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Sage Worksheets for Multivariable Calculus

Collection of worksheets for use with Sage, covering differentiation, graphing functions, line integrals, and optimization.

Line Integrals, Multivariable Calculus, Optimization, Graphing Multivariable Functions, General Tools, Vector Operations

Orbiting Binary Stars

Demonstrates binary star motion.

Vector-Valued Functions and Velocity/Acceleration, Multivariable Calculus

Kepler's Laws and Binary Star Motion

Webpage describing how Kepler's Laws apply to binary stars, with supporting figures and equations.

Vector-Valued Functions and Velocity/Acceleration

Projectile Motion

Allows the user to "fire" projectiles on a 2D graph. User may adjust the initial velocity and angle, the mass of the projectile, and air resistance. Provides several languages.

Vector-Valued Functions and Velocity/Acceleration

Kepler's Laws

Set eccentricity and watch the planet move around. Illustrates Kepler's second law by clearly showing how velocity varies at different points of an elliptical orbit.

Vector-Valued Functions and Velocity/Acceleration, General Collections of Applets

Identifying Quadric Surfaces from a Graph

Displays a quadratic surface and provides students with practice identifying the type of surface as well as its equations. Also has optional stereographic display.

Conic Sections & Quadric Surfaces, Multivariable Calculus

Double Integrals

Collection of nine video lectures on double integration, together with supporting notes and problem sets.

Double Integrals, Double Integrals, Applications

Regions Described by Double Integrals

Displays regions of integration in the plane for both rectangular and polar coordinates.

Double Integrals

Pencast of an Example Computing Flux

Works out solution of a simple flux integral problem, together with commentary

Surface Integrals

How Euler Did It: Mixed Partial Derivatives

Euler was the first person to recognize that mixed second partial derivatives are equal (in general) -- except that he discussed differentials instead.

History of Multivariable Calculus, Partial Derivatives, Differentiability