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

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