- In your own words, if someone asked you to describe what calculus is, how would you answer them?
- What do you prefer more, algebra or geometry? Why?
- How well do you know trigonometry? Briefly, discuss what you know about the unit circle.
- How about exponential and logarithmic functions? How are they related to one another?
In addition to reflecting upon and answering the questions above in a substantive manner, please read and respond to the posts of two of your classmates.
This assignment will be graded as homework, to be completed no later than the start of class on Mon, Sep 12.
In my own words, Calculus is a branch of mathematics which explains the relation of change in our world. Everything in this universe changes and Calculus is simply a method by which that change can be explained, defined, and qualitatively measured to predict future changes and trends. I personally prefer Algebra over Geometry because it is easier for me to analyze numerical information than visual representations. In Pre-Calculus I did pretty well with Trigonometry and learning the various degrees and Pi values of the Unit Circle; however, I do need some refreshing on the Unit Circle values. From what we have learned about exponential functions, I can say that they are used to show a trend of growth/decay in economy, population, or other factors. As for Logarithmic functions, I know that they are used to simplify long division and multiplication problems.
ReplyDeleteI didn't know logarithms could be used to simplify long division problems, thanks.
DeleteI agree with you. I enjoy algebra much more than geometry. I also cold use a little refreshing on some concepts of trigonometry.
DeleteYour definition of Calculus is very detailed and thorough. I also agree with you about preferring Algebra. I find it much easier.
DeleteHuh, I thought that logarithms were just used for Mrs. Bishop's DNA and protein labs.
DeleteCalculus is simply the mathematics of change. It takes all of the changes in everyday society and the world and puts them into a definable and understandable form. It allows for there to be a greater understanding of how things can be changed and measured in a quantitative way throughout everyday life. I personally prefer algebra over geometry. I am more of a numbers person. I would rather solve a problem that uses number and variables than a problem with shapes and angles. I understand geometry and shapes, it just doesn't attract the same interest as algebraic problems. Trigonometry is an aspect of analysis that I did well in. I understand most of the parts of the unit circle. For example, I know the values of angles and coordinates of the major angles on the unit circle. However, I could use some refreshing on the other aspects of trigonometry. Exponential functions are used to show expanding or shrinking in values. They can be used in everyday life to show changes in an economy overtime, or other examples that show either growth or decay. Logarithmic functions are not as familiar to me. I do not remember enough for an in depth explanation. All I can tell you is that they are used to solve logarithmic and other equations.
ReplyDeleteHey Alex, yeah I get why you like Algebra more than Geometry because I have the same reasons for liking it :)
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DeleteYah I need a little bit of refreshing too when comes to trigonometry, other than the unit circle.
Delete-If someone were to ask me what calculus is I now know that the short and sweet answer is "the mathematics of change". If the stranger had a minute I could go a bit deeper and describe how calculus studies limits, derivatives, functions, and integrals. I might even go into how calculus can apply these to solve problems in science, engineering, and even economics.
ReplyDelete-I prefer geometry over algebra any day. I am a visual learner so the concepts of geometry came very easily to me. More importantly they stick with me much longer than the concepts of algebra.
-I feel fairly comfortable with trigonometry, most of the information I can remember fairly easily. Things like the identities will come back with a little refreshing I'm sure. Mrs. Moncure did a good job of making sure that we knew the unit circle last year, I don't think that it is something I will soon forget. Like I stated before, being able to visualize something can go a long way for me.
-Exponential functions and Logarithmic functions can be seen as inverses of each other. I am not as comfortable with these as I am with the unit circle.
Yes I completely forgot about how exponential and logarithmic functions are opposites! Thanks for reminding me
ReplyDeleteIf I were to describe calculus to someone, I would describe it as the study of mathematical change which most commonly deals with integrals and derivatives.
ReplyDeleteIf I had to pick between geometry and Algebra, I would choose geometry because I am a more visual learner. Seeing the shapes and problems helps to solve them easier as opposed to the many formulas and equation work that goes along with algebra.
Trigonometry is not the easiest thing for me but it is not too difficult either. Everything will come back once it is refreshed and used more frequently.I know the unit circle fairly well. We used it a lot last year so it will not be hard to remember.
