Tutoring Calculus, Mean Value Theorem and Optimization

We started by looking at some problems with derivatives, they included the product rule, quotient rule, and the chain rule. The format of the problems was a bit different than usual.

After that, we looked at the mean value theorem and what it really means. Given two points and the values of a function in between, if the function is differentiable than one (possibly more) point will have the same slope as the average slope. The average slope is found using methods used in algebra.

Also looked at some optimization problems where the basic approach is to find an equation and then set the first derivative equal to zero since the slope will be zero at maxima and minima (and inflection points).

Tutoring Chemistry, Combustion reaction

We started by looking at a problem finding the heat of combustion for acetylene in oxygen. The approach was to draw the bond structure determine the number of each type. There were coefficients in front of some terms in the reaction as well. The heat of combustion for the exothermic reaction was negative.

Looked at a few problems that were closely linked to physics including the photo electric effect and talked about the relationship of wavelength, frequency, and the speed of light. Understanding physics will make parts of chemistry make more sense.

Looked at hybridization and resonance and did a problem with the electron configuration of Chromium.

A number of things in chemistry need to be committed to memory.

Tutoring Calculus, Chain Rule

We started by looking at extrema for functions, maxima and minima. They can be seen on graphs with a flat slope and can also be calculated by using the first derivative.

We looked at derivatives of some trigonometric functions including arc sine as well as the domain of the functions. It can help to look at the functions in a few ways. Two ways are on a unit circle and also as an oscillating function on the x-y graph.

U-substitution is a useful approach and includes the chain rule. I actually have a table of derivatives that uses u each time.  That can be a good way to think about derivatives since many times there will be something other than x that is being operated on by the function.

“Can Google solve mathematics and physics?”

“Can google solve mathematics and physics?”

It can solve some basic mathematics and physics and even some things you might not expect.

You do, however, need to know exactly what to input and how to input it (syntax). Google may understand some variations of a phrase but not others.

You can check out this post to see some examples,

Google Math (with applications to physics)

“How do I solve 4x+2y=-6 for y and then find two points on the graph” Algebra I

Solve for y
You want to solve for y =

So that means you should isolate y until it is by itself on one side of the = sign

You start with


Right now there are two terms on the left side of the =

4x and 2y

It would be better if you only had the term with y by itself

If you change the left side, you must make the same change to the right side

So your first step could be to subtract 4x from each side

Finding two points
Once you have an equation, you can pick any number you want for x and then determine what the y coordinate should be, by solving for y.

Each point has an x and y coordinate (x, y)

Or you could pick a y value and solve for x.

The values you pick should be easy to graph (probably near the origin).

Two values that can often be easy to work with are the y-intercept and the x-intercept.
You find the y-intercept by setting x = 0 and solving for y and you find the x-intercept by setting y = 0 and solving for x.

Tutoring Newtonian Physics, Day 1

We started by talking a little about what Newtonian physics is including what the units of force are and how you can break down Newtons in kg, s, and m.

Went into some problems include motion diagrams and plotting position vs time as well as velocity vs time.

Talked about normal forces and gravitational forces and how they often cancel when something is not moving vertically. And got into ‘resultant’ forces aka ‘net forces’ and how they can be zero for something at a constant velocity.

We also got into the differences between weight and mass and how kilograms compare to pounds. Thinking about the weight of a book, the weight of a person, etc.

Jet Engines and Decibels

I’m taking a class on drawing and one student drew two men talking behind two jet engines.

Elizabeth commented, “on a practical note, how’s he going to hear the fellow behind him? Protective ear gear, not looking at each other, an approximate 130db noise level from the engine…”

Tim replied, “They have wireless y’know. And anyway there’s two engines so that’d be 260dB!”

My response:

Cool drawings, might have to correct your acoustics statement though.

Two engines at 130 dB does not equal 260 dB. If we assume that each engine generates 130 dB, it would be more like 133 dB for two engines.

Decibels are not a linear system. It’s more like the Richter scale for earthquakes. That allows our ears to hear a greater range of intensity.

Let’s say we have one saxophone playing something compared to 10 saxophones playing that same thing in unison.

Then 10 saxophones in unison would sound twice as loud as the one saxophone.

dB level = 10 log(I/I0)

Where I0 is generally the threshold of hearing for humans.

Using a property of logs (a is the base, ten in this case)

loga (xy) = loga x + loga y

If you double the intensity, then you add 10log(2) to the original dB level. That means adding about 3 dB to the original 130 dB to get 133 dB. (That’s if the two engines are in unison)

Elizabeth saying approximately 130 dB is actually fairly accurate.

How to figure out gravity on Mars

Leave comments with any questions you have.

Finding Velocity of Geosynchronous Satellite – Video Lesson

How to find the velocity of a geosynchronous satellite.

Physics 2B Final Average

The average score on the final was 73.4%

The grading followed the cutoffs on the syllabus.