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Chabot College Fall 2009 Course Outline for Mathematics 15 APPLIED CALCULUS I • Catalog Description: MTH 15 - Applied Calculus I • • Units (Min) 3.00 units Differential calculus of algebraic, exponential, and logarithmic functions; introduction to integral calculus. Applications in business, economics and the life and social sciences. Prerequisite: MTH 31 (completed with a grade of "C" or higher) or , MTH 20 (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the Mathematics Assessment process. Units (Max) Contact Hours Week (Min) 3.00 Lecture Laboratory Clinical Total 3.00 • Week (Max) Term (Min) Term (Max) 3.00 3.00 3.00 0.00 0.00 3.00 3.00 1.00 0.00 4.00 52.50 0.00 0.00 52.50 52.50 17.50 0.00 70.00 Prerequisite Skills: None • Expected Outcomes for Students: Upon completion of this course, the student should be able to: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. • graph polynomial, rational, exponential and logarithmic functions; find limits numerically, graphically, and using limit properties; determine intervals of continuity graphically and using continuity properties; differentiate using the definition of the derivative; differentiate using the rules of differentiation including the chain rule; find equations of tangent lines; find marginal cost, marginal revenue and marginal profit; find all maxima, minima and points of inflection; solve applied optimization problems; differentiate implicitly; solve related rate problems; find antiderivatives using basic rules of integration and substitution; evaluate definite integrals using the Fundamental Theorem of Calculus; find total change given rate of change. Course Content: 1. Functions 2. 3. 4. 5. 6. • Methods of Presentation 1. 2. • A. Linear functions and equations of lines B. Quadratic functions C. Polynomial functions D. Rational functions E. Exponential and logarithmic functions Limits A. Definition B. One-sided C. Infinite Continuity A. Definition at a point and over an interval B. Properties of continuity C. Discontinuity D. One-sided Derivative A. Definition B. Geometric interpretation C. Rules of differentiation, including chain rule D. Second derivatives E. Implicit differentiation Application of the derivative A. Maximum-minimum problems B. Curve sketching C. Related rates D. Marginal analysis Integration A. Antiderivatives B. Substitution C. Riemann sums and the definite integral D. The Fundamental Theorem of Calculus E. Applications Lecture/Discussion Problem Solving Assignments and Methods of Evaluating Student Progress 1. Typical Assignments A. B. C. A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72,000 +60x, p= 200 + x/30, 0 < x < 6,000 1) Find the maximum revenue. 2) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 22 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels. How many trees should be planted in order to maximize the yield? It is estimated that a newly discovered oil field will produce oil at the rate of r(t)= ? thousand barrels/year, t years after production begins. Find the amount of oil that the field can be expected to yield during the first 5 years of production. 2. Methods of Evaluating Student Progress A. B. C. D. • Homework Quizzes Exams/Tests Final Examination Textbook (Typical): 1. Tan, Soo (2008). Applied Calculus Brooks Cole. • Special Student Materials 1. Scientific or graphing calculator