Lecture 35, 36, Review 1, and Review 2 Videos

Hi all,

Here is the video for Lecture 35.

Here is the video for Lecture 36.

Here is the video for Review 1.

Here is the video for Review 2.

Sorry for the late upload, I only recently saw that these were uploaded.


Best,

Branden

Lecture Notes 41 (Friday 12/11) FINAL DAY OF NOTES AND REVIEW

Hi all,

Here are the notes for the 12-1 Lecture.

I did not go to the 9-10. but will be posting videos of all the Review lectures soon.

Today the Professor covered integration by substitution, more information on the differential dx notation, and a hard epsilon delta proof.

Your final is either exactly a week or a little less than a week away, so be sure to study and prepare adequately. Do not forget to get enough sleep and eat well!

It has been a pleasure running the blog for this Math 1A Course.


Happy Studying.

Branden

Lecture Notes 40 (Wednesday 12/9)

Hi all,

Here are the 9-10 Lecture Notes.

I will post videos for the 12-1 Lecture soon as I have not been able to attend and take notes.

Today the Professor reviewed more about computing volumes with solids of revolution and Newton's Law of Cooling.


Best,

Branden

Lecture Notes 39 (Monday 12/9)

Hi all,

Here are the 9-10 Lecture notes.

I was not able to attend 12-1 Lecture today, but will post the video recording of this as soon as I receive it.

Today the professor reviewed Riemann sums, the definite integral definition using Riemann sums, exponential growth and decay and a non-examinable topic Work. In the 12-1, I believe he did not cover the topic of work and instead went over an additional volumes of revolution problem.

Keep studying!

Best,

Branden

Lecture Notes 38 (Friday 12/4)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor reviewed optimization and the corresponding vocabulary. In particular, the definitions and uses of critical points, absolute maxima and minima, local maxima and minima, concavity, inflection points, and the First and Second Derivative Tests. In 9-10, he also showed another example of a volume problem.

Continue studying for the final.

Have a nice weekend.

Branden

Lecture 34 Video

Hi all,

Here is the video for Lecture 34.

Best,

Branden

Lecture Notes 37 (Wednesday 12/2)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor continued our review for the final. He covered a few problems from his past final for Math 1A. In particular, he reviewed a related rates problem and gave a follow-up problem from Stewart to think about. He also talked about Volumes via solids of revolution and showed three possible ways to answer a problem from his past final regarding volumes. The Professor plans to send this past exam out via email soon.

The homework set today is of course to continue reviewing for the final.

Best,

Branden

Lecture Notes 36 (Monday 11/30)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor began reviewing for the final by going over Limits. In particular, the lecture focused on the precise definition of a limits using epsilon-delta and going through proofs using this definition.

The homework set is to study for the final and get additional practice with the precise definition of limit.

Best,

Branden

Lecture videos 30, 31, 32, 33

Hi all,

Here is the Lecture 30 video.

Here is the Lecture 31 video.

Here is the Lecture 32 video.

Here is the Lecture 33 video.


Best,

Branden

Lecture Notes 35 (Monday 11/23)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered Integration by Substitution using 3 different explanations. He began with an application and intuitive explanation of substitution, then a more mathematically well founded explanation and finally a more computationally driven explanation.

Today's Lecture marks the end of examinable material. Next week we will do Final Review Practice in Lecture.

The Homework set is to watch your email for a list of problems to work on and a potential list of topics to focus on studying over the break. When it is sent I will try to upload it here.

Best,

Branden

Lecture Notes 34 (Friday 11/20)

Hi all,

Here are my notes from the 9-10 Lecture.

Here are my notes from the 12-1 Lecture.

Today the Professor prove the Fundamental Theorem of Calculus in full.
The Professor plans to send a nice version of the proof of the Fundamental Theorem of Calculus today via email and I will upload it here when this happens.

The Homework Set today is to look over the proof when it is sent and understand it.

Best,

Branden

Lecture Notes 33 (Wednesday 11/18)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor spoke more about the Fundamental Theorem of Calculus, in particular the statement itself and how it makes sense in applications. He ended by explaining the Precise (or Limit) Definition of a Definite Integral from Stewart and how it agrees with our intuitive understanding of definite integrals.

The homework set today was to watch your email for information about the Definition of Definite Integrals and what to practice.

Best,

Branden

Lecture 32 Notes (Monday 11/16)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered more on the Fundamental Theorem of Calculus. He began with a visual demonstration of the theorem. We then wrote out precisely the Theorem in full (including both parts) and saw how to get from Part 1 of the FTC to Part 2.

