# Calc I Notes   © 2019, 2021, 2022, 2023, 2024, A2

Bring A Printed Copy to Class the Day the (Textbook Section) is on the Course Outline.
: 1. (Section 1.3-1.6) Limits connect-the-dots
2. (Section 2.3) Statement of Basic Derivative BLANK
3. (Section 2.3) Statements of Basic Derivative and Antiderivatives, CHEAT SHEET
4. (Section 2.1-2.5) Derivatives Connect-the-dots
4b. (Section 2.5) chain.rule
5. (Section 2.7) Pre Derivatives of Inverse Functions Review
6. (Section 3.3-3.5) How to Graph
7. (5.2) Definite Integrals Textbook Exercises
8. (Section 5.1-5.2) Casa Omar, Integration Connect-the-dots
9. (Section 5.3) Summation Connect-the-dots
10. (Section 5.1- 5.3) Antiderivatives Notes & Material
11. (Section 5.4) TI Calculator Calculus Functions Run as Graphing Features
12. (Section 5.4) TI Derivative, Definite Integral Program
TI Derivative, Integral Program Video
13. (Section 5.4) TI Programming Menu & Keys
14. (7.1) Area Between Curves
Instant Reference Material:
Graphs of "all" precalc & calc I functions     Summary of "all" functions
The Library of Functions     Symbols & words in gif format

Other Resources

 Equation solving calculator   https://www.symbolab.com/solver/equation-calculator/
 Graphing Tool   https://goodcalculators.com/graphing-calculator/
 Applications Calculator   https://goodcalculators.com/
 Derivative Calculator   https://www.derivative-calculator.net/
 Summation Calculator   https://goodcalculators.com/summation-calculator/
 Integral Calculator   https://www.integral-calculator.com/
 All Math Courses Calculators   https://www.emathhelp.net/calculators/
 Excel Easy - an Excel tutorial w/good notes + 7-day free trial   https://www.excel-easy.com/

This Stuff Looks Like:       Topics and Links
Samples Pre Calculus
Simplify:
a.) -6 [ -3 - 2(5 - 3)]
b.) 1 - cos2
Graph:
y = 3x + 4
Expand & Simplify:
log(100x2/z)
Explain:
a.) asymptote
b.) end behavior
Graph papers       Three Trig Planes Graph Paper

Calculator Reference 1 - Change Mode, Store Number, Evaluate Expression .gif
Calculator Reference 2 - Zooming Feature .htm
Calculator Reference 3 - Solve an Equation w/Solver .gif
Calculator Reference 4 - Derivatives and Numerical Integration

Laws of Exponents & Logs
Cheat Sheets of Trig Identities
Sheet 1 - Pythagorean Identities, Cofunctions, Odd/Even Functions
Sheet 2 - Sine, Cosine, & Tangent of the Sums & Differences
Sheet 3 - Double & Half Angle Formulas
Trig Stuff - Veronica's Bow Tie & All Students Take Calculus

Samples Limits
Show the algebra and calculus required to prove:

indeterminant, "So, What's A Fraction? & Zero(s) In Fractions"
Take the limit as x approaches ...
Limits connect-the-dots
SamplesContinuity
SamplesDerivatives & Their Applixcations, Including Graphing
Given y= x² +4x+4    State y' and y''

Sing the Derivatives Video
Derivatives connect-the-dots
DerivSin   -- full blown 4-page sketches ** Use this
Calculator Reference 4 - Derivatives and Numerical Integration
TI Derivative, Definite Integral Program
Parent Functions, Their Slope Functions, and Area Functions
Use a Pencil to Take a Derivative or Antiderivative of Sine & Cosine Functions
Derivative &Antiderivative Cheat Sheets-- derivatives, Trig and Hyperbolic Integrations
pdf format page 1 jpg   page 2 jpg   page 3 jpg   page 4 jpg
 Derivative Calculator at https://www.derivative-calculator.net/

