-- Calc I Resources
CALCULUS ON VIDEO
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So, What's A Fraction? & Zero(s) In Fractions
web page,
pdf of web page,
video of web page
local video
key words: ratio, comparison. numerator compared to denominator, "number of pieces" /"number of pieces in one whole," fractions in symbols and pictures, complex fractions, fractions with fractions,
division by zero, fractions with zero(s), undefined, indeterminant, Special Limits, f(0) is 0/0.
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D(sin(x)) is cos(x)
cos.jpg)
Sketchpad,
video,
local video
First, a quick review of basic sine and cosine trig needed to prove Dx( sin(x) ) = cos(x). Proof by
animated derivative of the slope of the tangent using a movable tangent line, then trace w/four derivatives of sine.
Hand-written by-definition proof included. Presented from calc I class notes. Linked to a the downloadable SketchPad used in the video.
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Take A Derivative by Singing!
video
local video
Think product rule, quotient rule, and chain rule in words like "first," "second," "inner," and "outer" rather than in symbols like u(x) and g(x). Three 3 typical derivatives are taken and a series of longer chain rule problems.
Notes:
Languages & Title,
Songs & Title,
jpg of just the song
blank copy of problems,
completed copy of problems,
blank copy of Long Chain Rule problems,
completed Long Chain Rule problems, Links to:
Derivative web page,
Languages of the Math Classroom,
APEX Calculus by Hartman, Heinold, Siemers, Chalishajar, Bowen
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"The Lecture Version of fX.f'X.f''X.intX.gsp -- Limits, Derivatives, Antiderivatives, FTC I, FTC II Presented Dynamically & Analytically
Sketchpad,
web page,
pdf,
PAGE - Teachers' Manual,
The Languages of the Math Classroom
video,
local video
Key words: end behavior, take a limit, as x approaches c, where f(c) is continuous/not continuous, as x approaches infinity,
derivative by definition, by secant, as the slope of a tangent, mark c, f(c), f' (c), f ' ' (c), increasing/decreasing, zero,
trig derivatives memory trick, partition, differential, Reimann bBoxes, sums, area under a curve, negative areas, use g(x),
cumulative distribution, integral, FTC I, FTC II, "plus c"
- Absement and 'nth Derivatives of Displacement' Presented Dynamically & Analytically
Sketchpad,
pdf,
video,
local video,
web page
Absement is the total or cumulative displacement from an initial position, the antiderivative of displacement or distance. A multitude of derivatives/antiderivatives of
displacement are now collected under the title "nth Derivatives" -- old idea, new words. A free Geometer’s SketchPad may be used to model this mathematics including time, definitions of derivatives, tangent lines, partitions, Riemann sums, absement and cumulative functions, and absement plus c. Function emojis, and GSP features of slide, and trace, will be shown in the context of absement.
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"HHCC - Hand-Held Calculator Calculus" and Support Programs
Qu. What might a calc I teacher do to help students, who only have a TI-83, get easy access to its built-in calc functions as is easily managed on the TI-84?
Ans. Program the TI-83.
This video: runs sample problem(s), provides programing instructions, provides the program and other calc I resources, guides the viewer through the programming. Support materials are provided.
1st.
pdf
2nd.
PAGE - TI83-84 Calculus -- Derivative, Numerical Integration,
3rd.
SHEET - Calc Functions on the HOME SCREEN and in GRAPH,
4th.
SHEET - compute a definite integral in GRAPH,
5th.
SHEET - graph f(x) and derivatives,
6th.
SHEET - graph f(x) and antiderivatives,
7th.
PAGE - programming web page, including HHCC programs
8th.
CALCULATORing TOC
9th.
Calculus Functions from the HHCC Video
10th.
notes on the video
video,
local video
Key words: derivative, definite integral, graph, compute
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Precalc & Calc I Inside Front & Back Cover Quick Reference Material
video tour
local video tour
Key words: "stuff" one needs in precalc and calc to do the homework, recall material a student should understand but has probably just forgotten and wishes to quickly check. Topics include: laws of exponents & logs, trig identities, values of the 6 basic functions of the 30s, 60s, 45s in all 4 quadrants, tables of derivatives and integrals.
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