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8/28: In Person Learning Today! Live Stream and/or Zoom Links Are On The Help Page - FINALIZED

You are encouraged to use my office hours (Zoom or in person) for help on the homework. However, you may not ask questions over homework on the day that the assignment is due.

Do NOT assume that any assignment beyond today's is correct! I often change them the day of class. When you see the word FINALIZED in the first line, I've reviewed the assignment, checked the links, and I'm reasonably confident that it will not change.

Help With HawkesLearning is Available Here

Reading Assignment Due Before Class On 8/30. There is nothing to turn in for reading assignments, but the material could appear on quizzes. **Complete all of these readings before class on Friday!**

* Read the course introduction (syllabus) at this link. This document contains
information that you may need to know. Some of it could appear on
an online quiz.

* Enroll in our section of this course in HawkesLearning. You should have an access code.** If you have any trouble bring your access code to class tomorrow (Thursday)!**

* Read the Carthage Academic Dishonesty Guidelines. There is a link at the top of this page.

* Read this page on free tutoring opportunities.

* Check the blog (see the link on the left side of this page) for updates. You should check the blog every day. I will provide homework hints, comments on how our class went, and more!

* Read this one-page keys to success document.

Before you leave the classroom today, you will take this quiz. Do not take this quiz before I tell you to do so.

Homework Assignment Due Before Class On 8/30

* Take this brief background survey before class on Friday. (Yes, this is required, and you will receive credit for doing it!) You will need to log in to your Carthage
account.

Homework Assignment Which You Need to Complete Before 8:00 On 9/4.

* Do the first assignment in HawkesTeach over lines and solving quadratics. We will work on quadratic equations on Thursday. There is no reading in Hawkes on this material.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 8/30.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(0) Brief Introduction

(1) Definition of a Function

(2) Dissecting Function Notation

(3) Evaluating Functions

(4) Function Composition

(5) Watch this video produced by Arizona State University. It could increase your grade significantly! You could also listen to this radio program. You can read the article, or click on the blue "Listen" button on the left side of the page. You can read the text as well, but listening might be more effective.

* **While you are watching the videos or immediately after watching the videos, take this quiz. **You should take this quiz before our next class! This will count as an online quiz. After you take the quiz, the answers should appear on the screen. You should also receive an email confirmation so you can check your answers.

Optional Material

* If you need a review of the material we covered today on lines, you could re-watch today's class on the Help Page. The link to the Help Page is on the left side of this page. Click on the link to Live Stream Links. For the remainder of this course, you will watch videos over the material before class so we can focus on topics that you found difficult.

* The Khan Academy can be a great study tool. I don't anticipate assigning any problems from that site, but if you want to use the site as a study or review tool, please create an account on Khan Academy. You can use your Carthage e-mail (Google) or your Facebook account as a login for Khan. Let me know right away if you have any difficulties. **Then add me as a Coach.** My coach ID is my e-mail address (my Carthage address with msnavely as the name). The class code is 5PDW2J. You do not need to create an account to view the optional videos.

* Here is a Khan Academy video on the point slope form.

* Here is a Khan Academy video using both the point slope form and the slope intercept form.

* Here is a Khan Academy video on factoring quadratic expressions, parts one and two.

* Here is a Khan Academy video on expanding expressions; here is another.

Today's VQ for class use - take the quiz at the link above, not here!

8/29: Class begins at 8:00 today, but we will often start class at 8:30 on Thursdays. - FINALIZED

Today's in-class work will an algebra review and will include an in-class quiz. Homework over this material is included in the assignment given yesterday.

Optional Material

* Here is a Khan Academy video on factoring quadratic expressions, parts one and two.

* Here is a Khan Academy video on expanding expressions; here is another.

8/30: In Person Learning Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/6.

