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Using Linear Algebra as a Method
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Classroom Contents
Linear Systems of Differential Equations
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- 1 Dr. Devaney Reintroduces the Mass Spring System
- 2 Using Linear Algebra as a Method
- 3 Review Matrix Notation With an Example
- 4 Practice Vector Notation for Linear Systems
- 5 Always Begin by Finding Equilibrium Points
- 6 All Linear System Origins Have an Equilibrium Point
- 7 Derive the Important Straight Line Solution
- 8 Discover a Property of Constants
- 9 Examine the Solutions in the Phase Plane
- 10 Two Solutions Reveal All in Linear Algebra
- 11 Devaney Reveals the Linearity Principle
- 12 Combine Solutions to Find a General Solution
- 13 The Phase Plane Visualizes the Alternate Solutions
- 14 Alternate Solutions Lead to a Saddle Phase Plane
- 15 Vectors Reveal a Quicker Route to a General Solution
- 16 Linear Independence Among Vectors
- 17 Linear Independence Leads to Constant Solutions
- 18 Finding Homogeneous and Non-Homogeneous Solutions
- 19 Straight Line Solutions Show Decaying Exponentials
