Calculus - Limits

Intro to Calculus/Calc 1 (depending on how far it goes).
V 0.0

Feel free to copy, add to, edit, and redistribute this curricula.

Note that sources stacked consecutively, with no topic separating them, are different sources which explain the same material and it is up to the learner to decide which resource(s) to use and how in depth they desire to go. It is not intended every resource be used.

Brackets after a source indicate the medium, with a time indicating a video of that runtime, and a wordcount indicating an article of that length.


Comprehensive Resources:
These resources generally cover the entire subject of Calculus, and their appropriate sections will be linked in this curriculum. If a student finds these satisfactory on their own, or wishes to reference them when they are not linked, their directories will be linked here.

-Paul's Online Notes  - - - - - - - - - - - - - - - - - - - - http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

-Khan Academy   - - - - - - - - - - - - - - - - - - - - - - - https://www.khanacademy.org/math/ap-calculus-ab

-Pheng Kim Ving "CALCULUS OF ONE REAL VARIABLE; A TUTORIAL" - http://www.phengkimving.com/calc_of_one_real_var/contents.htm#chap_01
()


Overview of calculus:

MySecretMathTutor                "Introduction to calculus"           [4:10]     https://www.youtube.com/watch?v=UukVP7Mg3TU
Socratica                        "What is Calculus? (Mathematics)     [9:13]     https://www.youtube.com/watch?v=w3GV9pumczQ
Tibees                           "Calculus explained through a story" [14:51]    https://www.youtube.com/watch?v=PWTdiAYQ2Cs
MIT OpenCourseWare               "Big Picture of Calculus"            [37:46]    https://www.youtube.com/watch?v=UcWsDwg1XwM
Simple English Wikipedia Page    "Caclulus"                     [~1800 words]    https://simple.wikipedia.org/wiki/Calculus
Full Wikipedia Page              "Caclulus"                     [~6000 words]    https://en.wikipedia.org/wiki/Calculus


Prerequisites:
-
-


1. Limits:

>1.1 Intro to limits:

Big picture:
Andrew Incognito  " Dr. Incognito teaches math- introduction to limits" [18:00]   https://youtu.be/JroM3rmBH50
Khan Academy      "Limits intro" [11:31]                                          https://youtu.be/riXcZT2ICjA
mathisfun         "Limits (An Introduction)" [861 words]                          https://www.mathsisfun.com/calculus/limits.html

a. Average Velocity/Secant Lines of functions
Khan Academy  "Secant lines and average rates of change" [5:16]            https://youtu.be/0z_MDIWMBwU
PatrickJMT    "Secant Line: Finding an Equation for a Secant Line" [5:04]  https://www.youtube.com/watch?v=wLtBPvMv6kw

b. Instantaneous Velocity/Slope of Tangent line
Khan Academy                 "Instantaneous Velocity" [4:37]                   https://youtu.be/pfTTHx9kCHk
Paul's Online Notes          "Tangent Lines and Rates of Change" [3843 words]  http://tutorial.math.lamar.edu/Classes/CalcI/Tangents_Rates.aspx
Jake Binnema (supplementary) "Secant Slope Calculator" [interactive app]       https://www.geogebra.org/m/XhJsJDtc

Resources that cover multiple of the above topics:
Socratica (a,b) "The Tangent Line and the Derivative (Calculus)" [11:38] - https://www.youtube.com/watch?v=O_cwTAfjgAQ

Practice Problems for 'Intro to Limits':
(a) https://www.khanacademy.org/science/ap-physics-1/ap-one-dimensional-motion/instantaneous-velocity-and-speed/e/average-velocity-and-average-speed-exercise
(b) http://tutorial.math.lamar.edu/Problems/CalcI/Tangents_Rates.aspx


>1.2 Basic Definition of limits:
a. Finding Limits from graph
MathBootCamps "Finding Limits Using a Graph" [547 words] - https://www.mathbootcamps.com/finding-limits-using-a-graph/
Brian McLogan "Evaluate all the limits from a given graph" [5:33] - https://youtu.be/3YFuOwcog6k
Pete Surgent "Find Limits Given a Graph" [6:12] - https://youtu.be/aVcqrDFcaCA
The Organic Chemistry Tutor "How to Evaluate Limits From a Graph" [11:31] - https://youtu.be/7Q2HwTHcxA0

b. One-sided limits
Wikipedia "One-sided limit" (ignore past 'examples')[352 words] - https://en.wikipedia.org/wiki/One-sided_limit
mathwarehouse "How to Solve One Sided Limits" [382 words](includes practice) - https://www.mathwarehouse.com/calculus/limits/limits-one-sided.php
Phem Kim Ving "One-Sided Limits" [827 words](includes practice) - http://www.phengkimving.com/calc_of_one_real_var/01_lim_and_continuity/01_01_lim/01_01_04_one_sided_lim.htm
Paul's Online Notes "One-Sided Limits" [1981 words] - http://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx

