2012-Levermore-OrdinaryDifferentialEquations-Graphical MethodsApplications

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Abstract

Levermore. David. 21012. First-Order Ordinary Differential Equations II:  Graphical Methods and Applications. University of Maryland. Notes. 23 pp/

5. First-Order Equations: General Theory

5.1. Well-Posed Problems 2

5.2. Existence and Uniqueness 3

6. First-Order Equations: Graphical Methods

6.1. Phase-Line Portraits for Autonomous Equations 5

6.2. Plots of Explicit Solutions 7

6.3. Contour Plots of Implicit Solutions 9

6.4. Direction Fields 12

7. First-Order Equations: Applications

7.1. General Guidelines 14

7.2. Tanks and Mixtures 14

7.3. Loans 17

7.4. Motion 18

7.5. Population Dynamics 21

Keywords: first-order, phase-plane, differential equations, tanks, loans, motion, population, direction field, graphical

 

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Researchers should cite this work as follows:

  • Brian Winkel (2017), "2012-Levermore-OrdinaryDifferentialEquations-Graphical MethodsApplications," https://simiode.org/resources/4367.

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