Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Recognise that a unique solution of a differential equation can be determined when sufficient initial conditions are given, and refer to a problem involving a differential equation and initial conditions as an initial value problem (IVP)
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Use integration to solve practical problems on the rate of change of a quantity Q, where dQ/dt or (d²Q)/(dt²) is given as a function of time t, together with sufficient initial conditions
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Determine f(x), given f'(x) and an initial condition f(a) = b where a and b are constants
Mathematics Advanced 11–12 – Year 12 · Integral calculus Draft mapping
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Verify by substitution that the function Q = Ae^(kt) satisfies the relationship dQ/dt = kQ with A being the initial value of Q
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.