Calculus3

Exam 4 Review

Gauss' Divergence Theorem, The Heat Equation, diffusion

Conservation laws, Weak form of conservation, Rankine-Hugoniot jump conditions, the wave equation, source-free electromagnetic waves and how the electric and magnetic fields satisfy the wave equation.

Stokes' Theorem, Maxwell's Laws, Gauss' Law for Electricity, Gauss' Law for Magnetism, Faraday's Law of Induction, Maxwell-Ampere Law

Surface integrals, surface elements, flux, orientable surfaces, frame-fields, Mobius strip, Klein bottle

Green's Theorem, the continuity equation, conservation of mass, path connected sets, simply connected sets, homotopic paths

Line integrals, Fundamental Theorem of Line Integrals, Flux, Circulation, Area

Vector fields, conservative vector fields, divergence, curl, Helmholtz Theorem

Exam 3 Review

Polar coordinates, triple integrals, cylindrical coordinates, spherical coordinates

Centers of mass, centroids, moments of inertia, Jacobians, change of coordinates

Double integrals, iterated integrals, Cavalieri's principle, Fubini's Theorem, horizontal cross-sections, vertical cross-sections, volume, area

Exam 2 Review

Least squares line of best fit, Lagrange multipliers, constrained optimization, objective functions, constraints.

Second Derivative Test for Relative Extrema in the multivariable case, The Extreme Value Theorem, Taylor Theorem in the multivariable case, Hessian

The Chain Rules, implicit partial differentiation, Einstein summation convention

Directional derivatives, gradient, differentials

Partial derivatives, Clairaut's Theorem, differentiability of multivariable functions, mixed second-order partial derivatives, tangent plane

Surfaces, hypersurfaces, topology, interior points, boundary points, open balls, closed balls, open sets, closed sets, limits

Exam 1 Review

Vector-valued functions, limits, derivatives, integrals, smooth curves.

Newton's Universal Law of Gravitation implies Kepler's Laws

Normal and tangential components of acceleration, curvature, torsion, Frenet frames, the Formulas of Frenet.

Motion, position, velocity, speed, acceleration, arc length, arc length parameter

Cylinders and Quadric Surfaces. Ellipsoid, Hyperboloid of One Sheet, Hyperboloid of Two Sheets, Elliptic Cone, Elliptic Paraboloid, Hyperbolic Paraboloid