The Derivative Function and Interpretations of the Derivative

The most difficult part of sections 2.2 and 2.3 was Lebniz's notation. In high school I had seen derivatives as f'(x)= dy/dx but i had never known that the notation was to indicate that the derivative is a limit of ratios. Just by using multiple notations to imply the same point [the derivative of a function] gets cofusing. I am kind of wondering why Gottfried Wilhelm Leibniz felt the need to use d instead of delta?

I think the class will have to work through estimating derivative values from looking at a graph. I mean the derivative is the slope of the tangent line of a point on that graph, but its not as easy as it sounds. Also looking at graphs everybody will need to be able to predict how a graph of f'(x) will look depending on f(x)

By the way, as we progress though the examples in the book, i am finding more biological uses for math and that's pretty exciting since its connecting math to something very important/interesting to me. See example 8- health care costs or problem 37-diaphragm pressure.

Instantaneous Rates of Change

What i found most confusing was how the book tried to use two different approaches when trying to explain that a derivative is the average rate of change at a point. I was personally confused when instantaneous velocity was defined to be the limit of the average velocity of the object over shorter and shorter periods of time intervals. Table 2.1 was just not that effective.

As a class I believe the most difficult area will be visualizing the derivative of the graph. At a point the derivative is the slope of the tangent line of the point on a graph. Again I believe we will need practice finding the derivative from data, a graph, and from an equation. But i think as we do some more examples it will become clearer.

Functions of Two Variables and Contour Diagrams

The most difficult idea from sections 9.1 and 9.2 was probably the Cobb-Douglass Production Model. It is a completely new concept to me, but the example about a small company going through expansion, was very helpful. There is the idea of holding one variable constant while seeing how the other changes. The other example modeling the production of the US economy was precise. apparently the equation P= 1.01L^0.75K^0.25 is very accurate, but how was this equation developed?

I see the class having difficulty with the contours on a topographical map. Contour diagrams are common in maps and weather charts, but honestly i never analyzed the functions before. For example figure 9.10 I have never seen how a pass between two mountains was represented.

Periodic Function

So I was a bit thrown of when the pages of 28 -32 did not correspond to periodic functions. so I stuck with reading section 1.10.

Essentially periodic functions have values that repeat and consistent intervals, and its really cool how there are loads of real life examples of periodic functions such as music or blood pressure.

The Most confusing or difficult part of a periodic function that I found was which mode to be in; radians or degrees. The book says to assume work in radians, but what is a radian??? I know degrees is 360 in a full circle, but where does radians come into play again? I think i knew the where and why once upon a time but its hard to use something you don't quite understand.

I think the most difficult part of periodic functions will be coming up with an equation just from looking at the graph. Its not as obvious as say a linear function. There are more pieces of the graph to consider; there are parameters that fluctuate as amplitudes, periods, and shifting occurs.

As for R, the second lab appears to be going better or I should say more smoothly. I think its due to the fact that we've now had exposure to HTML entering.

More to come....

Exponential Growth and Decay

It was kinda cool to think that a lot of events in life are actually exponential growth or decay. What I found to be most difficult was present and future values. Specifically inflation represented as the future value that is dependent on the interest rate. Its hard to keep track of interest when it is being compounded.

I would think that most of the class, myself included, would have the most difficulty with deciding which of the given functions (compounded annually v. compounded continuously) would be appropriate for a problem. For instance example 8 about the lottery. For the option of being paid out assuming a 6%interest rate, i didn't understand why r=-.06, is that compounded interest?

I just feel as if it were alluding to economics, which is in my opinion a difficult area of study.

I can relate better to the environmental examples.... i seem to have a better grasp on a concept when i can relate.

Exponential Functions and Natural Logarithms

R- hmm can't be sure if I am in complete awe yet. My partner, Katie and I, have spent some more time working with R and its a fun program, but very picky about how many parenthesis are necessary in a command. We are also having issues with adjusting limits on our window. But more on that later since we are not done with the lab as of yet.

The most difficult part about this section was from 1.6. There are a lot of properties of the e that can be used to solve word problems, but its actually difficult to remember that the actions are valid ways to solve a problem. Kind of like a tool in a toolbox that you didn't know you had. I was working through problem # 41 about when there would be 1 vehicle per person and in order to solve it i had to bring down the exponent. I eventually solved it, but i had to figure out which property was going to help me get to the next step. Turned out that it was ln (A^p)= p ln A.