* Read this handout on functions. It's a little silly, but it might help clarify some concepts.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Do the problems on this worksheet. Print the worksheet and write your solutions neatly on that page. Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Fill out this homework response form after you have completed the assignment. This will count as an online quiz.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/4.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Linear Equations and Inequalities

(2) Solving Quadratic Inequalities

(3) An Example

* While you are watching the videos or immediately after watching the videos, take this quiz. You should take this quiz before our next class! This will count as an online quiz. After you take the quiz, the answers should appear on the screen. You should also receive an email confirmation so you can check your answers.

Optional Material

* Here is a video on evaluating composite function, and here is another video on the same topic.

Optional: Sign up for your free MAA membership at this link.

Today's VQ for class use - take the quiz at the link above, not here!

9/2: Labor Day - No Class Today

9/4: In Person Learning Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/9.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/6.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Function Diagrams

(2) First Examples

(3) More Examples

(4) Products and Function Composition

* While you are watching the videos or immediately after watching the videos, take this quiz. You should take this quiz before our next class! This will count as an online quiz. After you take the quiz, the answers should appear on the screen. You should also receive an email confirmation so you can check your answers.

Optional Assignment(s)

* A video over linear equations; one over linear inequalities.

* Here is a Khan Academy video on solving quadratic inequalities, and here is another.

9/5: Last day to add or drop a course. - FINALIZED

CLASS WILL BEGIN AT 8:30 TODAY!

Quiz today over the material that we TALKED ABOUT IN CLASS on 8/28 (course expectation), 8/29 (Lines and Equations), and 8/30 (Functions). The videos assigned on 8/30 are NOT on this quiz, nor is the material we talked about in class on Wednesday.

I know this sounds silly, but please use the restroom before class.

This is a quiz. You may use a calculator, paper, and a writing utensil. That's all! NO PHONES ARE PERMITTED ON ANY QUIZ OR EXAM! If I see your phone at any time before you turn in your quiz, you will receive a 0 on this quiz. No excuses, no exceptions! Place your phone in a zippered pocket in your backpack and zip it shut or place your phone on the table at the front of the classroom. If you must use the restroom during the quiz, bring your phone to the front of the room and place it on the table before you leave the room.

During the quiz, you are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Norse code (used to communicate with Vikings), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use your notes, your text, any text, HawkesLearn, Google, WolframAlpha, anything on our course website, or any other internet resource that I've omitted.

9/6: In Person Learning Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/11.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes. You could also take a look at the "Learn" portion of our next assignment as well - there are some relevant example in there!

* Do the exercises on page 17 in the notes over function diagrams. **Write your answers on a separate piece of paper, NOT on the notes!**

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/9.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Defining the Trigonometric Functions

(2) Triangle Trigonometry

(3) Special Angles

(4) Finding Exact Values for Trigonometric Functions, part I

(5) Finding
Exact Values for Trigonometric Functions, part II

(6) Properties of Exponential Functions

Optional Material

* A video specifically on converting degrees to radians.

Today's VQ for class use - take the quiz at the link above, not here!

9/9: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/13.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class.

* Fill out this homework response form after you have complete the homework assignment.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/11.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Properties of the Logarithm Functions

(2) Equations Involving Exponential and Logarithm Functions

(3) The Arcsine Function, written \(\arcsin x\)

(4) The Arctangent Function, written \(\arctan x\)

(5) Finding Exact Values

(6) Function Composition Examples

(7) Examples With Variables

* The HawkesLearning assignment over these videos is officially assigned after our next class, but you should start it now so you can ask questions.

Optional material from the Khan Academy

* Here is another video on quadratic inequalities.

9/11: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/16.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 9/13.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Distance

(2) Definition of a Limit

(3) The First Example

(4) One-Sided Limits

(5) Conjecturing Values for Limits

(6) One More Example Involving a Graph - here is the graph of the function I used in the video

Optional Assignment(s)

* Here is a video on estimating limits from a graph.

