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
• Official department syllabus
• Selected homework solutions
• An introductory screencast to orient first-time users of Mathematica.
• 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.
• Direction fields and integral curves for some first order linear ODEs, Notebook: FirstOrderLinear.nb.
• The logistic equation and its applications to population biology. Notebook: Logistic.nb.
• Integral curves of some solutions to exact ODEs. Notebook: Exact.nb.
• Uses of the method of successive approximation (also known as Picard iteration) to solve some first order ODEs. Notebook: Picard.nb.
• Plotting solutions of some second order linear ODEs for which the characteristic equation has real and distinct roots. Notebook: SecondOrderLinear.nb.
• Verifying that the real and imaginary parts of the solution to a second order, linear, constant coefficient, homogeneous ordinary differential equation each solve the same equation when the characteristic equation has complex roots. Postscript and PDF versions are also available.
• Some examples of simple harmonic oscillators. Notebook: Harmonic.nb.
• Some examples of simple harmonic oscillators with forcing which may produce beats and resonance. Notebook: ForcedVibration.nb.
• Derivation of the Airy functions as solutions of Airy's differential equation. Notebook: Airy.nb.
• Explanations and examples of series solutions near a regular singular point. A PDF version is also available.
• A table of laplace transforms which is also available in PDF form.
• Some examples of systems of ordinary differential equations. Notebook: Systems.nb.