# 2 Classes (24 Units)

**18.02**(12),

**18.03**(12)

# 18.02 Calculus

Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.

This class has 18.01 as a prerequisite.

18.02 will be offered this semester (Spring 2019). It is instructed by L. Guth.

Lecture occurs 11:00 AM to 12:00 PM on Tuesdays and Thursdays in 54-100.

This class counts for a total of 12 credits.

You can find more information at the MIT + 18.02 - Google Search site or on the 18.02 Stellar site.

# 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.