The rest of the components in the circuit are standard: a 2k pot, a 100 nF capacitor, a 10 nF capacitor and 22k x 2, 220 ohm x 2, 2.2k, 3.3k resistors and +/- 9 V batteries. You can find these at a local Radioshack. Hence, the total cost of the circuit is around $10! Working with Chaos: Building the circuit Return to Table of Contents. A numerically generated phase-portrait of the non-linear system Zoomed in near (0,0) Zoomed in near (2,1) The critical point at (2,1) certainly looks like a spiral source, but (0,0) just looks bizarre. This approach of linearizing, analyzing the linearizations, and piecing the results together is a standard approach for non-linear systems.
Math 234 - Applied Mathematics I - Course Outline, Fall, 2014
This is a tentative outline and will be updated at least 24 hours in advance before each class. Lecture notes are posted under the sections.
Exam 1 – Sept 19 Exam 2 – Oct 8 Exam 3 – Oct 31 Exam 4 – Nov 21
Date | Topic/Section | Assignments |
Aug 27 | Matrix algebra/(8.1)
| Homework 1: Page 362: 5, 9, 11, 13, 17, 21, 23, 29, 37, 38 Turn in the following on Friday, Aug 29 - Page 362: 12, 18, 22(c) |
Aug 29 | Systems of Linear Equations/(8.2)
| Homework 2: Page 375: 3, 5, 9, 11, 15, 21 Turn in the following on Tuesday, Sept 2 - Page 375: Use Gaussian Elimination and Backward Substitution to solve the systems.Specify each elementary row operation and verify each solution: 6,12 (general solutions), 14 |
Sept 1 | Systems of linear equations/(8.2) | |
Sept 2 | Systems of linear equations/(8.2) | Homework 3: |
Sept 3 | Rank of a Matrix/(8.3)
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Sept 5 | Rank of a Matrix/(8.3) | |
Sept 8 | Determinants and Properties/(8.4),(8.5)
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Sept 9 | Inverse of a Matrix/(8.6)
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Sept 10 | Inverse of a Matrix/(8.6) | |
Sept 12 | Cramer's Rule/(8.7)
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Sept 15 | Eigenvalue Problem/(8.8)
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Sept 16 | Eigenvalue Problem/(8.8) (b) applications | |
Sept 17 | Review for Hour Exam #1: Section (8.1)-(8.8) | |
Sept 19 | ||
Sept 22 | Applications and Uses of Technology
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Sept 23 | Definitions and terminology/(1.1)-(1.2) | |
Sept 24 | Solution curves without the solution/(2.1)
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Sept 26 | Separable variables/(2.2)
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Sept 29 | Linear differential equations/(2.3)
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Sept 30 | Exact Equations/(2.4)
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Oct 1 | Exact Equations/(2.4) | |
Oct 3 | Solutions by substitutions/(2.5) Lecture Notes on Substitution | |
Oct 6 | Solutions by substitutions/(2.5) | |
Oct 7 | Review for Hour Exam #2: | |
Oct 8 | Hour Exam #2: | |
Oct 10 | No Class (Open House for Parents) | |
Oct 13 | Higher-order differential equations/(3.1) | |
Oct 14 | Reduction of order/(3.2) | |
Oct 15 | Homogeneous linear equations with constant coefficients/(3.3) | |
Oct 17 | Homogeneous linear equations with constant coefficients/(3.3) | |
Oct 20 | Nonhomogeneous linear equations/(3.4) | |
Oct 21 | Nonhomogeneous linear equations/(3.5) | |
Oct 22 | Leadership Day (no class) | |
Oct 24 | Cauchy-Euler equations/(3.6) | |
Oct 27 | Systems of linear differential equations and | |
Oct 28 | Homogeneous Linear Systems/(10.2) | |
Oct 29 | Review for Hour Exam #3 | |
Oct 31 | ||
Nov 3 | Nonhomogeneous linear systems/(10.4) | |
Nov 4 | Election Day (no class) | |
Nov 5 | Laplace transform/(4.1) | |
Nov 7 | Inverse of a Laplace transform/(4.2) | |
Nov 10 | Laplace transform of a derivative/(4.2) | |
Nov 11 | Translation Theorems/(4.3) | |
Nov 12 | Translation Theorems/(4.3) | |
Nov 14 | Translation Theorems/(4.3) | |
Nov 17 | Properties of Laplace Transforms/(4.4) | |
Nov 18 | Properties of Laplace Transforms/(4.4) (b) solving differential-integral equations | |
Nov 19 | Review for Hour Exam #4: | |
Nov 21 | Hour Exam #4: | |
Thanksgiving break! | ||
Dec 1 | Properties of Laplace Transforms/(4.4) | |
Dec 2 | Dirac Delta Functions/(4.5) | |
Dec 3 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 5 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 8 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 9 | Review for final | |
Dec 10 | Review for final | |
Dec 17 | (Wednesday) Final Exam - 1:00pm - 4:00pm |
Topics
Represent data using multiple representations, recognize and use linear and non linear (inverse variation) models, use residual analysis, use scatter plots, two way tables, correlation coefficients, and standard deviation
Overview of Changes
Significant changes The CCSS standards for statistics are addressed in this unit.
Description of Changes
The first three investigations of this unit have changed very little from the preceding edition. A few changes involve problem context and giving more attention to residual analysis as a technique for measuring the goodness-of-fit of a function model to given data. There is some additional coverage of slope, connecting with ideas from seventh grade units. The fourth and fifth investigations present new material that addresses the Common Core State Standards requirements regarding correlation and 2-way table analysis
Investigation 4 (NEW) - Variability and Association in Numeric Data
The problems of this investigation review and enhance student understanding and skill in data analysis by focusing on two key statistical concepts—correlation and standard deviation. Students explore positive and negative correlations shown in scatter plots of bivariate data, use of the correlation coefficient as a measure of linearity for scatter plots, and the standard deviation as a measure of spread in single variable distributions.
Investigation 5 (NEW) - Variability and Association in Categorical Data
The problems in this investigation review and enhance student understanding and skill in data analysis by focusing on use of 2-way tables to test the strength of association between categorical variables.
2.2 Linear And Nonlinear Relationsmr. Mac's Page Key
| New Investigation | Changes in CMP2 Investigation |
|---|---|
| Investigation 1 Exploring Data Patterns | Investigation 1 similar to Investigation 1 in CMP2 |
| Investigation 2 Linear Models and Equations | Investigation 1 similar to Investigation 1 in CMP2 |
| Investigation 3 Inverse Variation | Investigation 1 similar to Investigation 1 in CMP2 |
| Investigation 4 Variability and Associations in Numerical Data | Investigation 4 is new. See description above. |
| Investigation 5 Variability and Associations in Categorical Data | Investigation 5 is new. See description above. |