The mathematics of soap films : explorations with Maple /
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI :
American Mathematical Society,
[2000]
|
| Series: | Student mathematical library ;
v. 10. |
| Subjects: | |
| Online Access: | Table of contents |
Table of Contents:
- Ch. 1. Surface Tension
- The Basics of Surface Tension
- Experiments with Soap Films
- The Laplace-Young Equation
- Plateau's Rules for Soap Films and Consequences
- A Sampling of Capillary Action
- Ch. 2. A Quick Trip through Differential Geometry and Complex Variables
- Parametrized Surfaces
- Normal Curvature
- Mean Curvature
- Complex Variables
- Gauss Curvature
- Ch. 3. The Mathematics of Soap Films
- The Connection
- The Basics of Minimal Surfaces
- Area Minimization and Soap Films
- Isothermal Parameters
- Harmonic Functions and Minimal Surfaces
- The Weierstrass-Enneper Representations
- The Gauss Map
- Stereographic Projection and the Gauss Map
- Creating Minimal Surfaces from Curves
- To Be or Not To Be Area Minimizing
- Constant Mean Curvature
- Ch. 4. The Calculus of Variations and Shape
- Minimizing Integrals
- Necessary Conditions: Euler-Lagrange Equations
- Solving the Fundamental Examples
- Problems with Extra Constraints
- Ch. 5. Maple, Soap Films, and Minimal Surfaces
- Fused Bubbles
- Capillarity: Inclined Planes
- Capillarity: Thin Tubes
- Minimal Surfaces of Revolution
- The Catenoid versus Two Disks
- Some Minimal Surfaces
- Enneper's Surface
- The Weierstrass-Enneper Representation
- Bjorling's Problem
- The Euler-Lagrange Equations
- The Brachistochrone
- Surfaces of Delaunay
- The Mylar Balloon.