Differential equations arise in many areas of science and engineering to model continuous change, in particular to model time evolution of a system. Linear algebra is the study of linear systems of equations, linear functions, matrices and vector spaces. In math 320, we shall study these subjects together for three reasons: (1) The viewpoint of linear algebra is immensely helpful in uncovering the order underlying the topic of differential equations; it helps us understand the ``why'' and not just the ``how'' of our calculations, (2) Linear algebra is essential to the theory of differential equations, and (3) linear algebra is crucial to the computer approximations which are often the only way to solve the most challenging ordinary and partial differential equations.
- First-Order ODEs
- Mathematical Modeling and Numerical Methods
- Linear Systems and Matrices
- Vector Spaces
- Higher-Order Linear ODEs
- Eigenvalues and Eigenvectors
- Linear Systems of ODEs
- Matrix Exponential Methods (to solve non-homogeneous systems)
- Nonlinear Systems