This page contains some links to pages with material relevant to the
introductory ordinary differential equations course.
You will also find links to *Mathematica* notebooks which you
can download and modify for further exploration.

- Section 01 current semester syllabus
- An introduction to mathematical modeling using ordinary differential equations.
- Solving first order linear ordinary differential equations using integrating factors.
- Solving first order separable ordinary differential equations.
- Modeling physical phenomena using first order ODEs (linear and nonlinear examples).
- Modeling population dynamics using first order autonomous ODEs.
- Integral curves of some solutions to exact ODEs.
- Establishing the existence and uniqueness of solutions to first order initial value problems.
- An introduction to second order linear, constant coefficient, homogeneous ODEs and IVPs.
- Fundamental solutions of second order linear homogeneous ODEs.
- The Wronskian and linear independence.
- Solutions to second order, linear, constant coefficient, homogeneous ordinary differential equation when the characteristic equation has complex roots. The algebraic details of the verification that the real and imaginary parts solve the ODE are explained here.
- Solutions to second order, linear, constant coefficient, homogeneous ordinary differential equation when the characteristic equation has repeated roots. The general method of reduction of order is also discussed.
- Nonhomogeneous second order linear ODEs and the method of undetermined coefficients.
- Another look at nonhomogeneous second order linear ODEs and solutions found via the method of variation of parameters.
- An introduction to simple harmonic motion and vibration of mechanical systems. Notebook: vibration.nb.
- Simple harmonic oscillators with forcing in the presence and absence of damping. Notebook: forcing.nb.
- A review of power series.
- Series solutions to ordinary differential equations near an ordinary point.
- An introduction to regular singular points.
- Solving Euler equations.
- Finding series solutions near regular singular points.
- Bessel's equation and Bessel functions.
- An introduction to the Laplace transform.
- Solving an initial value problem using the Laplace transform. Students may find a table of Laplace transforms helpful.
- Finding the Laplace transform of unit step functions and other discontinuous functions.
- Using the Laplace transform to find the solution IVPs with discontinuous forcing functions.
- An introduction to impulse functions and their use in solving IVPs.
- The concepts of the convolution of two functions, the convolution integral and its use in solving IVPs.
- Some examples of systems of ordinary differential equations. Notebook: systems.nb.
- A review of matrices and matrix algebra.
- Final examination review.