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- catalog abstract ""The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics."--Jacket.".
- catalog contributor b11815361.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description ""The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics."--Jacket.".
- catalog description "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.".
- catalog description "Includes bibliographical references and index.".
- catalog extent "xiii, 266 p. :".
- catalog identifier "0821821180 (softcover : alk. paper)".
- catalog isPartOf "Student mathematical library, 1520-9121 ; v .10".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "Providence, RI : American Mathematical Society,".
- catalog subject "516.3/62 21".
- catalog subject "Maple (Computer file)".
- catalog subject "Minimal surfaces Data processing.".
- catalog subject "QA644 .O67 2000".
- catalog subject "Soap bubbles.".
- catalog subject "Surface tension.".
- catalog tableOfContents "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.".
- catalog title "The mathematics of soap films : explorations with Maple / John Oprea.".
- catalog type "text".