The Homework set today is to learn the full statement of the Fundamental Theorem of Calculus.

Best,

Branden

Lecture 31 Notes (Friday 11/13)

Hi all,

Here are Professor Coward's Handwritten Notes from 9-10 Lecture.

Here are Professor Coward's Handwritten Notes from 12-1 Lecture.

Today the Professor spoke about integration. He covered the intro to Definite Integrals and Indefinite Integrals as well as the Fundamental Theorem of Calculus (Part I) which connects this two ideas. We will speak more about all of this in the following lectures.

The homework set is to look at problems 33 and on in section 5.2 which deal with definite integrals in terms of area. ( I think you should be able to do most of 33-58 if you look over the section and today's notes). 

Have a nice weekend,

Branden

Lecture Videos 24,27,28,29

Hi all,

Here is the video for Lecture 24.

Here is the video for Lecture 27.

Here is the video for Lecture 28.

Here is the video for Lecture 29.

Best,

Branden

Lecture Notes 30 (Friday 11/6)

Hi all,

Here are the 9-10 Lecture Notes.

Here is Professor's Coward's Proof of MVT for 9-10

Here are the 12-1 Lecture Notes.

Here is Professor's Coward's Proof of MVT for 12-1

Here is Professor Coward's solution to the Optimization Problem gone over in class today.

Here is the student solution to a Related Rates problem shown in class today.

Today the Professor review the material that will be covered on Midterm 2 which is on Monday. He went over the major topics from chapter 3 and 4 and drew connections between the content. He also went over the proof of the Mean Value Theorem and examples related to Related Rates and Optimization.

The homework set is to study for your midterm!

Have a nice weekend,

Branden

Lecture 29 (Wednesday 11/4)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the professor went over some of the definitions related to the shape of a graph in the 9-10 lecture as well as L'Hopital's rule in both lectures. He went over some exercises from Ch. 4.4 in Stewart from exercsises 8-68. Check both lecture notes to see all problems he went over.

The homework set today is to look over the exercises in Ch. 4.4 8-68 and read ch. 4.4

Best,

Branden

Lecture Videos 21,22,23,25,26

Hi all,

Here is the Lecture 21 Video.

Here is the Lecture 22 Video.

Here is the Lecture 23 Video.

Here is the Lecture 25 Video.

Here is the Lecture 26 Video.

There are some issues with Lecture 24, I will keep you updated if this is able to be uploaded.

Best,

Branden

Lecture Notes 28 (Monday 11/2)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered the relationship between the derivatives of a function and the shape of a graph. In particular, he related the first derivative and increasing/decreasing as well as the second derivative and concave-up/concave-down to the shape of a graph. In the 9-10 lecture, he also began to cover L'Hospital's rule (4.4 in textbook).

The Homework set today is:

1.) Read 4.3 carefully (Including all exercises). Note in particular the definition of inflection points. 

2.) Try Stewart problems 33-44 (7th Edition)/37-48 (8th Edition). For harder exercises try 45-51 (7th Edition)/49-56 (8th Edition).

Best,

Branden

Lecture Notes 27 (Friday 10/30)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered Rolle's Theorem and the Mean Value Theorem. He gave a way to understand and properly state both. He also outlined the proof of Rolle's Theorem, which is not examinable, and went through the proof of the Mean Value Theorem, which is examinable. So you should be able to prove the Mean value Theorem for the coming midterm, but do not worry about being able to prove Rolle's Theorem (although you should work to understand the proof).

The homework set today is to read Ch. 4.2 and look over the exercises in the section, although you do not necessarily have to do all of them.


Best,

Branden

Lecture Notes 26 (Wednesday 10/28)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered a application of exponential growth/optimization(find absolute maxima and minima of a function) as it relates to probability and gambling.

The homework set today: 

1. Answer the follow-up question to today's lecture which is "What is the optimal bet, if we win WX dollars for each bet of x dollars with probability p, where p in [0,1]?"

2. Learn to state precisely both Rolle's Theorem and Mean Value Theorem. Both are found in Ch. 4.2.

Best,

Branden

Lecture Notes 25 (Monday 10/26)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered more about absolute and relative maxima and minima of a function. In particular,  he went over the definitions of both, issues with endpoints, Fermat's Theorem, critical numbers and the method for finding the absolute minima and maxima of a function.

The homework set today was to

1.) Read section 4.1 carefully
2.) Try problems 47-62
3.) * 63 as a harder extension and challenge problem.