9/12: Quiz today over the material covered on 9/4 (Inequalities), 9/6 (Function Diagrams), and 9/9 (Trig and Exponential Functions). The quiz will begin at 8:30. - FINALIZED

9/13: In-Person Instruction. - FINALIZED - UPDATED ON 9/11

Homework Assignment Which You Need to Complete Before 8:00 On 9/18.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Do the problems on this worksheet. Print the worksheet and write your solutions neatly on that page. Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/16.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Introduction to Derivatives

(2) The Definition of the Derivative

(3) The Basic Derivatives You Need to Memorize

(4) The Sum Rule

(5) The Product Rule

(6) The Function Composition Rule

(7) Examples of the Chain Rule

(8) The Quotient Rule

* While you are watching the videos or immediately after watching the videos, take this quiz. You should take this quiz before our next class!This will count as an online quiz. After you take the quiz, the answers should appear on the screen. You should also receive an email confirmation so you can check your answers.

Optional Material

* There are many examples online, but none use function diagrams.

Today's VQ for class use - take the quiz at the link above, not here!

9/16: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/20.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class.

* Do the problems on page 28 of the notes involving derivatives and function diagrams.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/18.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The \(k/0\) case

(2) Limits as \(x\rightarrow \infty\)

(3) Rational Functions

(4) Trigonometric Functions, Exponential Functions, and Polynomials

(5) Bonus Examples

(6) Even More Bonus Examples

* The HawkesLearning assignment over these videos is officially assigned after our next class, but you should start it now so you can ask questions.

Optional material from the Khan Academy

* Nothing comes to mind.

9/18: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/23.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 9/20.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Finding a Slope Using a Limit

(2) Finding a Derivative Using a Limit

(3) The Tangent Line to a Tangent Line

(4) A Polynomial Example

(5) A Rational Example

Optional Assignment(s)

* A video on the definition of the derivative, and an example.

9/19 : Class begins at 8:30. Quiz today over the material covered on 9/13 (Logs and Inverse Trig Functions), 9/15 (Limits), and 9/18 (Derivatives). - FINALIZED

9/20: In-Person Instruction Today! - FINALIZED - UPDATED 9/18

Homework Assignment Which You Need to Complete Before 8:00 On 9/25.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Do the problems on this worksheet. Print the worksheet and write your solutions neatly on that page. Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/23.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The Sum Rule

(2) The Product Rule

(3) The Triple Product Rule

(4) Examples

(5) The Quotient Rule

(6) Examples

(7) One More Example

Optional Material

* Many videos. Here is a page with product rule videos, and one with quotient rule videos.

9/23: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/27.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/25.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The Derivative of \(f(x)=a^x\)

(2) Can \((a^x)'=a^x\)?

(3) Examples I

(4) Examples II

(5) The Second Derivative

(6) Higher Order Derivatives

(7) Derivatives on the Computer

* The HawkesLearning assignment over these videos is officially assigned after our next class, but you should start it now so you can ask questions.

Optional material from the Khan Academy

* Here is a video on the second derivative, and one on the derivative of the exponential function.

9/25: In Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 9/30.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 9/27.

**Some of the videos below (for the rest of the semester!) were recorded in the spring of 2020. Ignore any references to this being a "Thursday class" - our lab was on Thursday at that time, and we had to cover new material on Thursdays because we lost an entire week due to cancelled classes. Special thanks to Wildwood Presbyterian Church in Grayslake, Illinois, for allowing me to use a classroom to record these videos.**

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The Derivative of \(f(x)=\sin x\)

(2) The Handholding Theorem The geometric proof of the limit in this video.

(3) Finishing the Proof

(4) The Derivative of \(f(x)=\cos x\)

(5) The Rest of the Trigonometric Derivatives

(6) Examples

Optional Assignment(s)

* Here is a video involving the trigonometric functions. There are many others.

9/26: CLASS BEGINS AT 8:00! Exam 1 over the material covered from 8/28-9/23 (Sum rule, product rule, quotient rule). Any question asked in homework, on quizzes, on video quizzes, or covered in the notes could appear on the exam. - FINALIZED

You are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Force code (used to communicate with Jedi knights), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use your notes, your text, any text, HawkesLearning, Google, WolframAlpha, WolframBeta, anything on our course website, or any other internet resource that I've omitted.

