MAST20030 - Differential Equations Notes

Description

This is a comprehensive compilation of information from MAST20030 lectures, the textbook, tutorials, practicals, workshops, problem booklets and other useful sources I found online to aid my study. Each section (particularly the harder concepts) is supported by easy to read and understand dot points, diagrams, pictures and thorough example exam-style questions. Includes all summarised formulae required to know for each topic. Topics included are: 1. Linear ODEs (wronskian, linear systems, reduction of order, matrix exponentials) 2. Series solutions (Taylor series, trial of series solutions in ODEs) 3. Laplace Transforms (Dirac delta function, Heaviside function, convolution) 4. Boundary value problems and Fourier Series 5. PDEs (heat equation, wave equation, Laplace equation, uniform convergence theorem, energy functional) 6. Fourier Transforms (solving ODEs and PDEs)