Math151 Lecture Notes Fall 2018
This page will be updated as the semester progresses.
Supplement I – Vectors
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Supplement I – The Dot Product
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Supplement I – Vector Functions and Parametric Curves
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Section 1.5 (Invers trig functions)
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Section 2.2 (The limit of a function)
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Section 2.3 (Calculating limits using the limit laws)
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Section 2.5 (Continuity)
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Section 2.6 (Limits at infinity; horizontal asymptotes)
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Section 2.7 (Derivatives and rates of change)
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Section 2.8 (The derivative as a function)
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Section 3.1 (Derivatives of plynomials and exponential functions)
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Section 3.2 (The product and quotient rules)
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Section 3.3 (Derivatives of trigonometric functions)
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Section 3.4 (The chain rule)
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Section 3.5 (Implicit defferentiation)
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Section 3.6 (Derivatives of logarithmic functions)
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Supplement II - Derivatives of Vector Functions
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Supplement II - Slopes and Tangents to Parametric Curves
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Section 3.7 (Rates of change in the natural and social sciences)
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Section 3.8 (Exponential growth and decay)
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Section 3.9 (Related rates)
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Section 3.10 (Linear approximations and differentials)
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Section 4.1 (Maximum and minimum values)
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Section 4.2 (The mean value theorem)
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Section 4.3 (How derivatives affect the shape of a graph)
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Section 4.4 (Indeterminate forms and L'Hospitale's rule)
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Section 4.7 (Optimization problems)
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Section 4.9 (Antiderivatives)
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Section 5.1 (Areas and distances)
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Section 5.2 (The definite integral)
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Section 5.3 (The fundamental theorem of calculus)
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Section 5.4 (The indefinite integral and the net change theorem)
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Section 5.5 (The substitution rule)
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