All I know about logarithmic and exponential functions is that they are inverse functions so the range for one is the domain for the other and vise versa.
I agree that Trigonometry will come back after we begin to use it again. We worked with it a lot last year, so we should easily remember it this year.
DeleteAs we were told in class, Calculus is the mathematics of change.
ReplyDeletePersonally, I prefer Geometry more because I'm a visual learner. Seeing the problem makes it a lot easier for me.
I have a basic understanding of Trigonometry. I probably forgot some concepts but it will probably become familiar once it comes up. As far as the unit circle, we used it a lot towards the end part of last year so I'm pretty familiar with it.
Exponential and logarithmic functions are related because they are the inverses of each other. When we did this lesson last year, I was comfortable with them. Coming into this year, I can't say the same.
I find it interesting that you like geometry over algebra. I am the opposite. iLife variable and numbers more than visuals. It is interesting to see different opinions.
DeleteIt's nice to see that I'm not the only one here who prefers geometry over algebra.
DeleteAs you stated in class, I would describe Calculus as the mathematics of change. It involves limits, derivatives, and integrals. Before class, I would not have been able to give the correct definition.
ReplyDeleteI prefer Algebra over Geometry. I find it easier to work with formulas and equations than shapes and angles. I tend to understand Algebra better than Geometry, and I would much rather work with variables and equations.
I learned a good amount of information about Trigonometry last year in Analysis, but I am somewhat rusty with the information now. I need to revisit it to brush up on the information. Last year, I learned the unit circle. I would easily remember the information if I restudied the unit circle.
Exponential and logarithmic functions are inverses of each other and are symmetrical over the y=x line. I did well with these last year, and I feel comfortable working with them.
I agree that I wouldn't have been able to give the right definition if asked before out first day. I also prefer Algebra, and it seems that most everyone does too.
DeleteI like Algebra over Geometry too. I did not, however, remember the bit about the y=x line and the logarithms and exponential functions.
DeleteIf someone asked, I would describe calculus as the mathematics of change. Beyond that, I wouldn't have much to offer.
ReplyDeleteI prefer geometry over algebra. I find it easier to understand, mostly because I can actually see what I'm working with.
I'd like to at least think that I know trigonometry pretty well, but with a year of little to no use, I'm sure I forgot more than I can think of. However, the unit circle did manage to stick.
Exponential and logarithmic functions not so much, but I think that a quick recap would be all I need to get back up to speed.
I agree, geometry is much easier to work since you can see what you are doing.
DeleteI would say that calculus is the mathematics of change because that it what is engraved into my brain after the first day.
ReplyDeleteI prefer algebra to geometry because I always thought algebra was more fun. I think the logic portion of our geometry class was what made it not as interesting as algebra for me.
I was okay with trigonometry, but I found out over the summer that I had forgotten it really quickly. I think that I'm still very familiar with the unit circle, though.
Logarithmic functions are just different ways to show exponential functions. If you switch the order around a little, they will look the same.
Ya, the whole trigonometry unit definitely disappeared over the summer for me to. Also, that is the same thing I would tell people about calculus too!
DeleteI would describe Calculus as the mathematics of change, as most of the other people in this class would also say.
ReplyDeleteI prefer algebra because I like to be able to work with the numbers without worrying about shapes or extra regulation. I also find it to be a little more challenging but not so hard that it is frustrating.
Trigonometry was a difficult part for me last year. Most of the time I struggle with simplifying problems with sin, cos, and tan and no actual numbers. I do understand the Unit Circle.
Logarithms are another form of exponential functions that can make it simpler to solve in some cases. That is about all I remember of them other than the laws and their basic use.
I also remember the laws and basic use., and thought simplifying was difficult too.
DeleteCalculus is the math of change. I liked algebra more it was more advanced and involved solving out problems. I had a pretty easy time compared to most of my classmates with trigonometry. I remember some of the major points on a triangle for finding degrees of triangles. And I don't remember anything about logarithms and exponential functions
ReplyDeleteI believe we will know a lot more about exponential and logarithmic functions by the end of this year
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