# 4 Classes (24 Units)

**18.03**(12),

**18.06**(12)

# 18.03 Differential Equations

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.

This class has 18.02 as a corequisite.

18.03 will be offered this semester (Spring 2019). It is instructed by D. Jerison.

Lecture occurs 1:00 PM to 2:00 PM on Mondays, Wednesdays and Fridays in 54-100.

This class counts for a total of 12 credits.

You can find more information at the MIT + 18.03 - Google Search site or on the 18.03 Stellar site.

# 18.06 Linear Algebra

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, singular value decomposition, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses linear algebra software. Compared with 18.700, more emphasis on matrix algorithms and many applications.

This class has 18.02 as a prerequisite.

18.06 will be offered this semester (Spring 2019). It is instructed by S. G. Johnson and A. Edelman.

Lecture occurs 11:00 AM to 12:00 PM on Mondays, Wednesdays and Fridays in 54-100.

This class counts for a total of 12 credits.

You can find more information at the MIT + 18.06 - Google Search site or on the 18.06 Stellar site.