I will provide a calculator for you to use. No phones!

*** Fill out this exam reflection before class on Monday.**

9/27: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/2.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 9/30.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The Chain Rule - Some Intuition

(2) The Formal Chain Rule

(3) The Power Rule

(4) Functions of the Form \(g(x)=e^{(f(x))}\)

(5) Functions of the Form \(s(x)=\sin(f(x))\) and \(c(x)=\cos(f(x))\)

(6) More Examples

Optional Material

* Here is a video on the chain rule.

*
I highly recommend the exercise entitled Practice: Identifying Composite Functions.

9/30: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/4.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/2.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) What is an implicit function? (There is instruction on how to take notes. Maybe a good reminder?)

(2) The chain rule revisited

(3) Implicit differentiation on a circle

(4) The first example

(5) The second example

Optional material from the Khan Academy

* Here is an additional 8-minute video on implicit differentiation.

* A video example on computing a derivative using implicit differentiation. (About 5 minutes)

* A video example on finding the slope of a tangent line using implicit differentiation. (About 5 1/2 minutes)

10/2: In-Person Instruction Today! - . FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/7.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 10/4.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The derivative of ln x and more

(2) The derivative of ln(f(x))

(3) The derivative of the arcsine function

(4) Examples involving arcsin(x) and arctan(x)

(5) What to do with x^x and similar functions

Optional Assignment(s)

* The derivative of the arcsine function.

* The derivative of the arctangent function.

* A video on choosing which rule to use. Highly recommended!

10/3 : Quiz over the material covered on 9/25 (exponentials), 9/27 (trig derivatives), and 9/30 (chain rule). As usual, the quiz will begin at 8:30. - FINALIZED

10/4: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/9.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/7.

No additional videos today!

Optional Material

* Any videos on finding derivatives could be used as a review.

10/7: In-Person Instruction Today! - We will have a differentiation workshop today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/11.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/9.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Introduction to Falling Object Problems (Ignore references to Thursday class - this video was made a while ago.)

(2) First example of a falling object problem

(3) Another example

(4) One last example (Of course, you can also ask questions in office hours or in class, in addition to the blog as mentioned in the video)

Optional material from the Khan Academy

* I didn't find the material on the Khan Academy helpful on this topic.

10/9: In Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/14.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 10/11.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Problem solving strategies and related rates

(2) The sliding ladder problem

(3) A leaky conical tank

Optional Assignment(s)

* Introduction to related rates

* A problem involving a triangle

* The sliding ladder problem

* Water pouring into a cone

10/10: Quiz over the material covered on 10/2 (implicit functions), 10/4 (derivatives of logarithms and inverse trig functions), and 10/7 (derivatives). The quiz will begin at 8:30. - FINALIZED

10/11: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/16.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Do the problems on this worksheet. **Print the worksheet and write your solutions neatly on that page.** Turn in this assignment at the beginning of class on the due date. Assignments turned in after 8:00 will be considered late. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/14.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

These videos were recorded a while ago. Ignore any references to things that don't seem relevant to our class.

(1) Linear Approximation

(2) An Example Involving an Exponential

(3) A Final Example, and Differentials (The differential of \(f(x):= x + \sin x\) is \(df = (1+\cos x)\, dx\). Part of this is invisible due to the glare on the board.)

Optional Material

* Here is an example that involves a rational function.

10/14: In-Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/21.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/16.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

These videos were recorded a while ago. Ignore any references to things that don't seem relevant to our class.

(1) Introduction to Extreme Values

(2) Definitions

(3) Two Examples

(4) An Example with a More Challenging Derivative

(5) An Example With a Cusp

Optional material from the Khan Academy

* Here is a video on finding extreme values.

* Another really good example.

10/16: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/23.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 10/21.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Rolle's Theorem and the MVT

(2) A Proof and an Example (this video is a little longer than most)

(3) An Example Revisited - Finding Where a Function Is Increasing - You can stop this video at 3:26 - maximum and minimum values are covered in the next section, but you can also continue to the end to see what's coming up!

