6: Systems of ODEs
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- 6.1: Introduction to Systems of ODEs
- Often we do not have just one dependent variable and just one differential equation, we may end up with systems of several equations and several dependent variables even if we start with a single equation.
- 6.2: Linear systems of ODEs
- This page summarizes concepts related to homogeneous and nonhomogeneous systems of ordinary differential equations (ODEs). It explains differentiation rules for matrix and vector-valued functions, solving first-order linear systems, superposition principles, and linear independence.
- 6.3: Eigenvalue Method
- In this section we will learn how to solve linear homogeneous constant coefficient systems of ODEs by the eigenvalue method.
- 6.4: Matrices and linear systems
- This page covers the fundamentals of matrix arithmetic, including operations like addition, multiplication, transposes, and inverses. It defines vectors and matrices and discusses the non-commutative nature of multiplication. The text explains matrix inverses, determinants, and their relationships, including methods for computing determinants using cofactor expansion.
Contributors and Attributions
- Jiří Lebl (Oklahoma State University).These pages were supported by NSF grants DMS-0900885 and DMS-1362337.