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2nd order linear differential equations with constant coefficients

3rd order linear systems

4th order linear systems

Amplitude, frequency, phase

Ballistic equations

Boundary value problem and initial value problem

Classification of the 2nd order linear systems

Euler method

Exact dfferential equations

Examples and overdamped, critically damped, under damped oscillators, also transient and stable solutions

Final test

General solution for the 3rd order linear system

IVP, complex eigenvalues

Improved Euler method. 2nd order linear differential equations with constant coefficients

Impulse or Dirac function

Initial and boundary value problems

Integrating

Laplace

Line integrals

Linear dependence & Linear systems

On potential vector fields

Phase portraits

Properties of Laplace transform

River current and solutions of the 1st order differential equations

Saddles, broken spirals, spirals, nodes and dicritical nodes

Separable and exact equations

Table of Laplace transforms

Test

The Heaviside step function & method of underdetermined coefficients

Variation of parameters



practice