Optional Assignment(s)

* A video showing how to find where a function is increasing/decreasing.

* Another example of finding where a function is increasing/decreasing.

10/17: NO CLASS - FALL BREAK

10/18: NO CLASS - FALL BREAK

10/21: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/25.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/23.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(0) Watch the rest of the last video in the previous section!

(1) Finding Maximum and Minimum Values

(2) Introduction to the Second Derivative

(3) An Example Using the Second Derivative to Determine Concavity

(4) An Improved Second Derivative Test

(5) The Last Computational Example

Optional material from the Khan Academy

* How to find inflection points from a graph.

* Finding inflection points.

* Mistakes when finding inflection points: one common mistake, and another mistake.

10/23: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/28.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 10/25.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Introduction to L'Hopital's Rule

(2) Two Related Examples

(3) The \(1^\infty\) Case

(4) The \(0^0\) Case

(5) The \(\infty-\infty\) Case

Optional Assignment(s)

* There are many examples online. Here is one in the 0/0 case. (You need to follow my restrictiopns on 0/0 - not his! Never say that something equals 0/0!)

* A limit as x approaches infinity

* A challenging example

10/24: Quiz today over the material covered on 10/9 (Falling Objects), 10/11 (Related Rates), 10/14 (Linear Approximation), 10/16 (Extreme Values), and 10/21 (Increasing/Decreasing). As usual, the quiz begins at 8:30. - FINALIZED

10/25: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 10/30.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Do the problems on this worksheet. **Print the worksheet and write your solutions neatly on that page.** Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/28.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Curve Sketching - Our First Example

(2) Curve Sketching - An Unusual Example

(3) Finding the Information Ourselves

(4) Factoring Helps!

(5) An Example With Asymptotes

Optional Material

* This is a 20 minute video, but it shows curve sketching start-to-finish.

* An example involving a logarithm function, but it's 25 minutes long.

10/28: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/1.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class. **Read Wednesday's Learn bullet for more instruction on Curve Sketching!**

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 10/30.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) How Newton's Method Works

(2) The Formula for Newton's Method

(3) Newton's Method as a Process

(4) A Calculator Example

(5) Making a Good Guess I

(6) Making a Good Guess II

(7) The Quadratic Formula and its Relatives

Today's Mathematica File for those who have Mathematica, or those who use Mathematica Online.

Optional material from the Khan Academy

* Here is one video from another source. Not much on the Khan Academy.

* Some pictures of comples Newton's Method in action: n=3 and n=5.

10/30: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/4.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 11/1.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Introduction to Optimization Problems

(2) The First Example Revisited

(3) A Different Constraint on a Rectangle

(4) A Curve Defines a Rectangle

(5) Making a Can

(6) Making a Square and a Circle

Optional Assignment(s)

* Here is an very good sum of squares problem.

* Maximizing profit.

10/31: Exam 2 over the material covered from 9/25 (Derivatives of Exponentials) to 10/28 (Curve Sketching). - FINALIZED

This exam should take you less than an hour, but you have the entire class period (8:00-9:40) to take it. Exams will be collected at 9:40.

You are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Course code (used to communicate with college registrars), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use your notes, your text, any text, HawkesLearning, YourMathLab, AnyoneElsesMathLab, Google, WolframAlpha, anything on our course website (except of course the link to the exam!), or any other internet resource that I've omitted.

I will provide a calculator for you to use. No phones!

11/1: In Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/6.

* Do the HawkesTeach Assignment over today's material. There is a reading assignment in Hawkes.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 11/4.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) What is an Antiderivative?

(2) An Important Public Service Announcement

(3) Computing and Verifying Antiderivatives

(4) Initial Conditions

(5) Rules for Antiderivatives

(6) Basic Examples

(7) Some Important Examples

(8) A Recurring Example, part I

Optional Material

* You could work through this entire series of lessons on the basic rules.

* This lesson discusses doing a little algebra before finding an antiderivative.

* Here is a lesson on trig and exponential functions.

