Amath 250 Course Notes Pdf May 2026

AMATH 250 webwork assignments focus on computation. Your PDF notes should focus on theory. Use the notes to understand why you set up the integrating factor the way you did.

The simplest class of ODEs consists of separable equations, which take the form $M(x)dx = N(y)dy$. The solution method involves integrating both sides independently. While conceptually simple, the course notes emphasize the potential for implicit solutions and the necessity of checking for singular solutions where $y' = 0$. amath 250 course notes pdf

For non-separable linear equations of the form $y' + p(t)y = g(t)$, the course introduces the Integrating Factor method. By multiplying the equation by $\mu(t) = e^\int p(t) dt$, the left-hand side becomes the derivative of a product, allowing for direct integration. This technique is foundational for solving radioactive decay models and Newton’s Law of Cooling. AMATH 250 webwork assignments focus on computation

We use eigenvalues ($\lambda$) and eigenvectors ($\vecv$) of matrix $A$. Complex Eigenvalues ($\lambda = \alpha \pm i\beta$):