Pub111

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Links to the Daily Agenda = Exam day
Mon Wed Fri Mon Wed Fri Mon Wed Fri Mon Wed Fri Mon Wed
Sept 7 9 12 14 16 19 21 23 26 28 30
Oct 3 5 7 10 12 14 17 19 21 24 26 28 31
Nov 2 4 7 9 11 14 16 18 21 23 25 28 30
Dec 2 5 7 9 12 16

Applied Calculus: Day-by-Day

NEW Course topic outline and study guide.

General Information :: StartR Series :: Problem Answers :: ... outline for instructors :: Day-by-day Instructor notes for semester

Announcements

  • Software Updates: Give this command: update.the.math135.software( ), or, if that doesn't work, start from scratch:
source("http://dl.dropbox.com/u/5098197/math135.r")

General Information about the Course

Clicker Questions Form

Moodle Assignment Discussion Forum

Preceptors

  • Vidarith Chan -- vchan@macalester.edu
  • Nicole Miller -- nmiller5@macalester.edu
  • Andrew Rich -- arich@macalester.edu
  • Shuang Zheng -- szheng@macalester.edu

Course materials

Getting help

  • MAX Center (Kagin Commons)
    Hours: Mon-Fri 9am-4:30pm, Sun-Thurs 7-10pm
  • Preceptor help sessions (MAX Center)
    Hours: 7-8:30pm on Sun (Zheng), Mon (Chan), Wed (Rich), Thurs (Miller)

Office Hours

  • Flath:
    • Mon 2:20-3:20 pm
    • Tue 1:15-2:10 pm
    • Wed W 2:20-3:20 pm
    • by appointment.
  • Kaplan: (Olin-Rice 231 --- the corner of the building by the wind turbine)
    • Wed. 2-3 pm
    • Fri. 1:30-2:30 pm
    • by appointment or just come in when you see me.

Computer Resources

  • R through the web-based RStudio system: beta.rstudio.org
    Give this command in RStudio to install the software
source("http://dl.dropbox.com/u/5098197/math135.r")

Class Schedule

Wed 7 Sept

Topic: What is calculus? Some modeling exercises. RStudio. (one-minute essay)

Readings:

  1. Applied Calculus (course textbook): AC §1.1
  2. Chapter 1 of Calculus Made Easy a 100-year old calculus book.
  3. Change we can believe in by Steven Strogatz in the New York Times.
  4. A recent Times Op-Ed about mathematics education: How to fix our math education
  5. Starting R: StartR -- Why a Language?

Assignment: Upload a picture of yourself to Moodle. To do this, go to the Profile item on your Moodle page, then select "edit profile" and upload a photo file in the usual way. Since the point of the photo is to help other people recognize you by sight, please pick a relatively recent photo.

On your own: For fun and your own edification ... a newspaper article about study skills

Instructor notes

Fri 9 Sept

Topic: Basic Types of Functions. Introduction to graphing in R (OME)

Readings: AC §1.2, §1.9, §1.10

Assignment:


In-class activities: Using RStudio and collaborating in Google Docs. Notes for instructors

On your own:

Instructor Notes DF & DTK

Mon 12 Sept

Topic: Basic modeling functions: exponentials and logs. Graphing mathematical functions in R (OME)

Readings:

Assignment:

On your own:

Instructor notes

Wed 14 Sept

Topic: Functions of two variables (OME)

Readings: AC §9.1, §9.2

Assignment:

In-class: Drawing contours from tables.

On your own:

Instructor Notes

Fri 16 Sept

Topic: Solving equations with functions. (OME)

Readings: Review AC §1.5, §1.6, §1.7, §9.1, §9.2

Assignment:

  • Final revision of your AcroScore exercises from this week (due by class time).
  • Fitting exponentials to data. ("Income" activity to be posted.)

In-class activities:

  • The first of our regular Friday 15 minute quizzes.

Instructor Notes

Mon 19 Sept

Topic: Finish exponentials and power-law functions. Continue with functions of Two Variables (OME)

Readings:

  • Review AC §9.1, §9.2

Assignment:

In Class:

On Your Own: Sept. 19 is International "Talk Like a Pirate Day". We'll be using ARRRR, the computer language of pirates!

Instructor notes DF

Wed 21 Sept

Topic: Units and Dimensions


Readings:

Assignment:

In Class

  • Using Google to convert units.
  • Energy and dimensional analysis Document to be posted.

On your own:


Instructor Notes

Fri 23 Sept

Topic: Solving equations with functions. (OME)

Readings: Review Quick Notes on Units and Excerpt from Giordano and Weir

Assignment:

In-class activities:

On Your Own:

  • Prof. Topaz mini-lectures on Dimensional Analysis: one and two


Instructor Notes


Group Project 1: Dimensions and the Atomic Bomb (due Oct. 10)

Some Background

A news article with some movie footage of the explosions.

  • Some videos: one and two
  • There are many videos on YouTube, many of which are civil defense training movies from the 1950s.

Two mini-lectures by Prof. Chad Topaz to orient you to the project:

  1. Lecture 1: Dimensional Analysis and the "Buckingham Pi Theorem"
  2. Lecture 2: An example problem --- The Volume of a Crater.

A "calibration test" done at at the Trinity site of 100 tons of TNT. Near the end of this video, there is an aerial view comparing the Trinity crater to that of the 100 ton calibration test. And this video of a cold-war era test of 500 tons in the 1960s, after the test-ban treaty came into effect.

The original paper by Sir G.I. Taylor on ``The formation of a blast wave by a very intense explosion

Mon 26 Sept

Topic: Dimensional Analysis. Introducing Fermi Problems. (OME)

Readings:

Assignment:


Instructor notes

Wed 28 Sept

Topic: (OME)

Readings:

  • Review the two readings about Fermi problems.

Assignment:

  • Start to form your groups for the Atomic Bomb project. Register your group here.
  • Make your own estimation to compare to NASA's of 1/3200 as the probability of a person being hit by one of the items of space debris in the recent uncontrolled satellite re-entry. You can find estimates of the number of pieces of debris in the newspaper.
  • At the very beginning of this video, the climber, Catherine Destivelle, is dangling from a rope. Make an estimate of how long the rope is, based on principles of dimensional analysis. (Hint: You might have to do an measurement with a short string and a small mass in your room. No rock climbing required or recommended!)


Instructor Notes Instructor Background on Fermi Problems

Fri 30 Sept

Topic: Fermi Problems (OME)

Readings:

Assignment:

In Class:


Instructor Notes

Mon 3 Oct

Topic: Finishing Fermi Problems. Start on Linear Algebra. (OME)

Notice: SOFTWARE UPDATE NEEDED. Give this command:

source("http://dl.dropbox.com/u/5098197/math135.r")

Readings: Linear Algebra Reader §1 and §2.

Assignment:

  • StartR on constructing functions from data Splines and Smoothers
  • Do two of the Fermi problems from the handout in class. Your choice. But be prepared to report the results of your two problems in class.

On your own:

Instructor notes

Wed 5 Oct

Topic: Linear Algebra (OME)

Readings: Linear Algebra Reader §1, §2, §3, and §4.

Assignment:

  • All the exercises contained in the reading. (Not in AcroScore.)

On your own:

Instructor Notes

Fri 7 Oct

Topic: (OME)

Readings: Linear Algebra Reader §5

Assignment:

In-class activities:

manipulate program

Instructor Notes

Mon 10 Oct

Topic: Curve Fitting and Linear Algebra (OME)

Readings: Review the Linear Algebra Reader.

Assignment:

  • Hand in your atomic-bomb project. Print out ONE COPY per group and hand it in during class. ALSO, EVERYONE in the group should cut-and-paste a link to their Google Doc report here on Moodle. Remember to do both!
  • StartR: Linear Algebra and Curve Fitting

On your own:

Instructor notes

Wed 12 Oct

Topic: Nonlinear Curve Fitting (OME)

Readings:

In Class:

manipulate(plotFun( A*sin(2*pi*t/3) +C ~ t, t=range(-5,10),A=two,C=one,ylim=c(-10,10)),one=slider(-10,10),two=slider(-10,10))

Assignment:

  • StartR: Nonlinear curve fitting (to be posted)

On your own:

Instructor Notes

Fri 14 Oct

Topic: Nonlinear Curve Fitting (OME)

Readings:

  • See the assignment

Assignment:

In-class activities:


Instructor Notes

Mon 17 Oct

Topic: Rise over Run: Three ambiguities (OME)

Readings: AC §1.3, §2.1, §2.2, §2.3

Assignment: only some are on AcroScore

On your own:

> mDerivs( sin(x^2)~x)

Instructor notes

Wed 19 Oct

Topic: From the derivative to the gradient (OME)

Readings: AC §2.4, §2.5, §9.3 (Note: it's Nine.three)

Assignment:

On your own: Prof. Topaz mini-lectures: Product and Quotient Rules, Derivatives of Periodic Functions, Partial Differentiation

In class: Sketching derivatives of simple functions

Instructor Notes

Fri 21 Oct

Mid-Term Exam: 1 hour in class.

  • You can bring one sheet of paper (any size), with notes. The notes must be written or typed by you, yourself. No copying from others! No cutting-and-pasting on the computer to patch together notes!
  • You will be able to use R or a calculator, as you wish. But you may not access any other materials, notes, etc. beyond the one sheet mentioned above.
  • Remember to write something for each question. If you write nothing, it's not possible to give partial credit.

Instructor Notes

Mon 24 Oct

Topic: (OME)

Readings: Review AC §2.3, §2.4, §2.5, and §9.3

Assignment: Practicing with interactive software

  • Practice sketching the derivative. Use the applet from the US Naval Academy Instructions:
    • To start drawing your curve, click and drag your mouse from the small region just to the left of the y-axis --- it's only about 2mm wide, and you must start in that region. Then drag your mouse (while holding the button down) toward the right to draw your curve.
    • Press "Original start" to erase your curve and start over.
    • Press "New start" to generate a new curve
    • Once you have your curve, press "Answer" and "Error" to see how your guess compares to the mathematical derivative
    Do this for several "new start" curves until you feel pretty comfortable in your ability to sketch the derivative. Don't worry about small errors --- getting the exact curve is what the mathematical formalism and software is for. If you're close, you've got it.
    Try to identify the features of the blue function that make it easy to guess the sign (positive, negative, exactly zero) of the derivative.
  • Differences between tangent lines and chords (secant lines). Use another Navy applet.
    • Compare the tangent-line slope at t=0.4 to the secant-line slope between t=0.4 and t=0.6 (that is, with dt=0.2).
    • Same thing, but make dt=-0.2.
  • Partial derivatives from still another Navy applet:
    When you click on the "floor" of the graph, you are selecting a value for x and y. A yellow point will be drawn to show you the values of x and y you are selecting, and a yellow line will run vertically up to the function f(x,y). By checking the "slice" and "tangent" check boxes, you'll see a faux-3d line that indicates the slope.
  • Find values of x and y that do each of the following:
    • Produce similar and large slopes in the direction of x and in y.
    • Produce similar but small slopes in the x and y directions
    • Produce a large slope with respect to x but a small slope with respect to y
    • Produce a small slope with respect to x but a large slope with respect to y

And ... if you haven't done them yet ...


Instructor notes

Wed 26 Oct

Topic: (OME)

Readings:

Assignment:

On your own:

Instructor Notes

Fri 28 Oct

Fall Break

Mon 31 Oct

Topic: Continuity and differentiability, change along paths, intro to symbolic methods (OME)

Readings:

  • Applied Calculus text: §3.1, §3.2

Assignment:

  • Welcome back from break! If you have time, get ahead on the assignment for Wednesday's class, which relates to the reading for today.

In class:

On your own:

Instructor notes

Wed 2 Nov

Topic: Symbolic derivatives of power law, polynomial, and exponential functions (OME)

Readings:

Assignment:

In class:

On your own:

Instructor Notes

Fri 4 Nov

Topic: Symbolic Differentiation II (OME)

Readings:

Assignment:

In-class activities:

On your Own:

Instructor Notes

Mon 7 Nov

Topic: Integration (OME)

Readings:

Assignment:

In Class:

On your own:

Instructor notes

Wed 9 Nov

Topic: Integration continued. (OME)

Readings:

  • Applied Calc §5.3, §5.4. Warning! Don't be misled into thinking that an integral is an area. That just happens to be a simple setting in which integrals have an intuitive meaning. Thinking that an integral is an area is like thinking that a wind sprint is football.

