Calculus I | |||
CALCULUS I | |||
CLASS CODE: | MATH 112 | CREDITS: 4 | |
DIVISION: | PHYSICAL SCIENCE & ENGINEERING | ||
DEPARTMENT: | MATHEMATICS | ||
GENERAL EDUCATION: | This course fulfills a General Education - Math requirement. | ||
DESCRIPTION: | Limits, continuity, derivatives, integrals, and transcendental functions. Properties and applications of the above. |
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TAUGHT: | Winter, Summer, Fall | ||
CONTENT AND TOPICS: | One- and two-sided limits, both finite and infinite, and limits at infinity. Continuity and the Intermediate Value Theorem. First and higher derivatives, including their interpretations and rules for calculating them. Rolle’s Theorem and the Mean Value Theorem. Implicit differentiation and related rates. Analysis of functions through their graphs, using such tools as the first and second derivative tests. Optimization, including applications. The differential and local linearization. Area under curves, the Riemann sum, antiderivatives, definite integrals and the Fundamental Theorem of Calculus. Integration by substitution and by parts. L'Hopital's rule and improper integration. Calculus of transcendental functions, including hyperbolic functions. As may of the following applications of integration as time allows: the area between curves, volume by slices, disks and shells, arc length, the area of a surface of revolution, center of mass, work and static fluid force. | ||
GOALS AND OBJECTIVES: | 1. Understand the meaning of the limit of a function. Use the delta-epsilon definition of the limit to prove the limit of a given function does or does not exist. 2. Prove a function is continuous or discontinuous at a point. 3. Find limits of various functions analytically. 4. Use the definition to find the derivative of a function. Describe when a derivative exists. 5. Apply basic differentiation rules to various functions. 6. Understand and use the chain rule to solve various problems including those involving implicit differentiation. 7. Use the derivative to solve application problems including optimization and related rates. 8. Find antiderivatives of various functions. 9. Use the Fundamental Theorem of Calculus to evaluate definite integrals. Use different integration techniques including change of variables and integration by parts. 10. Use integrals to solve various application problems including volumes, arc length, area of a surface of revolution and work. |
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REQUIREMENTS: | All students must have their own text (currently Larson, Hostetler & Edwards, Calculus, 7th. edition) and a graphing calculator. Homework assignments and exams are required by all faculty. Students must attend classes and may be required to participate in computer labs, group projects or other forms of learning and assessment, as determined by their instructor. | ||
PREREQUISITES: | Math 110 and Math 111 or high school or college preparation in Algebra and Trigonometry (or in Precalculus) equivalent to Math 110 and Math 111. For more information, the student should consult with the instructor or an adviser in the Mathematics Department. Students entering Calculus I are expected to know how to use those features of their graphing calculators that are typically used in precalculus courses. | ||
OTHER: | (1) Those who teach Calculus I use graphing calculators to varying degrees. Some only discuss them occasionally while others require their students to be able to do everything in the course using the calculator, as well as by hand. Some encourage their students to use Scientific Notebook, which includes basic features of the Maple computer algebra system. The Department of Mathematics operates a computer lab in which Calculus I students may use such software. (2) Some faculty teach delta-epsilon proofs; others don’t. Some faculty teach Newton’s Method and numerical integration; others don’t. (3) Calculus I meets five hours per week, for four semester credits. The fifth hour, traditionally a recitation hour, is used nowadays in the same manner as the other four. |
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EFFECTIVE DATE: | August 2001 |