Calculus II | |||
CALCULUS II | |||
CLASS CODE: | MATH 113 | CREDITS: 3 | |
DIVISION: | PHYSICAL SCIENCE & ENGINEERING | ||
DEPARTMENT: | MATHEMATICS | ||
GENERAL EDUCATION: | This course fulfills a General Education - Math requirement. | ||
DESCRIPTION: | Techniques of integration, infinite sequences and series, polar coordinates, and parametric curves. Math 113 and Math 215 cannot both be taken for credit. | ||
TAUGHT: | Winter, Summer, Fall | ||
CONTENT AND TOPICS: | Integration by parts and by partial fractions. Trigonometric integrals and integration by trigonometric substitution. Tables of integrals. Infinite sequences and series, and theorems regarding convergence. Taylor polynomials and series, with remainders. Calculus in the contexts of conic sections, polar coordinates and parametric curves. |
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GOALS AND OBJECTIVES: | 1. Use integrals to calculate volumes of solids of revolution. 2. Use integrals to calculate arc length and areas of surfaces of revolution. 3. Use integrals to calculate work, center of mass and fluid force. 4. Evaluate integrals involving trigonometric functions using identities. 5. Evaluate integrals using trigonometric substitution. 6. Evaluate integrals using partial fractions. 7. Understand sequences and find the limit of a convergent sequence. 8. Determine convergence or divergence of a geometric series and find its sum. 9. Determine convergence or divergence of series using the integral test, comparison tests, alternating series test, and ratio and root tests. 10. Determine the interval of convergence of a power series. 11. Find and use Taylor polynomials and series for various functions. 12. Solve calculus problems involving conic sections. 13. Solve calculus problems involving parametric equations. 14. Solve calculus problems involving polar coordinates. |
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REQUIREMENTS: | All students must have their own text. If the instructor requires a graphing calculator, each student must supply his or her own. Homework assignments and exams are required by all faculty. Students must attend classes and may be required to participate in computer labs, projects or other forms of learning and assessment, as determined by their instructor. | ||
PREREQUISITES: | Math 112 or the equivalent. Students entering Calculus II may be expected to know how to use those features of their graphing calculators that are typically used in first semester calculus courses. | ||
OTHER: | (1) The faculty members who teach Calculus II use technology to varying degrees, from the occasional use of graphing calculators to the frequent dependence on Scientific Notebook, which includes basic features of the Maple computer algebra system. The Department of Mathematics operates a computer lab where Calculus II students can use such software. (2) Calculus II meets three hours per week, for three semester credits. |
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EFFECTIVE DATE: | August 2003 |