Math 194/135/131: Applied Calculus
Professors Daniel Kaplan & Dan Flath
Macalester College
Fall 2004
MWF  8:30-9:30 --  Prof. Flath
MWF 9:40-10:40 -- Prof. Flath
MWF 1:10-2:20 - Prof. Kaplan, Olin-Rice 241
NEWS:

Syllabus.  (Handouts are available in PDF format by following the links.)

Wed Sept. 8  Syllabus and course policies: [Kaplan's section] [Flath's sections]
Topics: Introduction to calculus and modeling.

Fri. Sept. 10
Topics: Functions, graphs, tables, formulas, domain, range.
Readings: Sections 1.1, 1.8

Mon. Sept. 13  Assignment Due!
Topics: Dimensions, units and conversions.  Linear functions.
Readings: Section 1.2
Hand-in:
Sec 1.1#2,4,8.
Sec 1.8#4,20,34
page 69#2

Wed. Sept. 15
Topics: Dimensions and units (cont). Dynamics: recursive modeling.
Readings: Section 1.3

Friday Sept. 17  [Lab handout]
Computer Lab 1: R-software. (report due Wed. 22 Sept.)

Mon Sept 20  Assignment Due!
Topics: Exponential and log functions.
Readings: Sections 1.5, 1.6, 1.7.
Hand-in:
Sec1.2#18, 20, 26, 28.
Sec1.3#8, 16, 18, 22, 30.
page 70–71#16, 18.

Wed Sept 22   Assignment Due -- Lab report 1! 
Handout given: [Units and Dimensions problems]
Topics: Trigonometric functions, power laws, polynomials.
Readings: Sections 1.9, 1.10.
Hand-in Lab Report 1.

Fri Sept 24  [Lab Handout] [Data file whistle-scale.dat]
Computer Lab 2. (Report will be due Wed Sept 29.)
Reading: Lab 2 handout will be given out in class
(Lab session also held 10:45 Thursday Sept 23.)

Mon Sept 27   Assignment Due!
Topics: Functions of two variables, contour plots, tables.
Readings: Sections 9.1, 9.2.
Hand-in: Problems from "Units and Dimensions" assignment  handed out in class 22 Sept
as well as these problems from the textbook:
Sec1.5#16, 22, 24, 28.
Sec1.6#36.
Sec1.9#20.
Sec1.10#28.

Wed Sept 29   Assignment Due!
Topics: Linear functions of two variables, directional slopes.
Readings: Sections 9.1, 9.2.
Hand-in: Lab Report 2.

Fri Oct 1
Topics: Graphing with log-log, semi-log paper; contour diagrams from tables of values.
Readings: Sections 2.1, 2.2, 2.3.

Mon Oct 4   Assignment Due!
Topics: Review and catch-up.
Hand-in: Sec1.7#2, 14, 18. page.72#34, 40. Sec9.1#12, 16, 22.
Sec 9.2#12, 14, 22, 26,28.
Sec2.1#2, 16.
Sec2.2#22, 28.
Sec2.3#2, 6, 18.

Wed Oct 6 Test I

Fri Oct 8 
Topics: Derivatives. Rate of change, sensitivity of one variable to small
changes in another variable, slope, difference quotients, graphical differentiation.
Readings: Sections 2.1, 2.2, 2.3.

Mon Oct 11  [Lab 3 Handout]
[deriv.r file needed for the lab.  Right click and save it to a file named deriv.r]

Topics: [Review recursive dynamics.] Begin symbolic differentiation’ power functions and polynomials.
Readings: Section 3.1.
Lab 3 handed out: comparing numerical and symbolic differentiation. We will not meet in the lab for Lab 3.

Wed Oct 13
Topics: Derivatives of exp(kt), sin(kt+B), cos(kt+B).  Linear and quadratic approximation (Taylor polynomial) near a point.
Readings: Sections 3.2, 3.3, 3.5

Fri Oct 15 [Tsunami project handout]
Topics: Partial derivatives. Linear and quadratic Taylor polynomials.
Readings: Section 9.3

Mon Oct 18 Assignment Due!
Topics: Optimization
Readings: Sections 4.1, 4.2, 4.3
Hand in:
3.1#12, 33, 37, 38, 43.
3.3#32, 38, 39, 40,
3.5#22, 23
Page 368#1

Wed Oct 20 Assignment Due!
Topics: Fitting functions to data.
Readings: Focus on Modeling, p. 75 in text
Hand in: Lab 3 report.

