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3: Systems of ODEs
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- 3.1: Introduction to Systems of ODEs
- 3.2: Matrices and linear systems
- 3.3: Linear systems of ODEs
- 3.4: Eigenvalue Method
- In this section we will learn how to solve linear homogeneous constant coefficient systems of ODEs by the eigenvalue method.
- 3.5: Two dimensional systems and their vector fields
- 3.6: Second order systems and applications
- 3.7: Multiple Eigenvalues
- Often a matrix has “repeated” eigenvalues. That is, the characteristic equation det(A−λI)=0 may have repeated roots. As any system we will want to solve in practice is an approximation to reality anyway, it is not indispensable to know how to solve these corner cases. It may happen on occasion that it is easier or desirable to solve such a system directly.
- 3.8: Matrix exponentials
- In this section we present a different way of finding the fundamental matrix solution of a system.
- 3.9: Nonhomogeneous systems
- 3.E: Systems of ODEs (Exercises)
- These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.