320 - Linear Algebra and Differential Equations
Students in the Sciences and Engineering
Differential Equations and Linear Algebra 3E, Edwards and Penney, Prentice Hall.
Differential equations are the fundamental tools that modern science and engineering use to model physical reality. The importance of differential equations to these disciplines cannot be overemphasized. A distinct subject in its own right, linear algebra is a part of mathematics concerned with the structure inherent in mathematical systems. 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 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