# 18.03 Differential Equations

**Catalog description:**

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Also see the math departmentâ€™s subject overview for introductory math courses.

### Resources:

- Spring 2020 class website (homework, solutions, recitations)
- Spring 2018 lecture notes
- In recent years the 18.03 curriculum has been modernized, in particular to incorporate more linear algebra.

- Fall 2018 lecture notes
- Fall 2011 OCW (homework, solutions, exams, lecture videos)
- Fall 2010 OCW (homework, solutions, exams)
- Fall 2009 (18.034) OCW (homework, solutions, lecture notes)
- Spring 2006 class website (homework, solutions, exams, lecture videos)
- Spring 2012 - Spring 2020 Concourse version of 18.03 (no resources)
- 2024 MITx online version