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Paul's Online Math Notes - Surface Integrals

Online notes concerning surface integrals. Chapters are: Parametric Surfaces, Surface Integrals, Surface Integrals of Vector Fields, Stokes' Theorem, and Divergence Theorem.

Parametric Surfaces, Surface Integrals, Stokes' Theorems, Vector Potential

MIT Open Courseware: Vectors, Partial Derivatives, Multiple Integrals

This a full course on multivariable calculus. It contains videos of lectures and recitation sessions, text for each topic, examples, and problem sets and exams.

General Collections

Shin Yoshizawa's Curve Simulator

Applet in which user can drag a plane curve with the mouse to change its shape, and display features such as normals and osculating circles while user deforms the shape.

Properties of Curves, Vector-Valued Functions and Velocity/Acceleration

Mathlets: Parametric Curves and Surfaces:

This is a collection of several animations that involve the Frenet frame and the osculating circle.

Properties of Curves, Multivariable Calculus

Demonstration for Curvature and the Osculating Circle

This applet shows a curve in the \(xy\)-plane, the vector from the origin to a point on the curve, and the osculating circle. Also displayed is the curvature.

Properties of Curves, Multivariable Calculus

Cylindrical Coordinate Demonstration

Applet which allows the user to visualise and move a point by its rectilinear or cylindrical coordinates simultaneously.

Polar, Cylindrical and Spherical Coordinates

Change of Variables: Polar to Rectangular Coordinates

Provides a simple visualization of the polar to rectangular "change of coordinates" by displaying a polar rectangle adjacent to its mapping into rectangular coordinates, together with explanatory

Double Integrals, Polar, Cylindrical and Spherical Coordinates

CalcTool 3

This java applet provides a variety of graphing functionality supporting multivariable calculus.

General Tools, Vector Operations, Graphing Multivariable Functions, Partial Derivatives, Differentiability, Double Integrals, Vector Fields and Flowlines, Line Integrals

Demonstration for the TNB-Frame

Interactive java applet which allows the user to plot any two- or three-dimensional parametric curve together with associated tangent and normal vectors.

Properties of Curves, Vector-Valued Functions and Velocity/Acceleration

Interactive Velocity Applet

This resource provides a visualization of the velocity and acceleration vectors of a "puck" moving around in the plane.

Vector-Valued Functions and Velocity/Acceleration