Further differential equations
Section overview:
The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
CP2-Chp7-MethodsInDifferentialEquations.pptxCP2-Chp8-ModellingWithDifferentialEquations.pptxNotes:
Section 1 Notes - 1st order DEs: Nearer Maths review
Section 2 Notes - 1st order DEs: Integrating factors
Section 3 Notes - 2nd order DEs: Auxiliary equations, SHM and damped oscillations
Section 4 Notes - 2nd order DEs: Complementary functions and particular integrals
Section 5 Notes - 2nd order DEs: Simultaneous DEs
Summary questions:
Topic assessment 1 (with solutions) - 1st order DEs
Topic assessment 2 (with solutions) - 2nd order DEs
Extra resources:
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
Topic videos:
- Related rates of change [Nearer Maths recap]
- General and particular solutions [Nearer Maths recap]
- Separation of variables [Nearer Maths recap]
- Applying the separation of variables method (full problems) [Nearer Maths recap]
- Integrating factor: multiplying by a factor to give a perfect derivative
- Finding integrating factors
- Auxiliary equation method for 1st order DEs
- Auxiliary equation method for 2nd order DEs
- Finding particular solutions of 2nd order DEs (initial conditions)
- Finding particular solutions of 2nd order DEs (boundary conditions)
- Auxiliary equation with repeated roots
- Auxiliary equation with imaginary roots
- Auxiliary equation with complex roots
- Finding the complementary function of a 2nd order DE
- Using a trial function to find a particular integral of a 2nd order DE
- Particular integrals: polynomials
- Particular integrals: trigonometric functions
- Particular integrals: exponential functions
- Particular integrals: special cases
Extra fun! Differential equations are ridiculously important in higher level mathematics and science. So you get a full playlist of lovely extension material: