IntroModeling_Notes.out

\BOOKMARK [0][-]{chapter.0}{To the Student and the Instructor}{}% 1
\BOOKMARK [1][-]{section.0.1}{An Inquiry Based Approach}{chapter.0}% 2
\BOOKMARK [1][-]{section.0.2}{Online Texts and Other Resources}{chapter.0}% 3
\BOOKMARK [1][-]{section.0.3}{To the Instructor}{chapter.0}% 4
\BOOKMARK [0][-]{chapter.1}{Fundamental Notions from Calculus}{}% 5
\BOOKMARK [1][-]{section.1.1}{Sections from Active Calculus}{chapter.1}% 6
\BOOKMARK [1][-]{section.1.2}{Modeling Explorations with Calculus}{chapter.1}% 7
\BOOKMARK [0][-]{chapter.2}{An Introduction to Linear Algebra}{}% 8
\BOOKMARK [1][-]{section.2.1}{Why Linear Algebra?}{chapter.2}% 9
\BOOKMARK [1][-]{section.2.2}{Matrix Operations and Gaussian Elimination}{chapter.2}% 10
\BOOKMARK [1][-]{section.2.3}{Gaussian Elimination: A First Look At Solving Systems}{chapter.2}% 11
\BOOKMARK [1][-]{section.2.4}{Systems of Linear Equations}{chapter.2}% 12
\BOOKMARK [1][-]{section.2.5}{Linear Combinations}{chapter.2}% 13
\BOOKMARK [1][-]{section.2.6}{Inverses and Determinants}{chapter.2}% 14
\BOOKMARK [2][-]{subsection.2.6.1}{Inverses}{section.2.6}% 15
\BOOKMARK [2][-]{subsection.2.6.2}{Determinants}{section.2.6}% 16
\BOOKMARK [1][-]{section.2.7}{Technology For Linear Algebra}{chapter.2}% 17
\BOOKMARK [1][-]{section.2.8}{The Magic Carpet Ride}{chapter.2}% 18
\BOOKMARK [1][-]{section.2.9}{Span}{chapter.2}% 19
\BOOKMARK [1][-]{section.2.10}{Linear Independence, Linear Dependence, and Basis}{chapter.2}% 20
\BOOKMARK [1][-]{section.2.11}{The Column and Null Spaces of a Matrix}{chapter.2}% 21
\BOOKMARK [1][-]{section.2.12}{Modeling Explorations with Linear Algebra}{chapter.2}% 22
\BOOKMARK [2][-]{subsection.2.12.1}{Input-Output Economies}{section.2.12}% 23
\BOOKMARK [2][-]{subsection.2.12.2}{Traffic Networks}{section.2.12}% 24
\BOOKMARK [2][-]{subsection.2.12.3}{Balancing Chemical Equations}{section.2.12}% 25
\BOOKMARK [0][-]{chapter.3}{First Order Models}{}% 26
\BOOKMARK [1][-]{section.3.1}{Birth, Death, and Immigration Exploration}{chapter.3}% 27
\BOOKMARK [1][-]{section.3.2}{Models for Death, Birth, and Immigration}{chapter.3}% 28
\BOOKMARK [1][-]{section.3.3}{Difference Equations and Differential Equations}{chapter.3}% 29
\BOOKMARK [1][-]{section.3.4}{Stability, Equilibria, Phase Plots, and Slope Fields}{chapter.3}% 30
\BOOKMARK [1][-]{section.3.5}{Euler's Method: Numerical Solutions for Differential Equations}{chapter.3}% 31
\BOOKMARK [1][-]{section.3.6}{Classifying Difference and Differential Equations}{chapter.3}% 32
\BOOKMARK [1][-]{section.3.7}{Technique: Solving 1st Order Linear Homogeneous Equations}{chapter.3}% 33
\BOOKMARK [1][-]{section.3.8}{Technique: Solving 1st Order Linear Nonhomogeneous Equations}{chapter.3}% 34
\BOOKMARK [2][-]{subsection.3.8.1}{Solution Technique: Separation of Variables}{section.3.8}% 35
\BOOKMARK [2][-]{subsection.3.8.2}{Solution Technique: Undetermined Coefficients}{section.3.8}% 36