Fri Oct 22 Assignment Due! [optim.r file for Lab 4] [Lab 4 handout]
Computer Lab 4 (Report due Oct 27.)
Optimization.
Lab session also held 10:45 Thursday 21 Oct.

Mon Oct 25 Assignment Due!
Topics: Optimization and constrained optimization.
Readings: Sections 9.5, 9.6
Hand in:
9.3#2,4.6,14,20,28
4.1#6,15,16,22
4.2#2,18
4.3#17,24,30

Wed Oct 27  Assignment Due!  [Lab 5 handout - delayed to Nov 3.]
Topic: Definite integrals
Reading: Chapter 5
Hand in: Lab 4 Report
Lab 5 will be done as an independent homework.

Fri Oct 29 Fall Break

Monday Nov 1.
Review and catch up.
Hand in:
9.5#12, 16, 18
9.6#11, 16, 21
5.1#8, 10, 16
5.2#8, 12
5.4#2, 5, 8, 14
Tsunami project.


Wed Nov 3  [Lab 5 handout - finally!]
Topics: Begin differential equations: dynamics in continuous time. Graphical approach in one dimension.  Equilibria, stability, multi-stability.  Newton's law of cooling.  An ecological model
Readings: Sections 10.1, 10.2, 10.3


Fri Nov 5  Mid-term test II

Mon Nov 8
Topics: Differential equations in 1-dimension. Exponential growth. Analytic solutions using ansatz and substitution.  Euler method for numerical solutions.

Wed Nov 10 Assignment Due! [Graph paper for Euler integration and slope rose]
Topics: 2nd-order differential equations.  Applications to physics: undamped harmonic oscillator. Exercise on
Euler integration of exponential growth and decay, logistic growth.
Hand in: Lab 5 Report

Fri Nov 12
Topics: 2nd-order differential equations.  Damped harmonic oscillator.  Characteristic equation, complex characteristic values, Euler relationship (exp(i w t) = cos(w t) + i sin(w t)).  General linear differential equation in two variables.

Mon Nov 15  Assignment Due!
Hand in:
10.1#4, 8, 12
10.2#4, 16
10.3#2, 14

Wed Nov 17
The general linear differential equation in two variables.  Stability and eigenvalues.  Applications to love and war.


Friday Nov 19: [Computer Lab 6 handout] [software for the lab]
Computer Lab 6  The Phase Plane
Report due Wed. Nov. 24
(Lab session also available on Thurs. Nov 18 at 10:45)

Mon Nov 22: [Handout on terms to include in modeling]
Taylor polynomials in two variables.  Ways to find the coefficients experimentally.

Wed Nov 24
Terms to include in modeling, esp. the quadratic and  interaction terms.
Fitzhugh-Nagumo model of the action potential in nerve cells

Fri Nov 26 --- no class, Thanksgiving break

Mon Nov 29
Introduction to linear algebra.  Vectors, spaces, dimension, lengths.

Wed Dec 1 [Linear Algebra Exercises I]
Introduction to linear algebra (cont). Angles between vectors.  The dot product.  Model fitting as projection.

Fri Dec 3: [Lab 7 Handout] [R file for matrices and projection: matrix.r, and the instructions]
[MATLAB computer program for lab This is only useful if you have MATLAB installed on your computer.]
Computer Lab 7 Report due Wed. Dec. 8
(Lab session also available on Thurs. Dec 2 at 10:45)

Mon Dec 6
Projection.  Exercises with model fitting using projection by hand.  Subspaces.

Wed Dec 8 [Assignment due: Moved to Friday Dec 10:  Linear Algebra Exercises I]
Singular values and the overlap of subspaces.

Fri Dec 10 [Assignment due: Lab 7 Report] [Handout: Linear Algebra review for exam]
Applications of linear algebra.  Diffusion.  Markov chains. Constrained optimization (revisited)

Mon Dec 13
Newton's method for solving nonlinear equations and for optimization. The Frog SAT.
Linear Algebra wrap up and review

Wed. Dec 15 Last Day of Class
Overall review.

Study Guide for Final Exam
This contains problems that cover the last third of the course, since the second mid-term. 

Sat Dec 18: Final Exam (4-6PM)