10.7

reflective- Graphs of S and I are valuable to determine the quantity of an object needed to suffice something (ex: vaccinations)

difficult-this is a diffcult concept to grasp but after re-reading the chapter the topic becomes a lot more familiar.

10.5

reflective- I enjoy solving problems such as these because they require more algebraic solving then conceptualizing.

difficult- i didnt find this section that difficult because the problems, if one knows how to go about using the formulas given, are pretty straight forward.

10.4

reflective- although i found this section to be boring i understand that it is some of the most useful material in terms of calculating real world things such as the quantity of something such as pollution or interest.

difficult- overall this is somewhat difficult to grasp because of the number of concepts that one has to understand. i feel that after solving several problems i will get more comfortable doing growth and interest problems.

10.3

reflective- slope fields are a great way to visualize a specific differential equation.

difficult- slope fields ae not difficult because i covered it thoroughly in my previous calc class

10.2

reflective- i like problems like these because it requires actual algebraic solving.

difficult- this isnt too difficult because all it requires is differentiating the function and then putting it in the equation.

10.1

reflective- this is a good way to take a problem and be able to visualize it to answer it.

difficult- this is not that difficult considering there isnt any actual algebraic or estimating solving that must be done.

9.6

reflective- constrained optimization is key in determining the maximum efficiency of a function.

difficult- out of all the material we have covered thus far this has been the most difficult. there is a lot of material to grasp at once, but once i start doing more problems, ill become much more confident with the material.

4.3

reflective- the idea of global maxima/minima further expands on local max/min. This means that where as local max/min occur at nearby points, global maxima/minima occur at all other points.

difficult- when calculating global maxima/minima, one must remember to calculate all specific critical points within the interval.

4.2

reflective- finding the point of inflection is very similar to finding max/min. you make the 2nd derivative =0.

difficult- I have covered point of inflections thoroughly in my previous calc class.

4.1

reflective- by finding the local maxima/minima, one can better assess the derivative in graphical form.

difficult- one must remember that to find max/min, one must make the derivative = 0.

2.4

reflective-2nd derivatives allow one to further expand functions to other numbered derivatives, for example, 3rd derivatives, etc.

difficult- i have already done 2nd derivatives so they are no difficult to do. They are the same to calculate as first derivatives.

9.4

reflective- Finding partial functions algebraically gives me the sense that I have more control over the problem because of the computation necessary to complete the problem. In such problems, you plug in numbers rather than estimating.

difficult- The derivative problems in this section are similar to the ones in 9.3 so it's not that hard.

9.3

reflective- I enjoy finding the derivative of a function, but find estimating derivatives somewhat annoying, especially know that we have to watch if the deriv. of f is with respect to either x and y.

difficult- this isn't really difficult, just kind of annoying to do. One just has to watch out for what f corresponds to.

3.5

reflective- finding the derivatives of sinx and cosx are crucial, but only the start of other differentiable trig functions, such as tanx, secx, cscx, and cotx.

difficult- I am very confident with derivatives. In fact, I actually enjoy differentiating problems, so I look forward to differentiating future functions.

3.4

reflective- the product and quotient rule is very important to use, since future functions will be much more complex than they are now and may require several differential rules such as product and quotient.

difficut- these rules are easy to understand, but one must remember that the numerator gets differentiated first, then the denominator, and that the denominator is squared.

3.3

reflective- The chain rule is a necessary mathematical application because there are many functions which require several operations to differentiate it. for example, in (3(t^3)-t)^5 you have to differentiate the whole function as well as what is inside.

difficult- Chain rules are pretty easy, but they can get somewhat complex. One thing to keep in mind is to no forgot to differentiate the inside of the function.

3.2

reflective- it is interesting to see the relationship of graphs between the graph of an exponential funct. and the graph of the deriv. of that same exponential funct.

difficult- One may forget that the derivative of lnx is 1/x and the deriv. of e^x is e^x.

3.1

reflective- Finding the derivative of a function allows one to insert values and get actual values rather then having to estimate one.

difficult- this is relatively easy because i have done it before, but one can easily forget to subtract 1 from the exponent, especially if the exponent is negative.

