2012-Levermore. David - First-Order Ordinary Differential Equations II: Graphical Methods and Applications
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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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