A discussion of differentiation and integration concepts of the natural logarithm, exponential and inverse trigonometric functions and applications to volumes of revolution, work and arc length. Covers improper integrals and highlights ideas and contributions of Natpier, Huygens and Pascal. Graphing calculator is required.
- Show ability to formulate the functional representations of incremental components of area, volume, surface-area, work, fluid pressure, and be proficient in carrying these through to the integrand of the appropriate definite integral. The student will be successful in retrieving the antiderivative, and evaluating it, during the computation of such integrals.
- Interpret the concept of a definite integral geometrically, numerically, and analytically (e.g., limit of Riemann sums)
- Demonstrate capability to produce an inverse functions, when they exist. Show evidence of solid grasp of the differentiation and integration formulas and rules associated with inverse functions.
- Derive antiderivatives by knowledgeable appeal to the more sophisticated methods of integration by parts, recursion, trigonometric substitution, and partial fractions. The student will demonstrate ability to set up numerical approximations to definite integrals for which closed-form solutions may be impractical to attain. The student will be able to recognize such circumstances.
- Provide evidence of recognition and understanding of behavior of infinite sequences and series. Demonstrate techniques for testing their absolute or conditional convergence, if any. The student will recognize the appropriate logarithmic or trigonometric function to which the power series converges. Similarly, for each such function, the student will be able to generate associated partial sequences of the Maclaurin and Taylor series.
- Compute with conic sections properties presented in algebraic, polar, and other parametric form. Lengths of arc, surface areas, and an understanding of applications to specific problems will be demonstrated.
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