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