* This lesson explains the difference between \(\ln x\) and \(\ln |x|\).

11/4: In Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/8.

* Do the HawkesLearning assignment over today's material. You watched the videos to prepare for today's class.

* Do the problems on this worksheet. Print the worksheet and write your solutions neatly on that page. Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 11/6.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Introduction to Signed Area

(2) Signed Area From Functions

(3) Accumulation Functions

(4) A Recurring Example, part II

Optional material from the Khan Academy

* Nothing available for this lesson.

11/6: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/11.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 11/8.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

Today's Mathematica File, and for Mathematica Online.
For those of you without Mathematica, this site can help you check your work on Riemann sums.

(1) What if We Can't Use Geometry?

(2) A Second Example With Help From Mathematica

(3) An Example Using Data

(4) Riemann Sums

(5) The Definite Integral

(6) Properties of Integrals

(7) A Recurring Example, part III

Optional Assignment(s)

* Here is a video that uses midpoints. I don't use midpoints, but it's a good example of using rectangles.

* An example that uses a table of values rather than a function.

11/7: Quiz today over the material covered from 10/30 (Newton's Method), 11/1 (Optimization), and 11/4 (Antiderivatives). - FINALIZED

11/8: In-Person Instruction Today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/13.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 11/11.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) The Fundamental Theorem of Calculus

(2) Examples Using the FTC

(3) The Fundamental Theorem of Calculus, Second Form

(4) Examples Using the Second Form

(5) More Examples

Optional Material

* This video deals with the derivative of an integral, as does this one.

* An example where you need to do some algebra first, and one involving a logarithm function.

11/11: In-Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/15.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 11/13.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Reversing the Chain Rule

(2) Two More Trig Antiderivatives

(3) Four Examples

(4) Three More Examples

(5) One Example, Two Answers

Optional material

* Lots of good examples out there. Here is a basic example.

* Here is an example involving logarithms.

11/13: In-Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/18.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 11/15.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Substitutions and Definite Integrals

(2) Examples

(3) One Example, Two Substitutions

(4) Area Between Two Curves

(5) Two More Examples

(6) The Recurring Function, part IV

Optional Assignment(s)

* Here is one video with some basic example.

* An example with an exponential function.

11/14 : Quiz over the material covered on 11/6 (Signed Area), 11/8 (Riemann Sums) and 11/11 (Fundamental Theorem of Calculus). - FINALIZED

11/15: In Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/20.

* Do the problems on this worksheet. Print the worksheet and write your solutions neatly on that page. Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 11/18.

None!

11/18: In Person Instruction - We will have an integration workshop today! - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 11/22.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 11/20.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

This online demonstration shows how to visualize the solids we're studying today in some cases.

These videos were recorded a while back. Ignore any references to things that don't seem relevant to our class.

(1) The Amazing Adding Machine

(2) Motivating the Method

(3) Our First Examples

(4) Slicing the Can Vertically

(5) Examples

(6) More Examples

Optional material from the Khan Academy

* Here is an example with semi-circular cross-sections.

* Here is an example with triangular cross-sections.

11/20: In-Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 12/2.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 11/22.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

Here are the formulas for volumes of solids of revolution, and here is the Mathematica code for visualizing the solids. I also found some code for visualizing solids of revolution.

(1) Disks and Washers

(2) The First Example

(3) Examining the Region

(4) Rotation about y=-2

(5) Rotation About x=0

(6) Rotation About y=3

Optional Assignment(s)

* Here is an example involving \(y=x^2\).

* Here is an example about the \(y\)-axis.

* A generalization of the disk method.

11/21 : Quiz over the material covered on 11/13 (Substitutions), 11/15 (Substitutions on Definite Integrals) and 11/18 (Integration). - FINALIZED

11/22: In-Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 12/4.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 12/2.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) When Disks Aren't A Great Choice

(2) The Shell Method

(3) An Easier Way!

(4) One Region, Multiple Axes

Optional Material

* Here is an example involving shells and \(y=x^{1/3}\).

