First order equations and various applications. Higher order linear differential equations. Power series solutions: The Laplace transform: solution of initial value problems. Systems of linear differential equations: Introduction Partial Differential Equations.

For further information see the academic catalog: MATH219

#### Course Content

First order equations and various applications. Higher order linear differential equations. Power series solutions: The Laplace transform: solution of initial value problems. Systems of linear differential equations: Introduction Partial Differential Equations.

#### Learning Outcomes

At the end of the course the students are expected to:

• Understand the concept of a differential equation, the procedure of writing one when a system is described, and to interpret the solutions correctly.
• Be able to sketch direction fields and read off the qualitative features of the solutions from this, as well as to be able to use simple numeric solvers and interpret the solutions.
• Understand the theory of linear differential equations and systems in detail, to be able to use the various solution methods presented comfortably (undetermined coefficients, reduction of order, variation of parameters, annihilation, Laplace transform, series solutions, eigenvalues-eigenvectors), and to understand the connections to the concepts from linear algebra, in particular to be able to carry out simple proofs.
• Be able to solve the heat, wave and Laplace equations using Fourier series expansions when these partial differential equations have relatively simple boundary conditions.
• Be able to use complex numbers and linear algebra in the process of solving differential equations in an effective manner.