes*: | |||||||||
| Students will: | |||||||||
| 1. | Work on teams to discuss and model business and economic applications by transforming data in tables into graphs and using the graphs to determine maximum profit and revenue. Communication Outcome, Numerical Literacy Outcome, Active Learning Strategy | ||||||||
| 2. | Practice personal integrity by being punctual, dependable, and cooperative. Personal Development Outcome | ||||||||
| 3. | Express ideas using the language and notation of mathematics. Numerical Literacy Outcome | ||||||||
| 4. | Use critical thinking skills to: interpret and apply rules such as Simpson's Rule and the trapezoid rule to solve real-life problems such as finding the area of a pond. Problem-Solving and Decision Making Outcome, Transitional Strategy | ||||||||
| 5. | Use calculators to optimize functions and to approximate numerical derivatives and definite integrals. Technological Literacy Outcome | ||||||||
| *Strategies and outcomes listed after instructional processes reference Pellissippi State's goals for strengthening general education knowledge and skills, connecting coursework to experiences beyond the classroom, and encouraging students to take active and responsible roles in the educational process. | |||||||||
| IV. Expectations for Student Performance*: | |||||||||
| Upon successful completion of this course, the student should be able to: | |||||||||
| 1. | Calculate the limit of an algebraic function. B | ||||||||
| 2. | Recognize a continuous function. A | ||||||||
| 3. | Calculate the derivative of an algebraic function by the delta process. B | ||||||||
| 4. | Calculate the derivative of polynomials, products, quotients, powers, and implicit functions using delta-derived rules. B | ||||||||
| 5. | Use derivatives to solve application problems such as problems involving distance, velocity, and acceleration; and maximum-minimum problems. C | ||||||||
| 6. | Sketch curves using information gathered from the derivatives of a function. B, C | ||||||||
| 7. | Find the derivatives of exponential and logarithmic functions. B | ||||||||
| 8. | Integrate polynomial, power, logarithmic, and exponential functions and use this knowledge to evaluate definite and indefinite integrals. D | ||||||||
| 9. | Use derivatives to solve business/economic and life/physical sciences application problems. C | ||||||||
| 10. | Use integration to solve application problems that occur in business/economic and life/physical sciences. E | ||||||||
| 11. | Work with technology and applicable case studies/projects that involve real-world data to enhance the conceptual understanding and usefulness of mathematics and to provide training in an area that both business and industry are now demanding. D, F | ||||||||
| *Letters after performance expectations reference the course objectives listed above. | |||||||||
| V. Evaluation: | |||||||||
| A. Testing Procedures: | |||||||||
| Students are evaluated primarily on the basis of tests, case studies/projects, quizzes, homework, and the comprehensive final exam. A minimum of 5 major tests is recommended. | |||||||||
| B. Laboratory Expectations: | |||||||||
| None | |||||||||
| C. Field Work: | |||||||||
| None | |||||||||
| D. Other Evaluation Methods: | |||||||||
| None | |||||||||
| E. Grading Scale: | |||||||||
| 93
- 100 A
88 - 92 B+ 83 - 87 B 78 - 82 C+ 70 - 77 C 60 - 69 D Below 60 F |
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| VI. Policies: | |||||||||
| Attendance Policy: | |||||||||
| Pellissippi State Technical Community College expects students to attend all scheduled instructional activities. As a minimum, students in all courses must be present for at least 75 percent of their scheduled class and laboratory meetings in order to receive credit for the course. Individual departments/programs/disciplines, with the approval of the vice president of Academic and Student Affairs, may have requirements that are more stringent. | |||||||||