Day 1 in Mat229

• Welcome!
  • Introductions (3x5 cards)
    1. Name
    2. Where are you from?
    3. Working outside of school? If so, where?
    4. What is your calling? ("a calling has to do with one's larger purpose, personhood, deepest values, and the gift one wishes to give the world.... A calling is about the use one makes of a career." David Orr, Earth in Mind)
    5. What is your career objective?
    6. Something special about yourself.

• Some course details:
  • The course website may be useful: http://www.nku.edu/~longa/classes/mat229
  • Syllabus (logistics, etc.)
  • We'll be using Mathematica in class, and you should use it on your homework, whenever possible and convenient. You can get a personal student copy as an NKU student by following these directions.
  • This will not be entirely a "stand and deliver" course: expect to do your share of participating, at the board, in groups, etc.
  • You should do the reading in advance of our discussion of that section in class. So tomorrow we're starting in with section 6.1. You need to get that read today/tonight!
  • Assignments
  • Directed reading/summaries (e.g. Section 6.1 summary)
  • Departmental Syllabus
  • One of the more unusual aspects of the course was inspired by scenes like this:
    and this:
    

    I have instituted the "Class Agreement".

    

  • We'll have some additional assistance in this course:
    1. There is a calculus lab in MEP457, free to you. The hours will be posted soon. Usually there's no great rush the first week....
    2. one or two STEM FORCE students will serve as mentors/tutors. They'll be in soon to introduce themselves, and talk about what they're offering.

• Questions?

• A brief preview:

  1. One of the most important concepts in this course is that of function: I will expect you to be familiar with the major classes of functions (e.g. polynomials, trigonometric, etc.). We'll also meet other classes (e.g. exponential and logarithmic functions).

     The most important function is calculus is the linear function y=mx
     (or, more generally, the affine function: y=mx+b).

     These are used everywhere in science, business, etc., because they're so useful and can do so much (in particular, approximate more complicated functions over a small interval).

     An important example arose while I was up in Canada recently: how do we convert between Fahrenheit and Celsius? And as soon as we answer that question, we'll probably want to know: how do we convert between Celsius and Fahrenheit? That's the inverse function!

  2. What I like about calculus...
     • Starting with data:
     • Creating a model from the data, using calculus:

       (This model contains quadratic, exponential, and sinusoidal terms! It's a great "Calc II" model....)

     • The model is much simpler than the data of course:
     • Using the model. Now we can use this to extrapolate ppm into the future, to see when we'll hit certain benchmarks:
     Now why does it matter? Because the National Academy of Sciences says that if we he hit various benchmarks, we're going to lock in certain values of warming. The vertical line indicates when we'll hit 430 ppm, and so lock in 2 degrees C of warming according to the best estimates of the NAS:

     If we keep it up, we can lock in 4 degrees C of warming by 2099, according to the same model. Better to avoid that...

  3. Sequences and Series: Let's Make a Deal!
     • Playing for money: a sequence of dollar amounts
     • A sequence is a discrete function (can't take derivatives!), usually defined on the domain of natural numbers (1, 2, 3, ....).
     • Notice that this function would be a non-invertible function of the sequence of plays: there are multiple ways in which I could arrive at a total of $5 after 10 plays.
     • Given that I win, how long on average until I win? (series)

Next time: 6.1