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Chabot College Fall 2010 Course Outline for Mathematics 1 CALCULUS I • Catalog Description: MTH 1 - Calculus I 5.00 units • Elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and trigonometric functions, the definite integral. • Prerequisite: MTH 20 (completed with a grade of "C" or higher) or an appropriate skill level demonstrated through the mathematics assessment process. Units Contact Hours Week Term 5.00 Lecture Laboratory Clinical Total • 5.00 5.00 0 0.00 5.00 87.50 0 0.00 87.50 Prerequisite Skills: None • Expected Outcomes for Students: Upon completion of this course, the student should be able to: 1. use delta notation; 2. explain limits and continuity; 3. use Newton’s method; 4. apply the definition of the derivative of a function; 5. define velocity and acceleration in terms of mathematics; 6. differentiate algebraic and trigonometric functions; 7. apply the chain rule; 8. find all maxima, minima and points of inflection on an interval; 9. sketch the graph of a differentiable function; 10. apply implicit differentiation to solve related rate problems; 11. apply the Mean Value Theorem; 12. find the value of a definite integral as the limit of a Riemann sum; 13. integrate a definite integral using the Fundamental Theorem of Integral Calculus; 14. differentiate appropriate functions using the Fundamental Theorem of Integral Calculus; 15. find differentials and use differentials to solve applications; 16. integrate using the substitution method; 17. find the volume of a solid of revolution using the shell, disc, washer methods; 18. find the volume of a solid by slicing; 19. find the work done by a force; 20. find the hydrostatic force on a vertical plate; 21. find the center of mass of a plane region; 22. approximate a definite integral using Simpson’s Rule and the Trapezoidal Rule. • Course Content: 1. Review relations, functions and graphs 2. Review lines, equations and slopes 3. Limits and continuity 4. Mean Value Theorem 5. Differentials and their applications 6. Differentiation of algebraic functions 7. Differentiation of trigonometric functions 8. Chain rule 9. Related rate problems 10. Maxima, minima and points of inflection 11. Curve sketching 12. Applications of differentiation 13. Newton’s Method 14. Riemann sum 15. Definite integral and the Fundamental Theorem of Integral Calculus 16. Mean Value Theorem for Definite Integrals 17. Average value of a function 18. Integration by substitution 19. Simpson’s and Trapezoidal Rule 20. Areas of plane regions 21. Volume and surface area of solids of revolutions 22. Volume of solid by slicing 23. Center of mass for a plane region 24. Theorem of Pappus 25. Application of integral calculus to work and hydrostatic pressure problems • Methods of Presentation 1. Lecture/Discussion 2. Audio-visual materials • Assignments and Methods of Evaluating Student Progress 1. Typical Assignments A. Exercises from the textbook such as the following: Show, using implicit differentiation, that any tangent line at a point P to a circle with center O is perpendicular to the radius OP. B. Collaborative: Given a variety of functions, differentiate the functions. 2. Methods of Evaluating Student Progress A. B. C. D. E. • Exams/Tests Quizzes Class Participation Home Work Final Examination Textbook (Typical): 1. Hass/Weir /Thomas (2008). University Calculus Addison Wesley Publishing Company. • Special Student Materials 1. A scientific or graphing calculator may be required.