## Overview of Math 309

Math 309 continues the study of differential equations begun in Math 307, using the linear algebra tools of Math 308 to tackle problems involving more dimensions. Thus you will need to recall much of what you learned in both the prerequisite courses. In the first half of the course (Chapter 7 and a bit of Chapter 9), the scalar dependent variable (e.g., y(t)) is replaced by a vector dependent variable. In the second half (Chapter 10), the dependent variable is a scalar but we change from one independent variable to two (e.g., (x,t)). This increases the dimension of the solution space, and we will use linear algebra ideas to work within this space.

Both parts of the course have applications throughout science and engineering. We will sample applications, but focus on solving the mathematical problems. The main emphasis of the course is on using the tools studied, that is on calculation. As the problems become increasingly complex, so will the computations to solve them: expect long problems! Our tools will also provide us with the means to analyze the structure of solutions and solution spaces. To do this, we will discuss some theory (but with at most sketches of some of the proofs). As the title of the course (Linear Analysis) suggests, we will study mainly linear equations, but may look occasionally at how our tools might be applied to some nonlinear equations.