Maple worksheets on second order differential equations
- First order differential equations
- Second order differential equations
- Partial differential equations and the 1-dimensional wave equation
The following Maple worksheets can be downloaded.
They are all compatible with Classic Worksheet Maple 10.
Homogeneous 2nd order linear differential equations with constant coefficients - homog2DE.mws
- Introductory example.
- General method of solution of homogeneous 2nd order linear DE's with constant coefficients.
- The case where the auxiliary equation has equal roots.
- The case where the auxiliary equation has complex roots.
- Summary of standard forms for the solution.
Non-homogeneous 2nd order linear differential equations with constant coefficients - undetcoeff.mws
- The general form of a second order linear differential equation.
- General method of solution of non-homogeneous 2nd order linear DE's with constant coefficients.
- Introduction to the method of undetermined coefficients for determining a particular solution.
- A table of standard trial particular solutions.
Non-homogeneous 2nd order linear differential equations: variation of parameters - varparam.mws
- Determining a particular integral by variation of parameters: theory.
- Variation of parameters: summary of method.
- Variation of parameters: examples.
A procedure for solving 2nd order linear differential equations with constant coefficients - desolveCC.mws
- A procedure for solving 2nd order linear DE's with constant coefficients: desolveCC.
Simple harmonic motion and damped oscillations - oscillations.mws
- Simple harmonic motion
- Damped motion
- Over-damped systems
- Critically damped systems
- Under-damped systems
Forced oscillations - forced.mws
- Applying an external force to a damped system.
- The transient and steady state parts of a solution.
- Resonance .. introductory example.
- Beats .. introductory example.
- Resonance as a limiting situation with respect to the natural frequency and the frequency of the forcing term.
- An under-damped system for which the frequency of the forcing term coincides with the natural frequency.
Resonance of an under-damped oscillatory system - resonance.mws
- Genuine resonance and resonant angular frequency .. an example.
- Genuine resonance and resonant angular frequency .. general case.
- The dependence of the resonant angular frequency on damping.
A procedure for solving 2nd order differential equations with a "missing variable" - missingvar.mws
- A procedure for solving 2nd order DE's by substituting for the derivative: desolveMV.
- Examples with the dependent variable missing.
- Examples with the independent variable missing.
Procedures for differential equations - DEsol.zip
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