I think for the class as a whole the most difficult thing would be setting up the word problems. First, you need to figure out what the question is, then how to solve it. A lot of times there are hints to whether or not you are looking into an exponetial growth or decay problem. Most times in was a percentage of growth where in the function it would be used as (1.00+ x%) or if it were decay in would appear as (1.00- x%). once you figured out the rate of change, you had to remember the base was to be when time=0 or the initial quantity. So i geuss its best to just disect the problem until you have found all the pieces to put into the function.

more on feeling about R later...

linear functions and rates of change

So I am trying to get back on the right schedule with blogs, but to make sure all basis are covered I'll begin with sections 1.2 and 1.3.

The most difficult part from these sections was calculating the intercept (b) in order to fulfill the linear function of Y= f(x) = b + mx. The slope m was easier to calculate (rise over run) from using two different points. but b was more difficult because sometimes its confusing which equation to set equal to 0 in order to find the needed intercept. It is often necessary for me to re-read the question in order to see what the question was asking.

Being interested in medicine, my favorite question from the problem set from 1.3 # 26- 31 pertaining to maximum heart rates. By using two different equations to draw conclusions from; the MHR is actually not linear using the more accurate equation of MHR= 208-0.7a

Since next class is a lab, there isn't suppose to be a Blog... so stay tuned to hear about R

Functions and Composite Functions

The most difficult part about section 1.1 and 1.8 was opening the book! No, I am just kidding from section 1.1 I was having difficulty determining from the tables, graphs, formulas, and words which variables were the dependents and which were the independents. I had to actually stop and think aloud, if y were to happen, it would depend on x. Section 1.8 on compositions weren't too bad, i understand which function should be performed first, and then have that answer used in the next function. Graph transformations were a bit more difficult. I get the idea that graphs can be repositioned but multiple transformation or stretches may be more difficult.

What I found interesting was that and EKG pattern was used as an example. I volunteer at the ED at a hospital and I had seen the graphs before. I knew they measured electrical activity as a function of time, but it put functions in a more meaningful (and real-life example) light.

lecture 9.5.2007

Nothing, is not an acceptable answer. But today was more of an introduction to the course and material wasn't really discussed.

Scratch that thought; the two main concepts are functions and differential equations. I have had experience with functions, so i suppose differential equations would be the most difficult out of the two.

In class today when were brain-storming examples of how differential equations cab be used to answer questions, I think with the time restraint it was hard for everyone to come up with different variables or factors that alter and outcome of a situation.

In my small group we thought of obesity and the variables we could come up with were diet, exercise, genetics, culture, mother's cooking talents, and location. It sort of served as an ice breaker to be able to get out of our seats and talk about it.

Who is Lucky?

Well, my name is Lucky Homesombath; and yes, that is my given name. It has grown on me and now I love it.

At the moment I am beginning my sophomore year at Macalester.

I intend on earning my degree in biology with a minor in anthropology.

Applied Calculus would be my first mathematics course at Macalester, however I have taken calculus in high school, but that was over two years ago!

From my mathematical experiences, I would have to say that trigonometry (sine, cosine, etc.) was most challenging.

I asked to add applied calculus, because I like math, but it is also required for my biology major.

From taking calculus, I hope to have a deeper understanding of where calculus applies to biology. In my opinion, calculus is prevalent in physics and chemistry... but i haven't seen too much in biology yet.

As exciting as math is, I am also interested in music (listening, not playing unfortunately), dance, reading, I am very open to trying new activities.

My worst math teacher.... was back during Algebra 2, unless you were going to be his next prodigy he didn't give the time of day to help those who were struggling. As long as your were going to pass into the next class, he wasn't concerned whether or not the material was learned.

My best math teacher... was actually my high school calculus teacher. She was approachable, yet at the same time very professional. She valued our opinions on the topic and took into consideration how the students wanted to learn calculus. We were enjoying and learning. And for some reason I can vividly remember her crazy cackling laughter.

I think I am going to like applied calculus, and I like your laid back approach. and I agree that having the general understanding that mistakes will be made when learning calculus makes it easier to try and try again.

See you in class Friday,

Lucky H