Subsequently, students will learn to use power series to approximate an arbitrary function near a specific value. Series: Students will become familiar with various methods for determining convergence and divergence of a series. The relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus will also be emphasized. Integrals and the Fundamental Theorem of Calculus: Students will gain a firm understanding of area, volume and motion applications of integrals as well as the use of the definite integral as an accumulation function. Students will also become familiar with a variety of real-world applications of the derivative, including related rates, optimization, and growth and decay models. Limits: Students will gain a solid, intuitive understanding of limits and be able to compute one-sided limits, limits at infinity, infinity limits and the limit of a sequence.ĭerivatives: Students will learn to use different definitions of the derivative and be able to apply derivative rules and properties. The course is organized around the following foundational concepts of calculus: Students will learn problem-solving techniques that will maximize computational efficiency while minimizing computational errors. We will use graphing calculators and Desmos (an online graphing program) towards this end. Students will learn to use technology to help experiment, solve problems, interpret results and support conclusions. To offer a multifaceted approach to calculus: students will learn to express concepts, results and problems graphically, numerically, analytically and verbally.
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