MAT 136, Calculus I

Prof. Swift, Spring 2009

If the WeBWorK gives you troubles, for example it "loads" forever, please let me know and use one of these links instead of the one above: http://bakura.math.nau.edu/webwork2/JSwift_136/ or http://kuat.math.nau.edu/webwork2/JSwift_136/

Figures and Help in reverse Chronological Order

Here is a 6-page Review of Calculus. This was handed out in class on Friday, May 1.

Here is a figure demonstrating that you need to change the u-limits when doing substitution for a definite integral.

Here is a Summary of Riemann Sums and help on WeBWorK set 23 (especially the last problem).

Here is a web site with a demonstration of Riemann Sums. Here is another site. I have had some trouble with these sites.

Here is the handout on Newton's Method from class on Thursday, April 16. As a totally tangential aside, here are some interesting links to Newton's method: This is a well-designed applet, and here's a Wikipedea article explaining how you can do Newton's method where x is a complex number. In my research, I've used Newton's method to get these figures, which are solutions to a partial differential equation. Here's an animation showing how one solution depends on the parameter in the problem.

Solutions to in-class handout from Friday, April 10.

Pictures of f, f-prime, and f-double-prime.

Theorem (not in book). Assume that a function f is differentiable on an interval I. Then
f is increasing on I if and only if f '(x) ≥ 0 for all x in I and there is no interval J contained in I such that f '(x) = 0 for all x in J.
Examples:  f(x) = x² is increasing on [0, ∞), and f(x) = x³ is increasing on (-∞, ∞), even though f '(0) = 0 for both functions. If you want to learn more about this theorem and see some examples, you can look at this short note, but I won't be covering it in class.

Here are the solutions to the "gateway exam" we did in class to practice for Monday's exam.

The visual calculus page (mentioned earlier) has a Quiz on Differentiation which should help you study for Monday's exam.

Solutions to Handout from Thursday, March 26

Handout on Differentiation Shortcuts

Mathematica notebook ImplicitPlots.nb. Run it with the Mathematica program available at the CEFNS Secure Global Desktop.

Visual Calculus by Lawrence S. Husch at Knoxville. This has some good tutorials for differentitation.

Pencil and Paper Homework: Due in class Monday, Feb. 23, and worth 3 class points.
Use the definition of the derivative to show that f '(1) = 1/2, for the function f(x) = sqrt(x). (Shortcuts are not allowed.)
This is a chance for you to practice using proper syntax (put in "lim" where it should be, and don't put it where is shouldn't be.) I'll hand it back to you on Wednesday so you get feedback before Thursday's exam.

Mathematica demonstration on the definition of the derivative. If you don't have Mathematica on your computer you can go here to see the demonstration, or you can save the nb file to your laptop or Z drive and run it with the Mathematica program available at the CEFNS Secure Global Desktop.

Graphs of y = sin(p/x) on the intervals [-25, 25], [-5, 5], [-1, 1], and [-0.2, 0.2].
Graphs of y = x sin(p/x) on the intervals [-25, 25], [-5, 5], [-1, 1], and [-0.2, 0.2].
A Mathematica Notebook xSinOneOverX.nb that you can open using the CEFNS Secure Global Desktop.

The tangent line is the limit of secant lines.

These figures show how to reflect graphs on lines other than the x-axis or the y-axis.

Course information

The free on-line interactive text, by Paul Dawkins of Lamar University.

Student pictures: small pictures and big pictures.

Here is a link to NAU policy statements. These math department policies are part of the printed syllabus for our course, but are mot in the on-line version of our syllabus.

This link has detailed information on WeBWorK (in pdf format). This is slightly out of date: Your username and password are now synchronized to dana/Louie.
Some hints and a list of available functions in WeBWorK are here. (This page is linked to in problem 1 of set 00_WebWorK.)

COMPUTER LAB OPEN HOURS --- AMB 222
M-Th 9:00am - 5:00pm, F 9:00am - 4:00pm, except when the lab has been reserved at least a day in advance for use by a class.
You can go there before or after class with your friends and work on WeBWorK together.

The Problem of the Week can earn you extra credit for this class. I'll give you class points for all the point that appear on the ladder as of the day of our Final exam. Turn your answers in at the Math/Stat department office.