Best,

Branden

Lecture Notes 24 (Friday 10/23)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Note: I mistakenly labeled these as Lec. 25 Notes. Sorry about this!

Today the professor spoke more about Absolute Maxima and Minima of a function, as well as relative/local maxima and minima of a function. He also covered the Extreme Value Theorem.

The homework set was to define what it means to be an Absolute Minimum precisely as well as get practice from the Ch. 3 Review Exercises in Stewart as you feel is appropriate. 

Have a nice weekend,

Branden

Lecture Notes 23 (Wednesday 10/21)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor spoke about Hyperbolic Functions and started talking about absolute maxima and minima in the 9-10 lecture and in the 12-1 Lecture covered differentials and hyperbolic functions.

The homework set was to prove that cosh^2(x)-sinh^2(x)=1. 

Best,

Branden

Math 1A Lecture Videos 17-20

Hi all,

Here is the video for Lecture 17 (9-10)

Here is the video for Lecture 18 (9-10)

Here is the video for Lecture 19 (9-10)

Here is the video for Lecture 20 (9-10)

Best,

Branden

Lecture Notes 22 (Monday 10/19)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Here is the Professor's Handwritten solutions to both Related Rates Problems.

Here is the video about the Space Station the Professor Sent out via email.

Today the Professor went over an example of related rates in both classes. In the 9-10 he did problem 23 from Ch. 3.9 in Stewart about ships and in the 12-1 he did problem 25 in Ch. 3.9 of Stewart about filling a conical tank with water. In 9-10 he also began speaking about differentials. I recommend you all read through both sets of lecture notes to see two good examples of related rates as well as an introduction to differentials.

The homework set was to watch the video the professor sent out (link above) and to continue practicing Related Rates exercises in Ch. 3.9 of Stewart. 

Best,

Branden

Lecture Notes 21 (Friday 10/16)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered logarithmic differentiation through a few examples and began discussing the next section Related Rates. He motivated the discussion with an example relating to a catastrophe that happened at a space station where Math 1A could have been used to prevent any damage. He then went over a general overview of the techniques involved in relating the rates of change of two quantities and the different notations associated with this process.

The homework set today is to find the derivative of y=x^x and (harder) y=x^(x^x). See the 12-1 notes for a cleaner version of this. He also said he would send a link to a video about the space station catastrophe that you all should watch before Monday's class.

Best,

Branden

Lecture Notes 20 (Wednesday 10/14)

Hi all,

Here are the 9-10 Lectures Notes.

Here are the 12-1 Lecture Notes.

Here are the Problems Professor Coward sent out via email.

Today the Professor spoke about a further application of exponential functions which was Newton's Law of Cooling. He derived the solution to this differential equation, which is not in Stewart, using what we learned on Monday.

The Homework today is to work on the Fun Problems Professor Coward sent out via email as well as read Ch. 3.8 about Newton's Law of Cooling.

Best,

Branden

Lecture Notes 19 (Monday 10/12)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor spoke more about exponential growth and applications of the exponential function. In particular, he proved that the solution to dy/dy=ky is y=ce^(kt) using a result of the Mean Value Theorem (which we will encounter later in class). He also showed our first example of an application of this differential equation.

The Homework set today is to read Stewart 3.8 and do some exercises from this section. The Professor will let you pick any exercises in the section and recommends you try anywhere from 5-10 problems.

Best,

Branden

Lecture 18 Notes (Friday 10/9)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered the foundational concepts related to exponential functions and showed a visual demonstration of why the derivative of e^x is itself. This will be crucial in understanding the next major calculus topic related to exponential growth and decay.

Best,

Branden

Lecture 17 Notes (Monday 10/5)

Hi all,

Here are the 9-10 Notes,

Here are the 12-1 Notes.

Today the Professor reviewed for the midterm. He went over the homework from last time, a squeeze theorem problem and an IVT problem in both classes.

The homework is of course to study for your midterm using all of the resources provided by the GSI's, Coward and myself.

Happy studying,

Branden

Math 1A Lecture 14,15,16 Videos

Hi all,

Here is the Lecture 14 Video.

Here is the Lecture 15 Video.

Here is the Lecture 16 Video.

Best,

Branden

Math 1A Midterm Study Guide From Professor Coward

Hi all,

Here is the Midterm Study Guide Professor Coward sent out via email.

Best,

Branden

Lecture 16 Notes (Friday 10/2)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Here is the "Promised Fifteen" Handout from Chris Eur's Math 1A Site.

I have added a link to his website in the useful links tab at the right.