Differentiation Rules

Implicit Differentiation

Related Rates

Arc Functions & Their Derivatives

Mean.Rolle.f'(x).f''(x).gsp - - interval, critical values, maximums, minimums, function emoji, Mean Value and Roll's Theorems, derivative tests
Function & Graph Analysis - instructions on how to find extremes and perdict the future
DerAnyFx.gsp, derivative/antiderivative plot of any function - any f(x): x, f(x), f'(x), f''(x), ∫, f(x)dx
First & Second Derivative Tests   derivativeTests.gsp
Function Emojis

Optimization Quiz Grading Rubric, suggestions, problem 4.3.1, problem 4.3.2
SamplesDifferentials

SamplesAntiderivatives, Definite Integrals, Areas
A CUMULATIVE FUNCTION
absement Sketchpad - absity, absement, displacement,velocity, acceleration, jolt, jounce, ... -- derivatives & antiderivatives of displacement
nth derivatives of displacement - image
absement definition - antiderivative of displacement, cumulative displacement
Antiderivatives Notes & Material pdf file

Intro2AntiDerivative.gsp
ReimannSums.gsp -- n=8 and 32 LEFT, RIGHT, MIDPOINT slide [a,b] and set [a,b]
ReimannSumNotes.pdf -- for taking notes

Simplify

TI Derivative, Definite Integral Program
Antiderivatives / Integration Page including:
Arithmetic -- Integration Tricks/Techniques
Use Basic Geometry Rather Than Calc to Complete the Integration
Consider Using a Function in y rather than a Function in x

JUSTdots.gsp -- Plots points on an antiderivative, no support pages
Justderivatives.gsp -- derivatives by definition, by tangent line, by traces of f', f'', f''', f''' (ideal for the trig cycle and for y=ex)
JUSTdotsWreview.gsp -- Plots points on an antiderivative, includes some support pages fX.f'X.f''X.intX.gsp  -- limits, emojis f' by tangent, trig memory, partitian, Reimann boxes, RLM =8, f(x) - g(x), input a, b, CUMULATIVE AREA probability fx, HISTORY sum to integral, INTEGRATION only, + c, FTI FTII, g(x), EXTRA integration by dots notes
Casa Omar -- Antiderivative connect-the-dots
 Integral Calculator at https://www.integral-calculator.com/
Take an Antiderivative by Substitution
Parent Functions, Their Slope Functions, and Area Functions

SamplesFundamental Theorem of Calculus
FTC Summary Pg 1     FTC Summary Pg 2     FTC1and2.jpg
42deranti11.jpg w/Newton & Leibnitz image
Statement of FTC I & II w/Newton & Leibnitz image
Why + C image
SamplesVelocity and Net Change
SamplesLogarithmic and Exponential Functions & Models
Exponential or Power Functions
exp2.xls
Program to "Find" e
A Bit about e, the base of the Natural Logs
Even More About e, the base of the Natural Logs
Linear vs Exponential Growth
Log Papers

SamplesDifferential Equations
SamplesNumerical Integration
SamplesHistory of Calculus

Some Early Analytic Geometry History image
Modern Evolution of Limit & Its Symbol image
Cartesian Plane & Math History web page
50+ Centuries of Computation in a 21st-Century Format
Ancient Egyptian Multiplication, Division, Root Extraction -- Computation

The Calculus Controversy -- Gotthegist, Published on 20 May 2010 -- Who Created Calculus? video
Other Resources
Equation solving calculator at https://www.symbolab.com/solver/equation-calculator/
Graphing Tool at https://goodcalculators.com/graphing-calculator/
Derivative Calculator at https://www.derivative-calculator.net/
Summation Calculator at https://goodcalculators.com/summation-calculator/
Integral Calculator at https://www.integral-calculator.com/
TI Derivative, Definite Integral Program. You write the TI84 program in your calculator.