* Test – Differentiation MODULE 3: APPLICATIONS OF DIFFERENTIATION SUGGESTED PACE: 6 WEEKS Discussion about the limitations of the calculator to find the numerical derivative (for example, f ‘(0) for f (x) = |x|).
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* Oral Review: Discussion about using a calculator to find the value of a derivative at a point, and how to graph the derived function using a calculator. * Quiz – Definition and computation of derivatives
* Basic differentiation rules and rates of change * The derivative and the tangent line problem * Modeling rates of change and solving related rates problems * Equations involving derivatives and problems using their verbal descriptions * Chain rule and implicit differentiation * Approximate rate of change from graphs and tables of values * Instantaneous rate of change as the limit of average rate of change * Derivative interpreted as instantaneous rate of change * Basic rules for the derivatives of sums, products, and quotients of functions * Knowledge of derivatives of power and trigonometric functions * Graphic, numeric and analytic interpretations of the derivative * Derivative defined as the limit of the difference quotient * Test – Limits and Continuity MODULE 2: DIFFERENTIATION SUGGESTED PACE: 5 WEEKS * Elluminate Session: Discussion about conditions of continuity. Discussion about the limitation of a graphing calculator to show discontinuities in functions and the value of using a calculator to support conclusions found analytically. * Oral Review: Discussion about using the Calculator to experiment and produce a table of values to examine a function and estimate a limit as x approaches a point and as x grows without bound. * Finding limits graphically and numerically * Understanding graphs of continuous or non-continuous functions geometrically * Understanding continuity in terms of limits * Describing asymptotic behavior in terms of limits involving infinity * Calculating limits using algebraic methods * Intuitive understanding of limit process * Quiz – Functions, Graphs, and Rates of Change MODULE 1: LIMITS AND CONTINUITY SUGGESTED PACE: 2 WEEKS * Oral Review: Discussion about using Calculator zoom features to examine a graph in a good viewing window and calculator operations to find the zeros of a graph and the point of intersection of two graphs * Comparing relative magnitudes of functions – contrasting exponential, logarithmic and polynomial growth
* Using the Cartesian coordinate system to graph functions * Understanding the properties of real numbers and the number line MAJOR TOPICS AND CONCEPTS MODULE 0: PREPARATION FOR CALCULUS SUGGESTED PACE: 2 WEEKS This course includes a study of limits, continuity, differentiation, and integration of algebraic, trigonometric and transcendental functions, and the applications of derivatives and integrals.
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Walk in the footsteps of Newton and Leibnitz! An interactive text and graphing software combine with the exciting on-line course delivery to make Calculus an adventure.
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