Today the Professor covered more uses of implicit differentiation to find derivatives of inverse functions. In particular, we derived the derivative of y=arcsin(x), y=arccos(x). He also showed a hard limit proof involving a limit going to infinity at infinity and a squeeze theorem problem in the 12-1 lecture.

The Homework set was to find the derivative of y=arctan(x) using implicit differentiation and the process from class as well as study for your midterm next Wednesday.


Have a nice weekend,

Branden

Lecture 15 Notes (Wednesday 9/30)

Hi all,

Here are the 9-10 Lecture Notes.

Here are the 12-1 Lecture Notes.

Today the Professor covered more on differentiation rules and showed some examples from the Stewart Chapter 3 Review exercises that were assigned for homework. He then spoke about implicit differentiation and how to use it to find the derivative of curves which are not functions and to find the derivative of inverse functions. He also mentioned that he will be sending information about our upcoming midterm soon. Check the 12-1 notes for preliminary information.

The homework set was Ch. 3.5 5-20, 25-32.

Best,

Branden

Lecture 11,12,13 Videos for 9-10 Lecture

Hi all,

Here is the video for Lecture 11.

Here is the video for Lecture 12.

Here is the video for Lecture 13.

Note that the Lecture 10 video had some technical difficulties and is now irretrievable.  Sorry about that! You can still access the notes and let me know in the comments if you have any questions about what was gone over during this lecture.

Also note that I have added a link to the "Useful Links" tab at the right so you can access ALL lecture videos from Professor Coward's Vimeo account.

Best,

Branden

Lecture Notes 14 (Monday 9/28)

Hi all

Here are the notes for the 12-1 Lecture.

I am not posting my 9-10 Lecture notes since they are sloppy and exactly the same as the 12-1 lecture notes.

Today the Professor covered the differentiation laws, in particular the Sum, Constant Multiple, Chain, Product, and Quotient rules. He gave the statements and an example for each.

Homework set was to try exercises 3-32 of Section 3.1, 3-26 of Section 3.2, 1-16 of 3.3 and 7-46 of 3.4, especially if you have not seen calculus before. Then once you feel comfortable and especially if you have seen calculus before try 1-50 in the Stewart Chapter 3 review

Best,

Branden

Lecture Notes 13 (Friday 9/25)

Hi all,

Here are the notes for the 9-10 lecture.

Here are the notes for the 12-1 lecture.

Today the Professor spoke more about the definition of derivative. He also clarified more about the different notations and when they are used. He ended by showing the derivative of functions that will be fundamental in finding derivatives of any function.

The homework set was to read all of ch. 2 and try the two definition of derivative problems  which are stated in the lecture notes.

Have a nice weekend,

Branden

Lecture 12 Notes (Wednesday 9/23)

Hi all,

Here are the notes for the 9-10 lecture.

Here are the notes for the 12-1 lecture.

Here is a link to the Mathematical Letter about "Without loss of generality".

Here is a link to the statement of the Intermediate Value Theorem and an example solution to a problem the Professor also sent via email.

Today the Professor showed proofs using the technique of "Without loss of generality" explained in a letter to you all via email. He also spoke about asymptotes and how they are defined precisely using limits. He ended by introducing the definition of the derivative of the function.

Homework for today is to go through exercise 21-30 in Ch. 2.8 in Stewart and look over the problems in the Ch. 2 review as well.

Best,

Branden

Lecture 11 Notes (Monday 9/21)

Hi all,

Here are the notes for the 9-10 lecture.

Here are the notes for the 12-1 lecture.

Today the Professor spoke more about continuity in preparation for understanding the Intermediate Value Theorem. He did examples in both classes with this, but he did an extra (Hard) example in the 12-1 lecture that you may be interested in if you did not attend this lecture.

Best,

Branden

Lecture 9 Video (9-10)

Hi all,

Here is the video for the 9-10 lecture.

Lecture 10 is coming soon, but there are some technical difficulties so its release may be delayed.

Best,

Branden

Lecture Notes 10 (Friday 9/18)

Hi all,

Here are the notes for 9-10 lecture.

Here are the notes for 12-1 lecture.

Here is a link to the Professor's Midterm Review.

Today the Professor spoke more about proving limits to/at infinity as well as the Midterm Review he sent out via email. He did a few problems from the midterm review as well as one problem from the Stewart Chapter 2 Review.

The homework assigned was to work on the problems from the Midterm 1 Review PDF.

Have a nice weekend,

Branden

Lecture Notes 9 (Wednesday 9/16)

Hi all,

Here are the notes for the 9-10 lecture.

