Ordinary Differential Equations

Learning Outcomes

• Creating differential equations from word problems/application scenarios.
• Choosing the most appropriate method for solving a specific boundary value or initial value problem from among several different viable techniques. 
• Generating general and particular solutions to differential equations using appropriate solving techniques.
• Verifying that an expression or function is actually a solution to a differential equation.
• Interpreting the results of a differential equation solution.

Topics

• Separable 1st order DEs 
• Linear 1st order DEs
• Higher-order linear DEs with constant coefficients
• homogeneous - real distinct roots, complex roots, repeated real roots.
• non-homogeneous - overlapping and non-overlapping with the homogeneous solutions.
• Laplace Transforms 
• Introduction to Laplace as an integral transformation, change in domain from t to s.
• Forward and backwards Laplace transforms of functions using table of transforms.  New functions: piecewise/step functions. 
• Forward and backwards transformation of DEs using Laplace transforms
• Systems of differential equations
  Background/review - row reduction, computing eigenvalues and eigenvectors of matrices
• Transforming systems of 1st order DEs into matrix form.
• Building vector solutions to matrix form using eigenvectors and eigenvalues.