How would you introduce differentiation to a class?\nWould you begin with first principles?\nThanks
200343
You motivate differentiation with something students are familiar with; speed, rates of change, etc.  You do first have to give them a comfortable feel with limits, since the definition of the derivative involves limits and differentiation is a limiting process.  You then show the difference between average rate of change, and instantaneous rate of change (anyone taking a trip from point A to B in a car can get this one).  You introduce the slope of the line as the rate of change and then work to the idea that the slope of the secant line to a curve is the average rate, and by taking smaller differences in the independent variable you approach the instantaneous rate of change(this is where the whole limit thing is important).  Once the students feel comfortable with this explanation of what we are trying to do, then you move into the technical and rigorous side.
176548
You're going to have to ask the question a little more coherently if you want me to answer. I have no idea what you're talking about. Sounds like you might have a hard time in this class.
434953
I'm not sure, but why don't you include a quote from the teacher or the book using these terms?  I'm sure putting them in context would help with identifying them.
345393
In general, there is only one way - differentiate 53 times!\n\nIf you are looking for some specific function, there may be easy representations:\n\nfor example, the kth derivative of x^n w.r.t. x is\n\nn(n-1)...(n-k+1)x^(n-k)
105083
5 minutes FLIES by when you're teaching.  If you're doing Teach for America or a Teaching Fellows program, you'll be in a group of 10-12 other people.  You could give them each a line of a simple poem and have them line themselves up in the order they think the poem should go.  Once they agree on an order (I'd give them about a minute and use a timer), have them read their sentences in the order they decided.  Then you could have a discussion of why they put it in this order.  (i.e. why the story flows that way, what changes they might make having heard it, maybe how the tone changes when the sentences switch).\nAt the end you could read the poem how it was written as a conclusion.  If time, let the students reflect on the experience.\n\nAnyhow, hope this helps.  Good luck with your sample lesson!!
145358
If it is for a class let me know what kind of class...I can't think of anything right now but I'll try to help. Sorry.
217052
So you know what you have to teach. Physics also develops on itself a lot, so having a structured order of topics makes learning easier for the students.
217565
OK...I'm thinking that you are refering to class dynamics and this is what I am basing my answer on.  All classes have a dynamic.  For instance, one of my classes is very motivated.  The majority of the kids in the class care very much about their grades and come from very stable families that put a strong emphasis on education.  As a result, teaching them is a dream.  They are open to new ideas and easily adapt to change.  These kids are sponges and absorb everything.  Because the entire class dynamic is very motivated, they are learning more because they are all open to it and look down upon those that are not trying to learn as much as they can.  Also, I can be creative with them because they are always open for a challenge.\n\nIn another case, I have had a couple of classes that had very head-strong children in them.  The dynamics of these classes are awful.  Because of their strong personalities, I spent less time teaching and more time getting them to understand that I got the degree and they had not yet passed middle school.  As a result, these kids did not learn much from me and I admit that.\n\nSo the dynamics of a class directly influences how well one teaches and how much students learn.
450855
How about setting it up first in a truth table? \n\nIf you do, you'll see there's a counterexample. So there's no way to logically derive A from assumptions 1 and 2.
287503
Try to decide what are the major concerns that your class has.  Briefly address each issue and say how you feel about it and what you would do about it.  Be sure to say "thank you" at the end.
471359
It is the first derivative.
39420
Is there something that you know, so you can give some classes?
513911
it's just a summary..dont be afraid. its basically the way you understand the concept.maybe you can throw in your own little example.
224493
Ask your school's academic advisor. Judging by the class title this could just be basic math, but every school puts something different in basic math. So I cannot tell you anything.
349404
Check out http://www.ClassTopic.com They have some great topics that I've used in the past. Each topic has three good sources to get you started on the research, too.
74904
If you would like to focus on one learning style, maybe you could present a variety of classroom activities that would engage that kind of learner (and explain why each activity would be interesting to that style of learner).  If you'd like to do something more broad, maybe you could refer to a sample lesson plan and explain which activities engage which kind of learner at different points of the class.  This would allow you to explain each kind of learner (and could show how some lesson plans disproportionally favor a specific kind of learner).
542229
I've done a good bit with linear transforms in general (LaPlace,Fourier, Z), so hopefully I can help you. The most important thing for your class is to know whether or not they will allow the use of tables or not. Even the simplest function will usually require integration by parts to compute a transform directly. Usually I use tables of transforms coupled with properties of transforms (like the differentiation property, which lets you use algebra instead of calculus to solve an ordinary linear DE). I really can't go into any depth without pencil and paper. Check out the link below (it contains an example of using LaPlace transforms to solve a linear ordinary DE).