Differential Equations

Course code: WI2029LR

Summary Grade: 7.9

The summaries below contain summarized derivations of the most important solving methods discussed in the Differential Equations course. Next to this summary, there is also a good summary on blackboard (course WI2029LR - Course Documents - Dictaat).

  • Basic Differential Equations (75kb)
    This file contains info about separable differential equations and linear first-order and second-order differential equations. The methods of undetermined coefficients and variation of parameters are also discussed.
  • Power Series Solutions (75kb)
    What are power series and how can we use them to solve second order linear differential equations? Find it in this chapter.
  • The Laplace Transform (79kb)
    Definitions about the Laplace transform, the unit step function, the delta function and many more things are present here. There is even a special chapter on how to apply them.
  • Systems of First Order Linear Equations (81kb)
    How can we solve systems of first order linear differential equations? Various methods are described in this chapter.
  • Phase Portraits and Stability (74kb)
    What do trajectories of systems of differential equations look like? And how can we determine whether they are stable? It's all written in this file.
  • Fourier Series (97kb)
    What are Fourier Series and how can we use them to describe practical problems, like the conduction of heat or the vibration of a string? Read it here.
  • Sturm-Liouville Problems (63kb)
    Sturm-Liouville problems are some of the most difficult problems we need to be able to solve. Tricks that may help you on that can be found in this chapter.
Full Version

Problem Solving Guide Grade: 9.5

Having trouble solving a particular type of exam problem? Maybe this problem solving guide will help you out.

Hand-written Summary Grade: 8.1

This file contains a hand-written summary on differential equations. It is much more short and concise than the other files, but it does capture the most important points.

Exam Problems and Solutions Grade: 9.5

For the differential equations study days I've solved and worked out quite some exam problems. You can find it all in the file below. I would advise you to use the problem-only file first and try to solve the problems yourself. If you can't find the solutions, consult the solution file.

Formula Sheet Grade: 8.9

  • Differential Equations Formula Sheet (218kb)
    It's nice to know which equations you need to learn and which ones you don't. On your exam you get this formula sheet. You should study all the other equations (that are not on this sheet).

Lectures Grade: 7.1

A few years ago, the MIT (Massachusetts Institute of Technology) has recorded differential equations lectures and put them online. Their study material is very similar to ours, so we might benefit from those lectures as well. They can be viewed at http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/VideoLectures/index.htm. (It often may take a while to load the lectures, so be patient.)

Book Solutions Grade: 6.5

Differential Equations can be solved, simply by following steps that lead to the solution. But to recognize what steps you need to take, you need to practice. The Differential Equations book provides the problems. We provide the solutions.