Practice Problems
(a, b) http://tutorial.math.lamar.edu/Problems/CalcI/OneSidedLimits.aspx


>1.3 Computing limits:
a. Standard Methods
Dummies "How to Find the Limit of a Function Algebraically" [912 words] - https://www.dummies.com/education/math/calculus/how-to-find-the-limit-of-a-function-algebraically/
Caclulus I, By Andrew Incognito "Computing Limits" [1221 words](includes practice) -  https://ximera.osu.edu/incognito-calc1/calcBook/calcBook/limitsAnalytically/limitsAnalytically
George Brown College "Computing Limits: Part II" [~1000 words](includes practice) - https://www.georgebrown.ca/uploadedFiles/TLC/_documents/Computing%20Limits%20Part%202.pdf
Paul's Online Notes "Computing Limits" [2543 words] - http://tutorial.math.lamar.edu/Classes/CalcI/ComputingLimits.aspx


b. Squeeze Theorem
Caclulus I, By Andrew Incognito "Squeeze Theorem" [381 words](includes practice) -  https://ximera.osu.edu/incognito-calc1/calcBook/calcBook/squeezeTheorem/squeezeTheorem
Math Warehouse "What is the Squeeze Theorem" [633 words] - https://www.mathwarehouse.com/calculus/limits/what-is-the-squeeze-theorem.php
Wikipedia "Squeeze theorem" (ignore 'Statement for series', 'proof' optional)[text, short] - https://en.wikipedia.org/wiki/Squeeze_theorem
Khan Academy "Squeeze theorem intro" [7:11] - https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-8/v/squeeze-sandwich-theorem


Resources that cover multiple of the above topics:
Paul's Online Notes (a,b) "Computing Limits" [2543 words]  http://tutorial.math.lamar.edu/Classes/CalcI/ComputingLimits.aspx

Practice Problems
Paul's Online Notes (a,b) "Computing Limits - Practice Problems" [15 problems]  http://tutorial.math.lamar.edu/Problems/CalcI/ComputingLimits.aspx
Khan Academy (b) "Squeeze theorem" [Complete 4 problems correctly]  https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-8/e/squeeze-theorem


>1.4 Infinite limits:

Phem Kim Ving "Limits at Infinity and Infinite Limits" [~1000 words] (includes practice) - http://www.phengkimving.com/calc_of_one_real_var/01_lim_and_continuity/01_01_lim/01_01_05_lim_at_inf_and_inf_lim.htm
Paul's Online Notes "Infinite Limits" [3000 words] - http://tutorial.math.lamar.edu/Classes/CalcI/InfiniteLimits.aspx

Practice Problems


>1.5 Limits at Infinity:
Phem Kim Ving "Limits at Infinity and Infinite Limits" [~1000 words] (includes practice) - http://www.phengkimving.com/calc_of_one_real_var/01_lim_and_continuity/01_01_lim/01_01_05_lim_at_inf_and_inf_lim.htm
Paul's Online Notes "Limits at Infinity, Part 1" [2412 words] - http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx
Paul's Online Notes "Limits at Infinity, Part 2" [2529 words] - http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityII.aspx
Practice Problems


>1.6 Continuity:
Phem Vim King "Continuity" [~400 words] (includes practice) - http://www.phengkimving.com/calc_of_one_real_var/01_lim_and_continuity/01_02_continuity/01_02_01_continuity.htm

Practice Problems
(Two problems on rational functions and vertical asymptotes) https://www.geogebra.org/m/nGfXYFPc


>1.7 Precise Definition of limits:
patrickJMT "Precise Definition of a Limit - Understanding the Definition" [11:06] - https://www.youtube.com/watch?v=G0ax2x2_Em0
-Brief text and applet demonstrating how limits are defined. https://www.geogebra.org/m/Jf7rP6uK
-