\BOOKMARK [1][-]{section.3.9}{Sensitivity Analysis}{chapter.3}% 37
\BOOKMARK [1][-]{section.3.10}{Modeling Explorations with Difference and Differential Equations}{chapter.3}% 38
\BOOKMARK [0][-]{chapter.4}{Second Order Models}{}% 39
\BOOKMARK [1][-]{section.4.1}{Modeling Oscillations}{chapter.4}% 40
\BOOKMARK [1][-]{section.4.2}{Homogeneous Linear 2nd Order Differential Equations}{chapter.4}% 41
\BOOKMARK [1][-]{section.4.3}{Forced Oscillations}{chapter.4}% 42
\BOOKMARK [1][-]{section.4.4}{Energy in Mass Spring Systems \205 A Lab Exploration}{chapter.4}% 43
\BOOKMARK [1][-]{section.4.5}{Modeling Explorations with 2nd Order Differential Equations}{chapter.4}% 44
\BOOKMARK [0][-]{chapter.5}{Systems of Difference and Differential Equations}{}% 45
\BOOKMARK [1][-]{section.5.1}{Spread of Disease}{chapter.5}% 46
\BOOKMARK [1][-]{section.5.2}{Spreading a Juicy Rumor}{chapter.5}% 47
\BOOKMARK [1][-]{section.5.3}{The H1N1 Virus}{chapter.5}% 48
\BOOKMARK [1][-]{section.5.4}{Writing Systems of Difference Equations}{chapter.5}% 49
\BOOKMARK [1][-]{section.5.5}{Linear Systems}{chapter.5}% 50
\BOOKMARK [1][-]{section.5.6}{The Eigenvalue / Eigenvector Problem}{chapter.5}% 51
\BOOKMARK [2][-]{subsection.5.6.1}{Geometry of Eigenvectors and Eigenvalues}{section.5.6}% 52
\BOOKMARK [2][-]{subsection.5.6.2}{The Eigenvalue Eigenvector Problem}{section.5.6}% 53
\BOOKMARK [2][-]{subsection.5.6.3}{Technology for the Eigenvalue Eigenvector Problem}{section.5.6}% 54
\BOOKMARK [1][-]{section.5.7}{Markov Chains}{chapter.5}% 55
\BOOKMARK [1][-]{section.5.8}{Analysis of Linear Systems}{chapter.5}% 56
\BOOKMARK [2][-]{subsection.5.8.1}{Homogeneous Systems of Linear Difference Equations}{section.5.8}% 57
\BOOKMARK [2][-]{subsection.5.8.2}{Analysis of Equilibrium Behavior}{section.5.8}% 58
\BOOKMARK [2][-]{subsection.5.8.3}{Non Homogeneous Systems of Linear Difference Equations}{section.5.8}% 59
\BOOKMARK [1][-]{section.5.9}{Modeling Explorations with Systems}{chapter.5}% 60
\BOOKMARK [0][-]{chapter.6}{Infinite Series}{}% 61
\BOOKMARK [1][-]{section.6.1}{Sections from Active Calculus}{chapter.6}% 62
\BOOKMARK [0][-]{section*.49}{Appendices}{}% 63
\BOOKMARK [0][-]{Appendix.a.A}{MATLAB Basics}{}% 64
\BOOKMARK [1][-]{section.a.A.1}{Vectors and Matrices}{Appendix.a.A}% 65
\BOOKMARK [1][-]{section.a.A.2}{Looping}{Appendix.a.A}% 66
\BOOKMARK [2][-]{subsection.a.A.2.1}{For Loops}{section.a.A.2}% 67
\BOOKMARK [2][-]{subsection.a.A.2.2}{The While Loop}{section.a.A.2}% 68
\BOOKMARK [1][-]{section.a.A.3}{Conditional Statements}{Appendix.a.A}% 69
\BOOKMARK [2][-]{subsection.a.A.3.1}{If Statements}{section.a.A.3}% 70
\BOOKMARK [2][-]{subsection.a.A.3.2}{Case-Switch Statements}{section.a.A.3}% 71
\BOOKMARK [1][-]{section.a.A.4}{Functions}{Appendix.a.A}% 72
\BOOKMARK [1][-]{section.a.A.5}{Plotting}{Appendix.a.A}% 73
\BOOKMARK [1][-]{section.a.A.6}{Animations}{Appendix.a.A}% 74