Introduction to differential equations

Spherical modes In the same way that many functions can be described using a sum of sines and cosines (Fourier series), vibrations in space (e.g. of the earth) can be broken into spherical modes. Here, you can see two of these modes.

Whether you are interested in applied mathematics, engineering, or the natural sciences, a strong foundation in differential equations will imbue you with a better understanding of the physical world. This course will introduce you to the basic theory and applications of ordinary and partial differential equations. It differs from other similar courses (e.g. MAT 301 & MAT 303) by striking a balance between theoretical issues (e.g. existence and uniqueness) and applied issues (e.g. numerical or analytical approximations). The main objective of this course is to provide you with an understanding and appreciation for both approaches.

Outline of the course

Lectures

  1. Linear independence and Wronskians and PDF
  2. Inhomogeneous/higher-order ODEs and PDF
  3. Systems of ODEs and PDF
  4. Qualitative analysis and PDF
  5. Numerical methods and PDF
  6. Existence and Uniqueness and PDF
  7. Series Solutions I and PDF
  8. Series Solutions II and PDF
  9. Series Solutions III and PDF

Mini-Matlab workshops

Assignments