* An example with an upper and a lower function.

11/25: No Class - Thanksgiving Break

11/27: No Class - Thanksgiving Break

11/28 : No Class - Thanksgiving Break

11/29: No Class - Thanksgiving Break

12/2: In Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 12/9. NOTE EXTENDED DUE DATE!

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 12/6. NOTE EXTENDED DUE DATE!

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1) Arc Length

(2) When Everything Works Great

(3) Surfaces of Revolution

(4) The Surface Area of a Cone

(5) Another Example

Optional material from the Khan Academy

* An arc length example.

12/4: In-Person Instruction - Exam Review Day. This class is optional. All I will be doing is taking questions from you. I will live stream the session as usual. - FINALIZED

12/5 : Exam 3 over the material covered from 10/30 (Newton's Method) to 12/2 (Solids of Revolution). Arc Length is not on this exam. - FINALIZED

This is an exam, and you should not do anything that you would not do if you were taking the quiz in class in person. You may use the calculator I provide, paper, and a writing utensil. That's all! **Make sure that your phones are securely stowed in a zippered compartment in your backpack or placed on the table at the front of the room.**

You are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Source code (used to communicate with computer programmers), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use your notes, your text, any text, HawkesLearning, YourMathLab, AnyoneElsesMathLab, Google, WolframAlpha, anything on our course website (except of course the link to the exam!), or any other internet resource that I've omitted.
** That certainly includes communicating with other class members during the exam!**

12/6: In-Person Instruction - FINALIZED

Homework Assignment Which You Need to Complete Before 8:00 On 12/11.

* Check the blog every day for new entries.

12/9: In-Person Instruction - Exam Review Day. This class is optional. All I will be doing is taking questions from you. I will live stream the session as usual. - FINALIZED

12/10: Study Day - Classes do not meet.

12/11: Final Exams

Our final exam is today from 8:00-10:00. This cumulative final exam covers the entire course, including arc length and surface area.

This is an exam, and you should not do anything that you would not do if you were taking the quiz in class in person. You may use the calculator I provide, paper, and a writing utensil. That's all! **Make sure that your phones are securely stowed in a zippered compartment in your backpack or placed on the table at the front of the room.**

You are not permitted to communicate with any human being by any means, including but not limited to, talking, phone conversations, text messages, email messages, hand signals, smoke signals, semaphore, Morse code, Horse code (used to communicate with equestrians), social media, antisocial media, or any other means that I've omitted. You are not permitted to use any internet resource whatsoever. You are not permitted to use your notes, your text, any text, HawkesLearning, YourMathLab, AnyoneElsesMathLab, Google, WolframAlpha, anything on our course website (except of course the link to the exam!), or any other internet resource that I've omitted.
** That certainly includes communicating with other class members during the exam!**

12/12: Final Exams

12/13 : Final Exams

Monday Template

Homework Assignment Which You Need to Complete Before 8:00 On 12/25.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 12/23.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1)

* There is an optional video assignment in HawkesLearning over this material.

Optional material from the Khan Academy

* Here

Today's VQ for class use

Wednesday Template

Homework Assignment Which You Need to Complete Before 8:00 On 12/26.

* Do the HawkesTeach Assignment over today's material.

* Check the blog every day for new entries.

Required Assignment To Do Before Class on 12/23.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1)

Optional Assignment(s)

* A

Today's VQ for class use

Friday Template

Homework Assignment Which You Need to Complete Before 8:00 On 12/24.

* Do the problems on this worksheet. Print the worksheet and write your solutions neatly on that page. Turn in this assignment at the beginning of class on the due date. You can turn in your homework by placing your paper on the desk at the front of the room at the beginning of class or by scanning in the document and sending a copy to me by email. I prefer pdf format, but will accept an occasional image (jpg, gif, NOT heic) in a pinch.

* Check the blog every day for new entries.

Required Assignment to Prepare You For Class, To Be Completed Before Class On 12/22.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1)

Optional Material

* Here

Today's VQ for class use - take the quiz at the link above, not here!