2.3

reflective- Interpreting a derivative can be used in common life things, such as, building a house. One will be able to measure its cost divided by a measured area.

difficult- I understood everything because derivatives were heavily covered in my calculus course last year

2.2

reflective-since there are numerous variations of a derivative that u can get, such as, 1st derivative, 2nd, 3rd, etc, is there a certain number derivative that can not be derived?

difficult-i have a difficult time grasping exactly how to find the graph of f'(x).

2.1

reflective- Finding the instantaneous rate of change is prominent in several fields, especially those involved with aerial objects, such as those in NASA.

difficult- Personally, it is more difficult to estimate the derivative of a function graphically than it is numerically. Drawing graphs require one to know what a function looks like by just reading the function, which may result in confusing one type of graph of a function for another.

9.2

reflective- Contour diagrams are widely used to visualize a variety of maps (topographical, geographical, temperature). Through this, one can determine a variety of things such as mountain peaks.

difficult- I didnt quite understand the diagram of a pass between two mountains. I didn't see how the space in the middle symbolizes a pass btw 2 mountains, since it looks more like there are 4 mountains if u follow the diagram for a mountain peak in 9.9

9.1

reflective- Investigating the functions fo two variables are quite important, especially when dealing with science. One can learn more about a certain drug and how it reacts with a human body by calculating the concentration of a certain drug-the amount in the drug and the time since the drug was taken.

difficult- I don't quite understand where the "5-x" comes from in the formula C= f(x,t)=te^-t(5-x).

1.10

reflective- sine and cosine are two of the most vital and prominent trigonometric functions in calculus. All other trig functions can be expressed in terms of them. It is interesting how the simplest trig functions are the most crucial in this subject.

difficult- I did not find anything in this reading difficult because i previously studied it in my calculus course last year.

1.7

Reflective- Exponential growth and decay is a very important mathematical application because it is based on the change in nature. In a time when immigration is such a critical subject in modern United States politics, it is key to understand the change in legal and illegal immigrant population. By understanding what the initial quantity and continuous growth is, we may begin to assert such a task.

Difficult- What was difficult for me was grasping the concepts dealing with the equations involving present and future values because there were numerous different applications to grasp.

1.5 & 1.6

One thing that I tend to get mixed up are the properties of the natural logarithm in section 1.6, specifically, ln (AB) and ln (A/B). I just have to remember that ln (AB) = ln A + ln B and ln (A/B) = ln A - ln B, and not the other way around.

1.1 + 1.8

I'm having some issues answering question # 37 in 1.8. In the first part it asks u to distinguish the signs, but I dont know the exact reasons why A and B are both positive and C is negative, except for the fact that Q can't be negative. This means that only C can be negative because its an exponent. I was just wondering what the specifics for that question were.

9/6/07

The functions in sections 1.1 and 1.8 were not too difficult to understand. I guess one thing to watch out for when dealing with shifted graphs is to make sure that you calculate the function as a whole. In other words watch out to see if the graph is either
y=f(x)+k or y=f(x-k).

First Post

1. Henry Cardenas
2. Ist Year
3. Intended Latin American Studies major
4. AP Calculus BC (High School)
5. (Worst) My discomfort with numbers
6. (Best) The ability to solve problems when I am familiar with the steps.
7. I am taking this class because I want to get my math requirement out of the way.
8. I hope to leave this class with two things: 1. an open perspective on math and 2. the freedom to say that math isn't that bad.
9. The worst math teacher I ever had was last year in my calc class. She was "old school" so quizzes and 4 tests in the semester made up our grade, and she refused to be lenient. Not only were the tests extremely difficult at times, but sometimes we would have to do long problems in a very short period of time. The quizzes were taken from similar problems we have done for homework and in class, but the tests had problems we've never seen before. We were supposed to "think outside the box," which was kind of difficult when you're stressing about time and the test in general. Yeah, not a good time last year...
10. To be frank, I have had a pretty bad record of math teachers. I'm hoping this year will be different.