(Cross listed and equivalent to CSC208) An introduction to limits and continuity. Examines differentiation and integration concepts with applications to related rates, curve sketching, engineering optimization problems and business applications. Students may not receive credit for both MTH220 and CSC208.
- Successfully use techniques for evaluating the limits of algebraic and trigonometric functions. As the independent variable approaches finite values or grows without bound. Invoke the definition of continuity at a point to so test prescribed functions. Be able to graphically depict three common problems that lead to discontinuity at a point.
- Interpret the concept of derivative geometrically, numerically, and analytically (i.e., slope of the tangent, limit of difference quotients, extrema, Newton’s method, and instantaneous rate of change)
- Clearly demonstrate facility with fundamental differentiation formulas and rules. Be fully capable of employing implicit differentiation and the chain rule to elementary related-rate problems.
- Give written evidence of successful application to curve sketching, with extremal tests by first and second derivatives. Successfully recognize and perform applications of the derivative to solve optimization problems, as taken from several disciplines including business, biology, medicine, and the physical sciences.
- Demonstrate facility with each of the presented techniques of integration to derive antiderivatives. Be able to write down, and employ, the Fundamental Theorem of Calculus to an array of elementary numerical applications for each of the integrand types specified in the corresponding goal. Be able to find areas bounded by elementary functions. The student will demonstrate by simple example an understanding that continuity is sufficient, but not necessary, for Riemann integrability.
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