Course Outline for Meetings 5 Days Per Week for 14 Weeks + Final Week

Topics in Differential Equations and Linear Algebra

Goode

Edwards

Penney

Days

Project/Lab

Second Order Linear Differential Equations with Constant Coefficients (2 weeks)

Homogeneous – Modeling and Solving

2.3,2.1,2.5

5.1-5.3

4

Lab on solving diff eqs. Using damping factors, beats, and resonance

diffeq_beats_resonance.nb

Nonhomogeneous – Undetermined Coefficients

2.4

5.4-5.5

2

Beats and Resonance

2.6

5.6

2

Bungee Jumping Project

B J ILAP

B J ILAP

1

Bungee Jumping ILAP

Boundary Value Problems and a Partial Differential Equation 

 (1 week)

Heat Equation Introduction and Numerical Solution

Supple-ment

Supple-ment

2

Lab on the heat equation

heat_equation.nb

Heat Equation Analytical Solution with Eigenfunctions, Eigenvalues, and Fourier Series

3

EXAM

1

Systems of Difference and Differential Equations           (3 weeks)

Motivation for Eigenvalues and Eigenvectors through Lake Pollution ILAP Parts I & 2

L P ILAP

L P ILAP

2

Lake Pollution ILAP – Parts 1 & 2

lake_pollution_1.nb

Modeling and Solving Linear Systems of Homogeneous Differential Equations with Real Eigenvalues and Eigenvectors

8.1-8.5

7.1-7.3

3

Lab for solving and analyzing systems of linear differential equations

linear_systems.nb

Modeling and Solving Linear Systems of Homogeneous Differential Equations with Complex Eigenvalues and Eigenvectors

8.5

7.1-7.3

2

Analysis of Slope Fields and Solution Curves in the Phase Planes for Systems of Two Linear Des

8.11

7.3

2

Analysis of Nature of Solutions and Stability of Equilibrium Points Using Eigenvalues and Eigenvectors

8.8

7.4

2

Modeling and Numerically Solving Systems of Nonlinear Differential Equations

8.12

9.3-9.4

1

Lab for solving and analyzing nonlinear systems

nonlinear_systems.nb

Linearization of Nearly Linear Systems of Differential Equations Using Jacobian and Analysis of Eigenvalues of Jacobian Matrix at Equilibrium Points

8.12

9.1-9.2

2

EXAM

1

Vector Spaces and Transformations  (2 weeks)

Vector Spaces and Spanning Sets

5.1-5.4

4.1-4.2

2

General lab on  linear algebra

linear_algebra.nb

Linear Dependence and Independence

5.5, 5.6

4.3-4.4

1

Linear Transformations

6.1, 6.2

Supple-ment

2

Lab on linear transformations and kernels

lineartransformations.nb

Mappings and Kernels

6.3, 6.4

1

Relationship Between Null Space and Image Space and Eigensystem

6.5, 6.6

2

Diagonalization of Matrices

6.7

1

Lab on Diagonizability and Jordan-Canonical Form

diagonizable_m.nb

Leslie Matrices with Harvesting and Eigensystem Analysis

Worksheet

Worksheet

1

Lab on Leslie matrices

Math-Lesliew.nb

EXAM

1

Topics in Probability and Statistics

Lapin

Hastings

Days

Project/Lab

Statistics (1.5 week)

Overview of Sampling and Design of an Experiment

1.1-1.6

7.1

1

Exploratory Data Analysis

2.1

7.2

1

Lab on SPSS

usinfonew.sav (SPSS file)

SPSS_start.doc (Word file)

USinfo.xls (Excel version of data file)

Measures of Central Tendency and Dispersion 

2.2, 2.3

7.1

1

Use of the Empirical Rule to Analyze Statistical Process Control and Sampling Distributions

3.1, 3.2

6.1-6.2

2

Least Squares Curve Fitting and Regression

4.1, 4.2

10.1,10.5

1

Lab on fit functions

least_squares.nb

Nonlinear Curve Fitting

5.1 – 5.3

Worksheet

1

Probability (3 weeks)

General Overview

6.1

1.1-1.2

1

Compound Events and Tree Diagrams

6.2 – 6.4

1.4-1.5

4.1-4.2

2

Markov Models as a Linear Transformation

ILAP

ILAP

1

Lake Pollution ILAP - Part 4

markov_lake.nb

LPILAP_4.doc (Word file)

Reliability

6.5

4.1

1

Decision Analysis

Worksheet

Worksheet

1

Probability Density Functions and Cumulative Distribution Functions

7.1, 7.2

1.3

1

EXAM

1

Discrete Distributions – Binomial and Poisson -

Modeling, Analyzing Probabilities and Parameters

7.3, 8.1

2.1-2.5

2

Lab on using Excel for binomial distribution

binomial.xls (Excel file)

Continuous Distributions – Uniform, Exponential, and Normal – Modeling, Analyzing Probabilities and Parameters

7.4, 8.2

3.1-3.3

3

Lab on joint exponential distribution

exponential_distr.nb

Inferential Statistics (1.5 weeks)

Fitting Data Patterns with Distributions

ILAP

12.2

ILAP

2

Lake Pollution ILAP – Parts 5 and 6 with SPSS

LPILAP_5and6.doc (Word file with instructions)

LPdata.sav (SPSS data file)

LPILAP_56.xls (Excel version of data file)

Web Data Collection

Worksheet

Worksheet

1

WWW_data.doc (Word file)

EXAM

1

Confidence Intervals

10.2-10.3

8.4

1

Introduction to  Hypothesis Testing

11.1

9.2, 12.3

1

Simulation Project (for example, a baseball game)

Worksheet

5.1

1

Final Student Presentations and Wrap-up (.5 week)

2

FINAL COMPREHENSIVE EXAM

Week 15