HL Separation of variables 5.14
Integration to solve equations that contain a derivative ('differential equations')
Integration(sometimes called ‘anti-differentiation’) is the inverse function of differentiation. We can therefore ‘undo' and solve equations that contain a derivative ('differential equations') using integration techniques. One such technique requires separating the variables on to different sides of the equation, hence its name, ‘separation of variables’.
Instead of starting with ‘data’, plotting it, and finding which functions have a similar shape e.g. maximums, minimums, asymptotes etc, we can start with knowledge/a theory about what factors encourage, or discourage, its growth & decay, its rate of change. It is often easier to test in a laboratory what makes something grow or decay, and then define/measure it using an equation. Solving these differential equations is often much less time consuming and costly than collecting a large enough data sample(s) to find a function of the whole population.
Teaching slides - CALCULATIONS
Please find below some slides to help present and teach these ideas to students. You might like to use presentation mode (in the menu on the right side of the screen) when using these slides (hit ESCAPE to return to webpage view).
Student notes sheet
Student's Notes (with practice qu) sheet, to accompany the above teacher slides with space for their working out.
IB exam style, and practice, questions
HL Models & Variable Separation 5.14, use these Practice and Exam style questions to test if you feel ready, or what you need to review, ahead of moving on to the new topic or your end of unit test/mocks/final exams!
Syllabus
The method of solving differential equations using the separation of variables is part of syllabus section 5.14.