Assignment:

On your own:

In class:

Instructor Notes

Fri 11 Nov

Topic: (OME)

Readings:

Assignment:

In-class activities:


Instructor Notes

Mon 14 Nov

Topic: Bumps and S-functions. Polynomial approximations in one variable. (OME)

Readings:

  • AC §4.7, §4.8

Assignment:

  • §4.7: Problems 4, 10, 16, 22 (Not on AcroScore)

In-class:

On your own:

Instructor notes

Wed 16 Nov

Topic: Polynomials in two variables. Higher-order partial derivatives. (OME)

Readings:

  • Review AC §9.3, §9.4

Assignment:

In Class:

On your own:

Instructor Notes

Fri 18 Nov

Topic: Newton's method for solving and for optimization, gradient ascent method(OME)

Readings:

Assignment:

  • §9.5 problems 2, 6, 8, 20
  • In draft. See instructor's notes.

In-class activities:


Instructor Notes

Mon 21 Nov

Topic: Constrained Optimization and Lagrange Multipliers ("Shadow Costs") (OME)

Readings:

Assignment:

  • §9.6 problems 6, 8, 12, 18

In Class:

On your own:

Instructor notes

Wed 23 Nov

Topic: Multiple Objectives and constraints, trade-offs (OME)

Readings:

Assignment:


On your own:

Instructor Notes

Fri 25 Nov

Thanksgiving Break!

Mon 28 Nov

Topic: Wrapping up Constrained Optimization. Start on Modeling with Differential Equations: Exponential growth and decay. (OME)

Readings:

  • AC §10.1, §10.2

Assignment:

In-Class:

On your own:

Instructor notes 135 DE software

Wed 30 Nov

Topic: Logistic growth (OME)

Readings:

  • AC §10.3, §10.4

Assignment:

  • AC §10.4 #2, 4, 6

In Class:

On your own:

Instructor Notes

Fri 2 Dec

Topic: Dynamics in two variables. Compartment models. The harmonic oscillator. (OME)

Readings:

  • AC §10.5, §10.6

Assignment:

In-class activities:

On Your Own:

Instructor Notes

Mon 5 Dec

Topic: Interacting populations (OME)

Readings:

  • Review AC §10.6

Assignment:

  • AC §10.6 #12, 16, 17, 18

On your own:

Instructor notes

Wed 7 Dec

Topic: Oscillation and exponentials. SIR models (OME)

Readings:

  • AC §10.7

Assignment:

On your own:

Instructor Notes

Fri 9 Dec

Topic: Equilibrium and stability (OME)

Readings:

Assignment:

  • AC §10.6 problems 12, 16, 17, 18

In-Class:

spring = function(x,v){
 k=1; m=1;
 return(c(dx=v,dv=-(k/m)*x) )
}
mPP(spring, xlim=c(-5,5),ylim=c(-5,5))

On your Own:


Instructor Notes

Mon 12 Dec

Topic: Finishing up Differential Equations. Semester review (OME)

Readings:

Assignment:

  • On-line course evaluation This is required, but anonymous. When you have completed the survey, enter a short note saying so on Moodle here, so the instructors will know that you've done it. Thanks!

On your own:

Instructor notes

Fri 16 Dec - Final Exam

4:00-6:00 pm.

Final Exam

  • Time: Fri. 16 Dec. 4-6pm
  • Location:
    • Prof. Kaplan's sections: O/R 250
    • Prof. Flath's sections: O/R 350
  • You can bring and use any static written material (notes, the book, etc.), but you cannot use the Internet or other forms of communication. You can also bring and use a calculator. If you want to use R, you can use the professor's computer in the exam room.

Review Sessions:

  • Wednesday from 4:00-5:00 pm in O/R 245 (Kaplan)
  • Thursday from 3:30-4:30 pm in O/R 245 (Kaplan)
  • Friday from 11:00-12:00 am in O/R 245 (Kaplan)

Study Guide - Answers to Assigned Problems

Answers to problems (available by login to instructors and distributed to students at appropriate times in the semester)