# Calc I Notes   © 2019, 2021 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
5. (Section 2.7) Pre Derivatives of Inverse Functions Review
6A. (Section 5.1-5.2) Casa Omar, Integration Connect-the-dots
6B. (Section 5.3) Summation Connect-the-dots
7. (Section 5.4) TI Calculator Calculus Functions Run as Graphing Features
8. (Section 5.4) TI Derivative, Definite Integral Program
9. (Section 5.4) TI Programming Menu & Keys
Internet Calculators
 Derivative Calculator at https://www.derivative-calculator.net/

 Integral Calculator at https://www.integral-calculator.com/
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
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:

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''

Differentiation Rules
Derivatives
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/

Implicit Differentiation

Related Rates

Arc Functions & Their Derivatives
First & Second Derivative Tests use DerAnyFx, use 3 - any f(x): x, f(x), f'(x), f''(x)

SamplesDifferentials
optimization
SamplesAntiderivatives, Antiderivatives by Substitution Rule, Definite Integrals, Areas
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
Casa Omar -- Antiderivative connect-the-dots
 Integral Calculator at https://www.integral-calculator.com/
Arithmetic -- Integration Tricks/Techniques
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
SamplesVelocity and Net Change
SamplesInverse Functions
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

The Calculus Controversy -- gotthegist, Published on 20 May 2010
and other youtube math videos
50+ Centuries of Computation in a 21st-Century Format
Ancient Egyptian Multiplication, Division, Root Extraction -- Computation
Other Resources
Calculators:
TI Derivative, Definite Integral Program. You write the TI84 program in your calculator.
Derivative Calculator at https://www.derivative-calculator.net/
Integral Calculator at https://www.integral-calculator.com/

Student-Suggested Links, Spring 2021
 Neil McPherson · Professor Leonard Calc I Playlist Kyle Leone · Differentials · integrals · Integration by substitution Sri Satya (Meena) Vellala · integrals · anti derivatives Isabel Sananes · related rates problem Kush Patel · Riemann sums

Lectures & Videos:
khanacademy.org/ (Doesn't use Internet Explorer. Use another browser.)
mathispower4u.com/calculus.php
myopenmath.com/, videos and problems w/answers
calcvids.org/vids/

 © 2020, 2021, Agnes Azzolino,   www.mathnstuff.com/math/calc/calc1.htm