Here are the notes for the 12-1 lecture.

Today the Professor gave more practice with the different ways of writing a limit precisely. In particular, he showed how to write out precisely and prove limits from above/below and limits at/to infinity.

The homework for today is to be able to give the definition of  and prove any type of limit and to prove that the limit as x approaches negative infinity of 1/x^2 is 0 (See the notes for a cleaner version of this claim).


Best,

Branden

Lecture 8 Video 9-10 (Monday 9/14)

Hi all,

Here is the video for Lecture 8 9-10.

Best,

Branden

Lecture 8 Notes (Monday 9/14)

Hi all,

Here are the notes for the 9-10 lecture.

Here are the notes for the 12-1 lecture.

Today the Professor spoke more about the Squeeze Theorem and showed example applications of it in computing limits.

The homework for today is to write out all versions of the precise definition of a limit from section 2.4 and 2.6 (i.e. limits approaching a from above/below, and limits at/to infinity).

Best,

Branden

Lecture 6 & 7 Videos

Hi all,

Here is the video for Lecture 6 for 9-10

Here is the video for Lecture 7 for 9-10


Best,

Branden

Lecture 7 Notes (Friday 9/11)

Hi all,

Here are the notes from the 9-10 lecture.

Here are the notes from the 12-1 lecture.

Today the professor showed one more quadratic epsilon delta proof and went over the statement and proof of the squeeze theorem.

The homework for this weekend is to learn and understand the statement and proof of the squeeze theorem.

Best,

Branden

Lecture 6 Notes (Wednesday 9/9)

Hi all,

Here are the notes from the 9-10 lecture.

Here are the notes from the 12-1 lecture.

The professor covered more on limit laws and spoke briefly about continuity. He showed how to compute a limit using both of these facts. He also spoke about an application related to discontinuity analysis to determine whether Yelp star ratings affect business.

The homework assigned was to read section 2.1-2.4 in the Stewart Calculus textbook.

Best,

Branden

Lecture 4 & 5 Videos

Hi all,

Here is the video for Lecture 4.

Here is the video for Lecture 5.

Best,

Branden

Lecture Notes 5 (Friday 9/4)

Hi all,

Here are the 9-10 lecture notes.

Here are the 12-1 lecture notes.

Here is the handout sent via email by the professor mentioned in both sets of notes.

Today the Professor went over key problems from the epsilon delta handout that was sent via email and showed another example of doing an epsilon delta proof with a quadratic function. He also began covering the laws of limits and proved the sum law of limits.

The homework (shown in the notes) is to prove the difference law of limits.

Best,

Branden

Lecture 4 Note (Wednesday 9/2)

Hi all,

Here are the notes from the 9-10 lecture.

Here are the notes from the 12-1 lecture.

Today the Professor gave a more intuitive description of a precise definition of a limit using an example diagram in his Geometer's Sketchpad program. He then did some exercises from the textbook section 2.4 from exercises 19-32. Note: He did problem 29 in both lectures, but did an additional problem in the 12-1pm lecture. It is worth looking over!

Best,

Branden

Lecture 3 Video (9-10am) 8/31

Hi all,

Here is a link to a video from Professor Coward's third 9-10 am Lecture.

Best,

Branden

Lecture 3 Notes (Monday 8/31)

Hello all,

Here are the notes from the 9-10 Lecture.

Here are the notes from the 12-1 Lecture.

The Professor covered the quantifiers "For All/For Every" and "There Exists" as well as basic proofs associated with both. He also showed our first example of a full epsilon-delta limit proof.

The homework assigned today was to prove the claim that the limit as x approaches 3 of 10x is 30 (See the notes for a cleaner version of this claim).

Best,

Branden

Lecture 2 (9-10am) Video

Hi all,

Here is a video from today's 9-10 lecture!

Best,

Branden

Lecture 2 Notes (Friday 8/28)

Hello all,

Here are the notes form the Professor's 9-10am lecture.
Here are the notes from the Professor's  12-1pm lecture.

The Professor covered the third foundational concept from our course, logic. He went over the five most important logical statements that can be formed from two statements. This will be necessary to understand during our study of the precise definition of a limit.

Best,

Branden

Lecture 1 Notes (8/26)

Hello all,

Here are the notes form the Professor's first 9-10am lecture.
Here are the notes from the Professor's first 12-1pm lecture.

The Professor gave an introduction to the course and reviewed the foundations for our course. He spoke about vocabulary and concepts related to numbers and different number systems as well as functions.

Best,

Branden