Unit 1 covers the foundations of Calculus. Namely a strong understanding of algebra and a more complete understanding of limits. We pay particular attention to the limit as x approaches infinity and as x approaches zero. The ideas of continuity and intermediate value are developed as well.
limits_day_1.pdf | |
File Size: | 1375 kb |
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1.3._limits_properties.pdf | |
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continuity_and_ivt.pdf | |
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Chapter 2 is the introduction of the derivative. We study the derivative function as a limit, properties of derivatives and tie those to continuity properties. Highlights of the chapter are implicit differentiation, the chain rule and related rates.
rate_of_change_derivative_day_1.pdf | |
File Size: | 1894 kb |
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derivative__constant_constant_multiple_power_sin_cos.pdf | |
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related_rates_day_1.pdf | |
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Chapter 3 focuses on the uses of the derivative to: find maximums, find minimums, look at increasing and decreasing behavior and graph the function. Rolle's Theorem, the Mean Value Theorem, concavity and optimization are other key features of chapter 3.
notes_on_extrema.pdf | |
File Size: | 467 kb |
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Unit 4 is the introduction of integration and area under the curve.
antidifferentiation-1_2018.pdf | |
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summation_day_1_2018.pdf | |
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infinite_sums_2018.pdf | |
File Size: | 1664 kb |
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ftc1_2018.pdf | |
File Size: | 1658 kb |
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ftc_mvt_avg_value_and_ftc2.pdf | |
File Size: | 958 kb |
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Unit 5 is a continuation of differentiation and integration with exponentials and logarithms.
Chapter 3 focuses upon curve sketching and analysis of functions. Rolle's Theorem, the Mean Value Theorem and the Intermediate Value Theorm are highlights of the unit.